hypothesis confirmation

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Confirmation

Human cognition and behavior heavily relies on the notion that evidence (data, premises) can affect the credibility of hypotheses (theories, conclusions). This general idea seems to underlie sound and effective inferential practices in all sorts of domains, from everyday reasoning up to the frontiers of science. Yet it is also clear that, even with extensive and truthful evidence available, drawing a mistaken conclusion is more than a mere possibility. For painfully tangible examples, one only has to consider missed medical diagnoses (see Winters et al. 2012) or judicial errors (see Liebman et al. 2000). The Scottish philosopher David Hume (1711–1776) is usually credited for having disclosed the theoretical roots of these considerations in a particularly transparent way (see Howson 2000, Lange 2011, and Varzi 2008). In most cases of interest, Hume pointed out, many alternative candidate hypotheses remain logically compatible with all the relevant information at one’s disposal, so that none of the former can be singled out by the latter with full certainty. Thus, under usual circumstances, reasoning from evidence must remain fallible.

This fundamental insight has been the source of a lasting theoretical challenge: if amenable to analysis, the role of evidence as supporting (or infirming) hypotheses has to be grasped by more nuanced tools than plain logical entailment. As emphasized in a joke attributed to American philosopher Morris Raphael Cohen (1880–1947), logic textbooks had to be divided in two parts: in the first part, on deductive logic, unwarranted forms of inference (deductive fallacies) are exposed; in the second part, on inductive logic, they are endorsed (see Meehl 1990, 110). In contemporary philosophy, confirmation theory can be roughly described as the area where efforts have been made to take up the challenge of defining plausible models of non-deductive reasoning. Its central technical term— confirmation —has often been used more or less interchangeably with “evidential support”, “inductive strength”, and the like. Here we will generally comply with this liberal usage (although more subtle conceptual and terminological distinctions are sometimes drawn).

Confirmation theory has proven a rather difficult endeavour. In principle, it would aim at providing understanding and guidance for tasks such as diagnosis, prediction, and learning in virtually any area of inquiry. Yet popular accounts of confirmation have often been taken to run into troubles even when faced with toy philosophical examples. Be that as it may, there is at least one real-world kind of activity which has remained a prevalent target and benchmark, i.e., scientific reasoning, and especially key episodes from the history of modern and contemporary natural science. The motivation for this is easily figured out. Mature sciences seem to have been uniquely effective in relying on observed evidence to establish extremely general, powerful, and sophisticated theories. Indeed, being capable of receiving genuine support from empirical evidence is itself a very distinctive trait of scientific hypotheses as compared to other kinds of statements. A philosophical characterization of what science is would then seem to require an understanding of the logic of confirmation. And so, traditionally, confirmation theory has come to be a central concern of philosophers of science.

In the following, major approaches to confirmation theory are overviewed according to a classification that is relatively standard (see Earman and Salmon 1992; Norton 2005): confirmation by instances (Section 1), hypothetico-deductivism and its variants (Section 2), and probabilistic (Bayesian) approaches (Section 3).

1.1 Hempel’s theory

1.2 two paradoxes and other difficulties, 2.1 hd vs. hempelian confirmation, 2.2 back to black (ravens), 2.3 underdetermination and the duhemian challenge, 2.4 the extended hd menu, 3.1 probabilistic confirmation as firmness, 3.2 strengths and infirmities of firmness, 3.3 probabilistic relevance confirmation, 3.4 differences, ratios, and partial entailment, 3.5 new evidence, old evidence, and total evidence, 3.6 paradoxes probabilified and other elucidations, other internet resources, related entries, 1. confirmation by instances.

In a seminal essay on induction, Jean Nicod (1924) offered the following important remark:

Consider the formula or the law: \(F\) entails \(G\). How can a particular proposition, or more briefly, a fact affect its probability? If this fact consists of the presence of \(G\) in a case of \(F\), it is favourable to the law […]; on the contrary, if it consists of the absence of \(G\) in a case of \(F\), it is unfavourable to this law. (219, notation slightly adapted)

Nicod’s work was an influential source for Carl Gustav Hempel’s (1943, 1945) early studies in the logic of confirmation. In Hempel’s view, the key valid message of Nicod’s statement is that the observation report that an object \(a\) displays properties \(F\) and \(G\) (e.g., that \(a\) is a swan and is white) confirms the universal hypothesis that all \(F\)-objects are \(G\)-objects (namely, that all swans are white). Apparently, it is by means of this kind of confirmation by instances that one can obtain supporting evidence for statements such as “sodium salts burn yellow”, “wolves live in a pack”, or “planets move in elliptical orbits” (also see Russell 1912, Ch. 6). We will now see the essential features of Hempel’s analysis of confirmation.

Hempel’s theory addresses the non-deductive relation of confirmation between evidence and hypothesis, but relies thoroughly on standard logic for its full technical formulation. As a consequence, it also goes beyond Nicod’s idea in terms of clarity and rigor.

Let \(\bL\) be the set of the closed sentences of a first-order logical language \(L\) (finite, for simplicity) and consider \(h, e \in \bL\). Also let \(e\), the evidence statement, be consistent and contain individual constants only (no quantifier), and let \(I(e)\) be the set of all constants occurring (non-vacuously) in \(e\). So, for example, if \(e = Qa \wedge Ra\), then \(I(e) = \{a\}\), and if \(e = Qa \wedge Qb\), then \(I(e) = \{a,b\}\). (The non-vacuity clause is meant to ensure that if sentence \(e\) happens to be, say, \(Qa \wedge Qb \wedge (Rc \vee \neg Rc)\), then \(I(e)\) still is \(\{a, b\}\), for \(e\) does not really state anything non-trivial about the individual denoted by \(c\). See Sprenger 2011a, 241–242.) Hempel’s theory relies on the technical construct of the development of hypothesis \(h\) for evidence \(e\), or the \(e\)-development of \(h\), indicated by \(dev_{e}(h)\). Intuitively, \(dev_{e}(h)\) is all that (and only what) \(h\) says once restricted to the individuals mentioned (non-vacuously) in \(e\), i.e., exactly those denoted by the elements of \(I(e)\).

The notion of the \(e\)-development of hypothesis \(h\) can be given an entirely general and precise definition, but we’ll not need this level of detail here. Suffice it to say that the \(e\)-development of a universally quantified material conditional \(\forall x(Fx \rightarrow Gx)\) is just as expected, that is: \(Fa \rightarrow Ga\) in case \(I(e) = \{a\}\); \((Fa \rightarrow Ga) \wedge (Fb \rightarrow Gb)\) in case \(I(e) = \{a,b\}\), and so on. Following Hempel, we will take universally quantified material conditionals as canonical logical representations of relevant hypotheses. So, for instance, we will count a statement of the form \(\forall x(Fx \rightarrow Gx)\) as an adequate rendition of, say, “all pieces of copper conduct electricity”.

In Hempel’s theory, evidence statement \(e\) is said to confirm hypothesis \(h\) just in case it entails, not \(h\) in its full extension, but suitable instantiations of \(h\). The technical notion of the \(e\)-development of \(h\) is devised to identify precisely those relevant instantiations, that is, the consequences of \(h\) as restricted to the individuals involved in \(e\). More precisely, Hempelian confirmation can be defined as follows:

• evidence \(e\) directly Hempel-confirms hypothesis \(h\) if and only if \(e \vDash dev_{e}(h)\); \(e\) Hempel-confirms \(h\) if and only if, for some \(s \in \bL\), \(e \vDash dev_{e}(s)\) and \(s \vDash h\);
• evidence \(e\) directly Hempel-disconfirms hypothesis \(h\) if and only if \(e \vDash dev_{e}(\neg h)\); \(e\) Hempel-disconfirms \(h\) if and only if, for some \(s \in \bL, e \vDash dev_{e}(s)\) and \(s \vDash \neg h\);
• evidence \(e\) is Hempel-neutral for hypothesis \(h\) otherwise.

In each of clauses (i) and (ii), Hempelian confirmation (disconfirmation, respectively) is a generalization of direct Hempelian confirmation (disconfirmation). To retrieve the latter as a special case of the former, one only has to posit \(s = h\) \((\neg h\), respectively, for disconfirmation).

By direct Hempelian confirmation, evidence statement \(e\) that, say, object \(a\) is a white swan, \(swan(a) \wedge white(a)\), confirms hypothesis \(h\) that all swans are white, \(\forall x(swan(x) \rightarrow white(x))\), because the former entails the \(e\)-development of the latter, that is, \(swan(a) \rightarrow white(a)\). This is a desired result, according to Hempel’s reading of Nicod. By (indirect) Hempelian confirmation, moreover, \(swan(a) \wedge white(a)\) also confirms that a particular further object \(b\) will be white, if it’s a swan, i.e., \(swan(b) \rightarrow white(b)\) (to see this, just set \(s = \forall x(swan(x) \rightarrow white(x))\)).

The second possibility considered by Nicod (“the absence of \(G\) in a case of \(F\,\)”) can be accounted for by Hempelian disconfirmation. For the evidence statement \(e\) that \(a\) is a non-white swan—\(swan(a) \wedge \neg white(a)\)—entails (in fact, is identical to) the \(e\)-development of the hypothesis that there exist non-white swans—\(\exists x(swan(x) \wedge \neg white(x))\)—which in turn is just the negation of \(\forall x(swan(x) \rightarrow white(x))\). So the latter is disconfirmed by the evidence in this case. And finally, \(e = swan(a) \wedge \neg white(a)\) also Hempel-disconfirms that a particular further object \(b\) will be white, if it’s a swan, i.e., \(swan(b) \rightarrow white(b)\), because the negation of the latter, \(swan(b) \wedge \neg white(b)\), is entailed by \(s = \forall x(swan(x) \wedge \neg white(x))\) and \(e \vDash dev_{e}(s)\).

So, to sum up, we have four illustrations of how Hempel’s theory articulates Nicod’s basic ideas, to wit:

• (the observation report of) a white swan (directly) Hempel-confirms that all swans are white;
• (the observation report of) a white swan also Hempel-confirms that a further swan will be white;
• (the observation report of) a non-white swan (directly) Hempel-disconfirms that all swans are white;
• (the observation report of) a non-white swan also Hempel-disconfirms that a further swan will be white.

The ravens paradox (Hempel 1937, 1945). Consider the following statements:

Is hypothesis \(h\) confirmed by \(e\) and \(e^*\) alike? That is, is the claim that all ravens are black equally confirmed by the observation of a black raven and by the observation of a non-black non-raven (e.g., a green apple)? One would want to say no, but Hempel’s theory is unable to draw this distinction. Let’s see why.

As we know, \(e\) (directly) Hempel-confirms \(h\), according to Hempel’s reconstruction of Nicod. By the same token, \(e^*\) (directly) Hempel-confirms the hypothesis that all non-black objects are non-ravens, i.e., \(h^* = \forall x(\neg black(x) \rightarrow \neg raven(x))\). But \(h^* \vDash h\) (\(h\) and \(h^*\) are just logically equivalent). So, \(e^*\) (the observation report of a non-black non-raven), like \(e\) (black raven), does (indirectly) Hempel-confirm \(h\) (all ravens are black). Indeed, as \(\neg raven(a)\) entails \(raven(a) \rightarrow black(a)\), it can be shown that \(h\) is (directly) Hempel-confirmed by the observation of any object that is not a raven (an apple, a cat, a shoe), apparently disclosing puzzling “prospects for indoor ornithology” (Goodman 1955, 71).

\(Blite\) (Goodman 1955). Consider the peculiar predicate “\(blite\)”, defined as follows: an object is blite just in case (i) it is black if examined at some moment \(t\) up to some future time \(T\) (say, the next expected appearance of Halley’s comet, in 2061) and (ii) it is white if examined afterwards. So we posit \(blite(x) \equiv (ex_{t\le T}(x) \rightarrow black(x)) \wedge (\neg ex_{t\le T}(x) \rightarrow white(x))\). Now consider the following statements:

Does \(e\) confirm hypotheses \(h\) and \(h^*\) alike? That is, does the observation of a black raven before \(T\) confirms equally the claim that all ravens are black as the claim that all ravens are blite? Here again, one would want to say no, but Hempel’s theory is unable to draw the distinction. For one can check that the \(e\)-developments of \(h\) and \(h^*\) are both entailed by \(e\). Thus, \(e\) (the report of a raven examined no later than \(T\) and found to be black) does Hempel-confirm \(h^*\) (all ravens are blite) just as it confirms \(h\) (all ravens are black). Moreover, \(e\) also Hempel-confirms the statement that a raven will be white if examined after \(T\), because this is a logical consequence of \(h^*\) (which is directly Hempel-confirmed by \(e\)). And finally, suppose that \(blurple(x) \equiv (ex_{t\le T}(x) \rightarrow black(x)) \wedge (\neg ex_{t\le T}(x) \rightarrow purple(x)).\) We then have that the very same evidence statement \(e\) Hempel-confirms the hypothesis that all ravens are blurple, and thus also its implication that a raven will be \(purple\) if examined after \(T\)!

A seemingly obvious idea, here, is that there must be something inherently wrong with predicates such as \(blite\) or \(blurple\) (and perhaps non-raven and non-black , too) and thus a principled way to rule them out as “unnatural”. Then one could restrict confirmation theory accordingly, i.e., to “natural kinds” only (see, e.g., Quine 1970). Yet this point turns out be very difficult to pursue coherently and it has not borne much fruit in this discussion (Rinard 2014 is a recent exception). After all, for all we know, it is a perfectly “natural” feature of a token of the “natural kind” water that it is found in one physical state for temperatures below 0 degrees Celsius and in an entirely different state for temperatures above that threshold. So why should the time threshold \(T\) in \(blite\) or \(blurple\) be a reason to dismiss those predicates? (The water example comes from Howson 2000, 31–32. See Schwartz 2011, 399 ff., for a more general assessment of this issue.)

The above, widely known “paradoxes” then suggest that Hempel’s analysis of confirmation is too liberal : it sanctions the existence of confirmation relations that are intuitively very unsound (see Earman and Salmon 1992, 54, and Sprenger 2011a, 243, for more on this). Yet the Hempelian notion of confirmation turns out to be very restrictive, too, on other accounts. For suppose that hypothesis \(h\) and evidence \(e\) do not share any piece of non-logical vocabulary. \(h\) might be, say, Newton’s law of universal gravitation (connecting force, distances and masses), while \(e\) could be the description of certain spots on a telescopic image. Throughout modern physics, significant relations of confirmation and disconfirmation were taken to obtain between statements like these. Indeed, telescopic sightings have been crucial evidence for Newton’s law as applied to celestial bodies. However, as their non-logical vocabularies are disjoint, \(e\) and \(h\) must simply be logically independent, and so must be \(e\) and \(dev_{e}(h)\) (with very minor caveats, this follows from Craig’s so-called interpolation theorem, see Craig 1957). In such circumstances, there can be nothing but Hempel-neutrality between evidence and hypothesis. So Hempel’s original theory seems to lack the resources to capture a key feature of inductive inference in science as well as in several other domains, i.e., the kind of “vertical” relationships of confirmation (and disconfirmation) between the description of observed phenomena and hypotheses concerning underlying structures, causes, and processes.

To overcome the latter difficulty, Clark Glymour (1980a) embedded a refined version of Hempelian confirmation by instances in his analysis of scientific reasoning. In Glymour’s revision, hypothesis \(h\) is confirmed by some evidence \(e\) even if appropriate auxiliary hypotheses and assumptions must be involved for \(e\) to entail the relevant instances of \(h\). This important theoretical move turns confirmation into a three -place relation concerning the evidence, the target hypothesis, and (a conjunction of) auxiliaries. Originally, Glymour presented his sophisticated neo-Hempelian approach in stark contrast with the competing traditional view of so-called hypothetico-deductivism (HD). Despite his explicit intentions, however, several commentators have pointed out that, partly because of the due recognition of the role of auxiliary assumptions, Glymour’s proposal and HD end up being plagued by similar difficulties (see, e.g., Horwich 1983, Woodward 1983, and Worrall 1982). In the next section, we will discuss the HD framework for confirmation and also compare it with Hempelian confirmation. It will thus be convenient to have a suitable extended definition of the latter, following the remarks above. Here is one that serves our purposes:

• \(e\) directly Hempel-confirms \(h\) relative to \(k\) if and only if \(e\wedge k \vDash dev_{e}(h)\); \(e\) Hempel-confirms \(h\) relative to \(k\) if and only if, for some \(s \in \bL, e\wedge k \vDash dev_{e}(s)\) and \(s\wedge k \vDash h\);
• \(e\) directly Hempel-disconfirms \(h\) relative to \(k\) if and only if \(e\wedge k \vDash dev_{e}(\neg h)\); \(e\) Hempel-disconfirms \(h\) relative to \(k\) if and only if, for some \(s\in \bL, e\wedge k \vDash dev_{e}(s)\)a and \(s\wedge k \vDash \neg h\);
• \(e\) is Hempel-neutral for \(h\) relative to \(k\) otherwise.

One can see that in the above definition the auxiliary assumptions in \(k\) are the \(e\)-development of further closed constant-free hypotheses (in fact, equations as applied to specific measured values, in typical examples from Glymour 1980a), where such hypotheses are meant to be conjoined in a single statement (\(\alpha\)) for convenience. This implies that the only terms occurring (non-vacuously) in \(k\) are individual constants already occurring (non-vacuously) in \(e\). For an empty \(\alpha\) (that is, tautologous: \(\alpha = \top\)), \(k\) must be empty too, and the original (restricted) definition of Hempelian confirmation applies. As for the proviso that \(\alpha \not\vDash h\), it rules out undesired cases of circularity—akin to so-called “macho” bootstrap confirmation, as discussed in Earman and Glymour 1988 (for more on Glymour’s theory and its developments, see Douven and Meijs 2006, and references therein).

2. Hypothetico-deductivism

The central idea of hypothetico-deductive (HD) confirmation can be roughly described as “deduction-in-reverse”: evidence is said to confirm a hypothesis in case the latter, while not entailed by the former, is able to entail it, with the help of suitable auxiliary hypotheses and assumptions. The basic version (sometimes labelled “naïve”) of the HD notion of confirmation can be spelled out thus:

• \(e\) HD-confirms \(h\) relative to \(k\) if and only if \(h\wedge k \vDash e\) and \(k \not\vDash e\);
• \(e\) HD-disconfirms \(h\) relative to \(k\) if and only if \(h\wedge k \vDash \neg e\), and \(k \not\vDash \neg e\);
• \(e\) is HD-neutral for hypothesis \(h\) relative to \(k\) otherwise.

Note that clause (ii) above represents HD-disconfirmation as plain logical inconsistency of the target hypothesis with the data (given the auxiliaries) (see Hempel 1945, 98).

HD-confirmation and Hempelian confirmation convey different intuitions (see Huber 2008a for an original analysis). They are, in fact, distinct and strictly incompatible notions. This will be effectively illustrated by the consideration of the following conditions.

Entailment condition (EC) For any \(h,e,k \in \bL\), if \(e\wedge k\) is consistent, \(e\wedge k \vDash h\) and \(k \not\vDash h\), then \(e\) confirms \(h\) relative to \(k\).

Confirmation complementarity (CC) For any \(h, e, k \in \bL\), \(e\) confirms \(h\) relative to \(k\) if and only if \(e\) disconfirms \(\neg h\) relative to \(k\).

Special consequence condition (SCC) For any \(h, e, k \in \bL\), if \(e\) confirms \(h\) relative to \(k\) and \(h\wedge k \vDash h^*\), then \(e\) confirms \(h^*\) relative to \(k\).

On the implicit proviso that \(k\) is empty (that is, tautologous: \(k = \top\)), Hempel (1943, 1945) himself had put forward (EC) and (SCC) as compelling adequacy conditions for any theory of confirmation, and devised his own proposal accordingly. As for (CC), he took it as a plain definitional truth (1943, 127). Moreover, Hempelian confirmation (extended) satisfies all conditions above (of course, for arguments \(h\), \(e\) and \(k\) for which it is defined). HD-confirmation, on the contrary, violates all of them. Let us briefly discuss each one in turn.

It is rather common for a theory of ampliative (non-deductive) reasoning to retain classical logical entailment as a special case (a feature sometimes called “super-classicality”; see Strasser and Antonelli 2019). That’s essentially what (EC) implies for confirmation. Now given appropriate \(e\), \(h\) and \(k\), if \(e\wedge k\) entails \(h\), we readily get that \(e\) Hempel-confirms \(h\) relative to \(k\) in two simple steps. First, given that \(e\) and \(k\) are both quantifier-free, \(dev_{e}(e\wedge k) = e\wedge k\) according to Hempel’s full definition of \(dev\) (see Hempel 1943, 131). Then it trivially follows that \(e\wedge k \vDash dev_{e}(e\wedge k)\), so \(e\wedge k\) is (directly) Hempel-confirmed and its logical consequence \(h\) is likewise confirmed (indirectly). Logical entailment is thus retained as an instance of Hempelian confirmation in a fairly straightforward way. HD-confirmation, on the contrary, does not fulfil (EC). Here is one odd example (see Sprenger 2011a, 234). With \(k = \top\), just let \(e\) be the observation report that object \(a\) is a black swan, \(swan(a) \wedge black(a)\), and \(h\) be the hypothesis that black swans exist, \(\exists x(swan(x) \wedge black(x))\). Evidence \(e\) verifies \(h\) conclusively, and yet it does not HD-confirm it, simply because \(h \not\vDash e\). So the observation of a black swan turns out to be HD-neutral for the hypothesis that black swans exist! The same example shows how HD-confirmation violates (CC), too. In fact, while HD-neutral for \(h\), \(e\) HD-disconfirms its negation \(\neg h\) that no swan is black, \(\forall x(swan(x) \rightarrow \neg black(x))\), because the latter is obviously inconsistent with (refuted by) \(e\).

The violation of (EC) and (CC) by HD-confirmation is arguably a reason for concern, for those conditions seem highly plausible. The special consequence condition (SCC), on the other hand, deserves separate and careful consideration. As we will see later on, (SCC) is a strong constraint, and far from sacrosanct. For now, let us point out one major philosophical motivation in its favor. (SCC) has often been invoked as a means to ensure the fulfilment of the following condition (see, e.g., Hesse 1975, 88; Horwich 1983, 57):

Predictive inference condition (PIC) For any \(e, k \in \bL\), if \(e\) confirms \(\forall x(Fx \rightarrow Gx)\) relative to \(k\), then \(e\) confirms \(F(a) \rightarrow G(a)\) relative to \(k\).

In fact, (PIC) readily follows from (SCC) and so it is satisfied by Hempel’s theory. It says that, if evidence \(e\) confirms “all \(F\)s are \(G\)s”, then it also confirms that a further object will be \(G\), if it is \(F\). Notably, this does not hold for HD-confirmation. Here is why. Given \(k = Fa\) (i.e., the assumption that \(a\) comes from the \(F\) population), we have that \(e = Ga\) HD-confirms \(h = \forall x(Fx \rightarrow Gx)\), because the latter entails the former (given \(k\)). (That’s the HD reconstruction of Nicod’s insight, see below.) We also have, of course, that \(h\) entails \(h^* = Fb \rightarrow Gb\). And yet, contrary to (PIC), since \(h^*\) does not entail \(e\) (given \(k\)), it is not HD-confirmed by it either. The troubling conclusion is that the observation that a swan is white (or that a million of them are, for that matters) does not HD-confirm the prediction that a further swan will be found to be white.

One attractive feature of HD-confirmation is that it largely eludes the ravens paradox. As the hypothesis \(h\) that all ravens are black does not entail that some generally sampled object \(a\) will be a black raven, the HD view of confirmation is not committed to the eminently Hempelian implication that \(e = raven(a) \wedge black(a)\) confirms \(h\). Likewise, \(\neg black(a) \wedge \neg raven(a)\) does not HD-confirm that all non-black objects are non-raven. The derivation of the paradox, as presented above, is thus blocked.

Indeed, HD-confirmation yields a substantially different reading of Nicod’s insight as compared to Hempel’s theory (Okasha 2011 has an important discussion of this distinction). Here is how it goes. If object \(a\) is assumed to have been taken among ravens —so that, crucially, the auxiliary assumption \(k = raven(a)\) is made—and \(a\) is checked for color and found to be black, then, yes, the latter evidence, \(black(a)\), HD-confirms that all ravens are black \((h)\) relative to \(k\). By the same token, \(\neg black(a)\) HD-disconfirms \(h\) relative to the same assumption \(k = raven(a)\). And, again, this is as it should be, in line with Nicod’s mention of “the absence of \(G\) [here, non-black as evidence] in a case of \(F\) [here, raven as an auxiliary assumption]”. It is also true that an object that is found not to be a raven HD-confirms \(h\), but only relative to \(k = \neg black(a)\), that is, if \(a\) is assumed to have been taken among non-black objects to begin with; and this seems acceptable too (after all, while sampling from non-black objects, one might have found the counterinstance of a raven, but didn’t). Unlike Hempel’s theory, moreover, HD-confirmation does not yield the debatable implication that, by itself (that is, given \(k = \top\)), the observation of a non-raven \(a\), \(\neg raven(a)\), must confirm \(h\).

Interestingly, the introduction of auxiliary hypotheses and assumptions shows that the issues surrounding Nicod’s remarks can become surprisingly subtle. Consider the following statements (Maher’s 2006 example):

\(\alpha_1\) simply specifies that no object is both white and black, while \(\alpha_2\) says that, if there are swans at all, then there also is some black swan. Also posit, again, \(e = swan(a) \wedge white(a)\). Under \(\alpha_1\) and \(\alpha_2\), the observation of a white swan clearly dis confirms (indeed, refutes) the hypothesis \(h\) that all swans are white. Hempel’s theory (extended) faces difficulties here, because for \(k = dev_{e}(\alpha_1 \wedge \alpha_2)\) it turns out that \(e\wedge k\) is inconsistent. But HD-confirmation gets this case right, thus capturing appropriate boundary conditions for Nicod’s generally sensible claims. For, with \(k = \alpha_1 \wedge \alpha_2\), one has that \(h\wedge k\) is consistent and entails \(\neg e\) (for it entails that no swan exists), so that \(e\) HD-disconfirms (refutes) \(h\) relative to \(k\) (see Good 1967 for another famous counterexample to Nicod’s condition).

HD-confirmation, however, is also known to suffer from distinctive “paradoxical” implications. One of the most frustrating is surely the following (see Osherson, Smith, and Shafir 1986, 206, for further specific problems).

The irrelevant conjunction paradox . Suppose that \(e\) confirms \(h\) relative to (possibly empty) \(k\). Let statement \(q\) be logically consistent with \(e\wedge h\wedge k\), but otherwise entirely irrelevant for all of those conjuncts (perhaps belonging to a completely separate domain of inquiry). Does \(e\) confirm \(h\wedge q\) (relative to \(k\)) as it does with \(h\)? One would want to say no, and this implication can be suitably reconstructed in Hempel’s theory. HD-confirmation, on the contrary, can not draw this distinction: it is easy to show that, on the conditions specified, if the HD clause for confirmation is satisfied for \(e\) and \(h\) (given \(k\)), so it is for \(e\) and \(h\wedge q\) (given \(k\)). (This is simply because, if \(h\wedge k \vDash e\), then \(h\wedge q\wedge k \vDash e\), too, by the monotonicity of classical logical entailment.)

Kuipers (2000, 25) suggested that one can live with the irrelevant conjunction problem because, on the conditions specified, \(e\) would still not HD-confirm \(q\) alone (given \(k\)), so that HD-confirmation can be “localized”: \(h\) is the only bit of the conjunction \(h\wedge q\) that gets any confirmation on its own, as it were. Other authors have been reluctant to bite the bullet and have engaged in technical refinements of the “naïve” HD view. In these proposals, the spread of HD-confirmation upon frivolous conjunctions can be blocked at the expense of some additional logical machinery (see Gemes 1993, 1998; Schurz 1991, 1994).

Finally, it should be noted that HD-confirmation offers no substantial relief from the blite paradox. On the one hand, \(e = raven(a) \wedge ex_{t\le T}(a) \wedge black(a)\) does not , as such, HD-confirm either \(h = \forall x(raven(x) \rightarrow black(x))\) or \(h^* = \forall x(raven(x) \rightarrow blite(x))\), that is, for empty \(k\). On the other hand, if object \(a\) is assumed to have been sampled from ravens before \(T\) (that is, given \(k = raven(a) \wedge ex_{t\le T}(a))\), then \(black(a)\) is entailed by both “all ravens are black” and “all ravens are blite” and therefore HD-confirms each of them. So HD-confirmation, too, sanctions the existence of confirmation relations that seem intuitively unsound (indeed, indefinitely many of them: as we know, other variations of \(h^*\) can be conceived at will, like the “blurple” hypothesis). One could insist that HD does handle the blite paradox after all, because \(black(a)\) (given \(k\) as above) does not HD-confirms that a raven will be white if examined after \(T\) (Kuipers 2000, 29 ff.). Unfortunately (as pointed out by Schurz 2005, 148) \(black(a)\) does not HD-confirm that a raven will be black if examined after \(T\) either (again, given \(k\) as above). That’s because, as already pointed out, HD-confirmation fails the predictive inference condition (PIC) in general. So, all in all, HD-confirmation can not tell black from blite any more than Hempel-confirmation can.

The issues above look contrived and artificial to some people’s taste—even among philosophers. Many have suggested a closer look at real-world inferential practices in the sciences as a more appropriate benchmark for assessment. For one thing, the very idea of hypothetico-deductivism has often been said to stem from the origins of Western science. As reported by Simplicius of Cilicia (sixth century A.D.) in his commentary on Aristotle’s De Caelo , Plato had challenged his pupils to identify combinations of “ordered” motions by which one could account for (namely, deduce) the planets’ wandering trajectories across the heavens as observed by the Earth. As a matter of historical fact, mathematical astronomy has engaged in just this task for centuries: scholars have been trying to define geometrical models from which the apparent motion of celestial bodies would derive.

It is fair to say that, at its roots, the kind of challenges that the HD framework faces with scientific reasoning is not so different from the main puzzles that arise from philosophical considerations of a more formal kind. Still, the two areas turn out to be complementary in important ways. The following statement will serve as a useful starting point to extend the scope of our discussion.

Underdetermination Theorem (UT) for “naïve” HD-confirmation For any contingent \(h, e \in \bL\), if \(h\) and \(e\) are logically consistent, there exists some \(k \in \bL\) such that \(e\) HD-confirms \(h\) relative to \(k\).

(UT) is an elementary logical fact that has been long recognized (see, e.g., Glymour 1980a, 36). In purely formal terms, just positing \(k = h \rightarrow e\) will do for a proof. To appreciate how (UT) can spark any philosophical interest, one has to combine it with some insightful remarks first put forward by Pierre Duhem (1906) and then famously revived by Quine (1951) in a more radical style. (Indeed, (UT) essentially amounts to the “entailment version” of “Quinean underdetermination” in Laudan 1990, 274.)

Duhem (he himself a supporter of the HD view) pointed out that in mature sciences such as physics most hypotheses or theories of real interest can not be contradicted by any statement describing observable states of affairs. Taken in isolation, they simply do not logically imply, nor rule out, any observable fact, essentially because (unlike “all ravens are black”) they involve the mention of unobservable entities and processes. So, in effect, Duhem emphasized that, typically, scientific hypotheses or theories are logically consistent with any piece of checkable evidence. Unless, of course, the logical connection is underpinned by auxiliary hypotheses and assumptions suitably bridging the gap between the observational and non-observational vocabulary, as it were. But then, once auxiliaries are in play, logic alone guarantees that some \(k\) exists such that \(h\wedge k\) is consistent, \(h\wedge k \vDash e\), and \(k \not\vDash e\), so that confirmation holds in naïve HD terms (that’s just the UT result above). Apparently, when Duhem’s point applies, the uncritical supporter of whatever hypothesis \(h\) can legitimately claim (naïve HD) confirmation from any \(e\) by simply shaping \(k\) conveniently. In this sense, hypothesis assessment would be radically “underdetermined” by any amount of evidence practically available.

Influential authors such as Thomas Kuhn (1962/1970) (but see Laudan 1990, 268, for a more extensive survey) relied on Duhemian insights to suggest that confirmation by empirical evidence is too weak a force to drive the evaluation of theories in science, often inviting conclusions of a relativistic flavor (see Worrall 1996 for an illuminating reconstruction along these lines). Let us briefly consider a classical case, which Duhem himself thoroughly analyzed: the wave vs . particle theories of light in modern optics. Across the decades, wave theorists were able to deduce an impressive list of important empirical facts from their main hypothesis along with appropriate auxiliaries, diffraction phenomena being only one major example. But many particle theorists’ reaction was to retain their hypothesis nonetheless and to reshape other parts of the “theoretical maze” (i.e., \(k\); the term is Popper’s, 1963, p. 330) to recover those observed facts as consequences of their own proposal. And as we’ve seen, if the bare logic of naïve HD was to be taken strictly, surely they could have claimed their overall hypothesis to be confirmed too, just as much as their opponents.

Importantly, they didn’t. In fact, it was quite clear that particle theorists, unlike their wave-theory opponents, were striving to remedy weaknesses rather than scoring successes (see Worrall 1990). But why, then? Because, as Duhem himself clearly realized, the logic of naïve HD “is not the only rule for our judgments” (1906, 217). The lesson of (UT) and the Duhemian insight is not quite, it seems, that naïve HD is the last word and scientific inference is unconstrained by stringent rational principles, but rather that the HD view has to be strengthened in order to capture the real nature of evidential support in rational scientific inference. At least, that’s the position of a good deal of philosophers of science working within the HD framework broadly construed. It has even been maintained that “no serious twentieth-century methodologist” has ever subscribed to the naïve HD view above “without crucial qualifications” (Laudan 1990, 278; also see Laudan and Leplin 1991, 466).

So the HD approach to confirmation has yielded a number of more articulated variants to meet the challenge of underdetermination. Following (loosely) Norton (2005), we will now survey an instructive sample of them.

Naïve HD can be enriched by a resolute form of predictivism . According to this approach, the naïve HD clause for confirmation is too weak because \(e\) must have been predicted in advance from \(h\wedge k\). Karl Popper’s (1934/1959) account of the “corroboration” of hypotheses famously embedded this view, but squarely predictivist stances can be traced back to early modern thinkers like Christiaan Huygens (1629–1695) and Gottfried Wilhelm Leibniz (1646–1716), and in Duhem’s work itself. The predictivist sets a high bar for confirmation. Her favorite examples typically include stunning episodes in which the existence of previously unknown objects, phenomena, or whole classes of them is anticipated: the phases of Venus for Copernican astronomy or the discovery of Neptune for Newtonian physics, all the way up to the Higgs boson for so-called standard model of subatomic particles.

The predictivist solution to the underdetermination problem is fairly radical: many of the relevant factual consequences of \(h\wedge k\) will be already known when this theory is articulated, and so unfit for confirmation. Critics have objected that predictivism is in fact far too restrictive. There seem to be many cases in which already known phenomena clearly do provide support to a new hypothesis or theory. Zahar (1973) first raised this problem of “old evidence”, then made famous by Glymour (1980a, 85 ff.) as a difficulty for Bayesianism (see Section 3 below). Examples of this kind abound in the history of science as elsewhere, but the textbook illustration has become the precession of Mercury’s perihelion, a lasting anomaly for Newtonian physics: Einstein’s general relativity calculations got this long-known fact right, thereby gaining a remarkable piece of initial support for the new theory. In addition to this problem with old evidence, HD predictivism also seems to lack a principled rationale. After all, the temporal order of the discovery of \(e\) and of the articulation of \(h\) and \(k\) may well be an entirely accidental historical contingency. Why should it bear on the confirmation relationship among them? (See Giere 1983 and Musgrave 1974 for classical discussions of these issues. Douglas and Magnus 2013 and Barnes 2018 offer more recent views and rich lists of further references.)

As a possible response to the difficulties above, naïve HD can be enriched by the use-novelty criterion (UN) instead. The UN reaction to the underdetermination problem is more conservative than the temporal predictivist strategy. According to this view, to improve on the weak naïve HD clause for confirmation one only has to rule out one particular class of cases, i.e., those in which the description of a known fact, \(e\), served as a constraint in the construction of \(h\wedge k\). The UN view thus comes equipped with a rationale. If \(h\wedge k\) was shaped on the basis of \(e\), UN advocates point out, then it was bound to get that state of affairs right; the theory never ran any risk of failure, thus did not achieve any particularly significant success either. Precisely in these cases, and just for this reason, the evidence \(e\) must not be double-counted: by using it for the construction of the theory, its confirmational power becomes “dried out”, so to speak.

The UN completion of naïve HD originated from Lakatos and some of his collaborators (see Lakatos and Zahar 1975 and Worrall 1978; also see Giere 1979, 161–162, and Gillies 1989 for similar views), although important hints in the same direction can be found at least in the work of William Whewell (1840/1847). Consider the touchstone example of Mercury again. According to Zahar (1973), Einstein did not need to rely on the Mercury data to define theory and auxiliaries as to match observationally correct values for the perihelion precession (also see Norton 2011a; and Earman and Janssen 1993 for a very detailed, and more nuanced, account). Being already known, the fact was not of course predicted in a strictly temporal sense, and yet, on Zahar’s reading, it could have been : it was “use-novel” and thus fresh for use to confirm the theory. For a more mundane illustration, so-called cross-validation techniques represent a routine application of the UN idea in statistical settings (as pointed out by Schurz 2014, 92; also see Forster 2007, 592 ff.). According to some commentators, however, the UN criterion needs further elaboration (see Hitchcock and Sober 2004 and Lipton 2005), while others have criticized it as essentially wrong-headed (see Howson 1990 and Mayo 1991, 2014; also see Votsis 2014).

Yet another way to enrich naïve HD is to combine it with eliminativism . According to this view, the naïve HD clause for confirmation is too weak because there must have been a low (enough) objective chance of getting the outcome \(e\) (favorable to \(h\)) if \(h\) was false, so that few possibilities exist that \(e\) may have occurred for some reason other than the truth of \(h\). Briefly put, the occurrence of \(e\) must be such that most alternatives to \(h\) can be safely ruled out. The founding figure of eliminativism is Francis Bacon (1561–1626). John Stuart Mill (1843/1872) is a major representative in later times, and Deborah Mayo’s “error-statistical” approach to hypothesis testing arguably develops this tradition (Mayo 1996 and Mayo and Spanos 2010; see Bird 2010, Kitcher 1993, 219 ff., and Meehl 1990 for other contemporary variations).

Eliminativism is most credible when experimentation is at issue (see, e.g., Guala 2012). Indeed, the appeal to Bacon’s idea of crucial experiment ( instantia crucis ) and related notions (e.g., “severe testing”) is a fairly reliable mark of eliminativist inclinations. Experimentation is, to a large extent, precisely an array of techniques to keep undesired interfering factors at a minimum by active manipulation and deliberate control (think of the blinding procedure in medical trials, with \(h\) the hypothesized effectiveness of a novel treatment and \(e\) a relative improvement in clinical endpoints for a target subsample of patients thus treated). When this kind of control obtains, popular statistical tools are supposed to allow for the calculation of the probability of \(e\) in case \(h\) is false meant as a “relative frequency in a (real or hypothetical) series of test applications” (Mayo 1991, 529), and to secure a sufficiently low value to validate the positive outcome of the test. It is much less clear how firm a grip this approach can retain when inference takes place at higher levels of generality and theoretical commitment, where the hypothesis space is typically much too poorly ordered to fit routine error-statistical analyses. Indeed, Laudan (1997, 315; also see Musgrave 2010) spotted in this approach the risk of a “balkanization” of scientific reasoning, namely, a restricted focus on scattered pieces of experimental inference (but see Mayo 2010 for a defense).

Naïve HD can also be enriched by the notion of simplicity . According to this view, the naïve HD clause for confirmation is too weak because \(h\wedge k\) must be a simple (enough), unified way to account for evidence \(e\). A classic reference for the simplicity view is Newton’s first law of philosophizing in the Principia (“admit no more causes of natural things than such as are both true and sufficient to explain their appearances”), echoing very closely Ockham’s razor. This basic idea has never lost its appeal—even up to recent times (see, e.g., Quine and Ullian 1970, 69 ff.; Sober 1975; Zellner, Keuzenkamp, and McAleer 2002; Scorzato 2013).

Despite Thomas Kuhn’s (1957, 181) suggestions to the contrary, the success of Copernican astronomy over Ptolemy’s system has remained an influential case study fostering the simplicity view (Martens 2009). Moreover, in ordinary scientific problems such as curve fitting , formal criteria of model selection are applied where the paucity of parameters can be interpreted naturally as a key dimension of simplicity (Forster and Sober 1994). Traditionally, two main problems have proven pressing, and frustrating, for the simplicity approach. First, how to provide a sufficiently coherent and illuminating explication of this multifaceted and elusive notion (see Riesch 2010); and second, how to justify the role of simplicity as a properly epistemic (rather than merely pragmatic ) virtue (see Kelly 2007, 2008).

Finally, naïve HD can be enriched by the appeal to explanation . Here, the naïve HD clause for confirmation is meant to be too weak because \(h\wedge k\) must be able (not only to entail, but) to explain \(e\). By this move, the HD approach embeds the slogan of the so-called inference to the best explanation view: “observations support the hypothesis precisely because it would explain them” (Lipton 2000, 185; also see Lipton 2004). Historically, the main source for this connection between explanation and support is found in the work of Charles Sanders Peirce (1839–1914). Janssen (2003) offers a particularly neat contemporary exhibit, explicitly aimed at “curing cases of the Duhem-Quine disease” (484; also see Thagard 1978, and Douven 2017 for a relevant survey). Quite unlike eliminativist approaches, explanationist analyses tend to focus on large-scale theories and relatively high-level kinds of evidence. Dealing with Einstein’s general relativity, for instance, Janssen (2003) greatly emphasizes its explanation of the equivalence of inertial and gravitational mass (essentially a brute fact in Newtonian physics) over the resolution of the puzzle of Mercury’s perihelion. Explanationist accounts are also distinctively well-equipped to address inference patterns from non-experimental sciences (Cleland 2011).

The problems faced by these approaches are similar to those affecting the simplicity view. Agreement is still lacking on the nature of scientific explanation (see Woodward 2019) and it is not clear how far an explanationist variant of HD can go without a sound analysis of that notion. Moreover, some critics have wondered why the relationship of confirmation should be affected by an explanatory connection with the evidence per se (see Salmon 2001).

The above discussion does not display an exhaustive list (nor are the listed options mutually exclusive, for that matter: see, e.g., Baker 2003; also see Worrall 2010 for some overlapping implications in an applied setting of real practical value). And our sketched presentation hardly allows for any conclusive assessment. It does suggest, however, that reports of the death of hypothetico-deductivism (see Earman 1992, 64, and Glymour 1980b) might have been exaggerated. For all its difficulties, HD has proven fairly resilient at least as a basic framework to elucidate some key aspects of how hypotheses can be confirmed by the evidence (see Betz 2013, Gemes 2005, and Sprenger 2011b for consonant points of view).

3. Bayesian confirmation theories

Bayes’s theorem is a very central element of the probability calculus (see Joyce 2019). For historical reasons, Bayesian has become a standard label to allude to a range of approaches and positions sharing the common idea that probability (in its modern, mathematical sense) plays a crucial role in rational belief, inference, and behavior. According to Bayesian epistemologists and philosophers of science, (i) rational agents have credences differing in strength, which moreover (ii) satisfy the probability axioms, and can thus be represented in probabilistic form. (In non-Bayesian models (ii) is rejected, but (i) may well be retained: see Huber and Schmidt-Petri 2009, Levi 2008, and Spohn 2012.) Well-known arguments exist in favor of this position (see, e.g., Easwaran 2011a; Pettigrew 2016; Skyrms 1987; Vineberg 2016), although there is no lack of difficulties and criticism (see, e.g., Easwaran 2011b; Hájek 2008; Kelly and Glymour 2004; Norton 2011b).

Beyond the core ideas above, however, the theoretical landscape of Bayesianism is quite as hopelessly diverse as it is fertile. Surveys and state of art presentations are already numerous, and ostensibly growing (see, e.g., Good 1971; Joyce 2011; Oaksford and Chater 2007; Sprenger and Hartmann 2020; Weisberg 2015). For the present purposes, attention can be restricted to a classification that is still fairly coarse-grained, and based on just two dimensions or criteria.

First, there is a distinction between permissivism and impermissivism (see Meacham 2014 and Kopec and Titelbaum 2016 for this terminology). For permissive Bayesians (often otherwise labelled “subjectivists”), accordance with the probability axioms is the only clear-cut constraint on the credences of a rational agent. In impermissive forms of Bayesianism (often otherwise called “objective”), further constraints are put forward that significantly restrict the range of rational credences, possibly up to one single “right” probability function in any given setting. Second, there are different attitudes towards so-called principle of total evidence (TE) for the credences on which a reasoner relies. TE Bayesians maintain that the relevant credences should be represented by a probability function \(P\) which conveys the totality of what is known to the agent. For non-TE approaches, depending on the circumstances, \(P\) may (or should) be set up so that portions of the evidence available are in fact bracketed. (Unsurprisingly, further subtleties arise as soon as one delves a bit further into the precise meaning and scope of TE; see Fitelson 2008 and Williamson 2002, Chs. 9–10, for important discussions.)

Of course, many intermediate positions exist between extreme forms of permissivism and impermissivism so outlined, and more or less the same applies for the TE issue. The above distinctions are surely rough enough, but useful nonetheless. Impermissive TE Bayesianism has served as a received view in early Bayesian philosophy of science (e.g., Carnap 1950/1962). But impermissivism is easily found in combination with non-TE positions, too (see, e.g., Maher 1996). TE permissivism seems a good approximation of De Finetti’s (2008) stance, while non-TE permissivism is arguably close to a standard view nowadays (see, e.g., Howson and Urbach 2006). No more than this will be needed to begin our exploration of Bayesian confirmation theories.

Let us posit a set \(\bP\) of probability functions representing possible states of belief about a domain that is described in a finite language \(L\) with \(\bL\) the set of its closed sentences. From now on, unless otherwise specified, whenever considering some \(h, e, k \in \bL\) and \(P \in \bP\), we will invariably rely on the following provisos:

• both \(e\wedge k\) and \(h\wedge k\) are consistent;
• \(P(e\wedge k), P(h\wedge k) \gt 0;\)
• \(P(k) \gt P(h\wedge k)\) (unless \(k \vDash h\));
• \(P(e\wedge k) \gt P(e\wedge h\wedge k)\) (unless \(e\wedge k \vDash h\)); and
• \(P(e\wedge h\wedge k) \gt 0\), as long as \(e\wedge h\wedge k\) is consistent.

(These assumptions are convenient and critical for technical reasons, but not entirely innocent. Festa 1999 and Kuipers 2000, 44 ff., discuss some limiting cases that are left aside here owing to these constraints.)

A probabilistic theory of confirmation can be spelled out through the definition of a function \(C_{P}(h, e\mid k): \{\bL^3 \times \bP\} \rightarrow \Re\) representing the degree of confirmation that hypothesis \(h\) receives from evidence \(e\) relative to \(k\) and probability function \(P\). \(C_{P}(h,e\mid k)\) will then have relevant probabilities as its building blocks, according to the following basic postulate of probabilistic confirmation:

(P0) Formality There exists a function \(g\) such that, for any \(h, e, k \in \bL\) and any \(P \in \bP\), \(C_{P}(h,e\mid k) = g[P(h\wedge e\mid k),P(h\mid k),P(e\mid k)]\).

Note that the probability distribution over the algebra generated by \(h\) and \(e\), conditional on \(k\), is entirely determined by \(P(h\wedge e\mid k)\), \(P(h\mid k)\) and \(P(e\mid k)\). Hence, (P0) simply states that \(C_{P}(h, e\mid k)\) depends on that distribution, and nothing else. (The label for this assumption is taken from Tentori, Crupi, and Osherson 2007, 2010.)

Hempelian and HD confirmation, as discussed above, are qualitative theories of confirmation. They only tell us whether evidence \(e\) confirms (disconfirms) hypothesis \(h\) given \(k\). However, assessments of the amount of support that some evidence brings to a hypothesis are commonly involved in scientific reasoning, as well as in other domains, if only in the form of comparative judgments such as “hypothesis \(h\) is more strongly confirmed by \(e_{1}\) than by \(e_{2}\)” or “\(e\) confirms \(h_{1}\) to a greater extent than \(h_{2}\)”. Consider, for instance, the following principle, a veritable cornerstone of probabilistic confirmation in all of its variations (see Crupi, Chater, and Tentori 2013 for a list of references):

(P1) Final probability For any \(h,e_{1},e_{2},k \in \bL\) and any \(P \in \bP\), \(C_{P}(h,e_{1}\mid k) \gtreqless C_{P}(h, e_{2}\mid k)\) if and only if \(P(h\mid e_{1} \wedge k) \gtreqless P(h\mid e_{2} \wedge k).\)

(P1) is itself a comparative, or ordinal , principle, stating that, for any fixed hypothesis \(h\), the final (or posterior) probability and confirmation always move in the same direction in the light of data, \(e\) (given \(k\)). Interestingly, (P0) and (P1) are already sufficient to single out one traditional class of measures of probabilistic confirmation, if conjoined with the following (see Crupi and Tentori 2016, 656, Schippers 2017, and also Törnebohm 1966, 81):

(P2) Local equivalence For any \(h_{1},h_{2},e,k \in \bL\) and any \(P\in \bP\), if \(h_{1}\) and \(h_{2}\) are logically equivalent given \(e\) and \(k\), then \(C_{P}(h_{1},e\mid k) = C_{P}(h_{2}, e\mid k).\)

The following can then be shown:

Theorem 1 (P0), (P1) and (P2) hold if and only if there exists a strictly increasing function \(f\) such that, for any \(h, e, k \in \bL\) and any \(P \in \bP\), \(C_{P}(h, e\mid k) = f[P(h\mid e\wedge k)]\).

Theorem 1 provides a simple axiomatic characterization of the class of confirmation functions that are strictly increasing with the final probability of the hypothesis given the evidence (and \(k\)) (proven in Schippers 2017). All the functions in this class are ordinally equivalent , meaning that they imply the same rank order of \(C_{P}(h, e\mid k)\) and \(C_{P^*}(h^*,e^*\mid k^*)\) for any \(h, h^*,e, e^*,k, k^* \in \bL\) and any \(P, P^* \in \bP.\)

By (P0), (P1) and (P2), we thus have \(C_{P}(h, e\mid k) = f[P(h\mid e \wedge k)]\), implying that the more likely \(h\) is given the evidence the more it is confirmed. This approach explicates confirmation precisely as the overall credibility of a hypothesis ( firmness is Carnap’s 1950/1962 telling term, xvi). In this view, “Bayesian confirmation theory is little more than the examination of [the] properties” of the posterior probability function (Howson 2000, 179).

As we will see, the ordinal level of analysis is a solid and convenient middleground between a purely qualitative and a thoroughly quantitative (metric) notion of confirmation. To begin with, ordinal notions are in general sufficient to move “upwards” to the qualitative level as follows:

• \(e\) \(C_{P}\)- confirms \(h\) relative to \(k\) if and only if \(C_{P}(h, e\mid k) \gt C_{P}(\neg h, e\mid k);\)
• \(e\) \(C_{P}\)- disconfirms \(h\) relative to \(k\) if and only if \(C_{P}(h, e\mid k) \lt C_{P}(\neg h, e\mid k);\)
• \(e\) is \(C_{P}\)- neutral for \(h\) relative to \(k\) if and only if \(C_{P}(h, e\mid k) = C_{P}(\neg h, e\mid k).\)

Given Theorem 1, (P0), (P1) and (P2) can be combined with the definitions in (QC) to derive the following qualitative notion of probabilistic confirmation as firmness:

• \(e\) \(F\)- confirms \(h\) relative to \(k\) if and only if \(P(h\mid e \wedge k) \gt \bfrac{1}{2};\)
• \(e\) \(F\)- disconfirms \(h\) relative to \(k\) if and only if \(P(h\mid e \wedge k) \lt \bfrac{1}{2};\)
• \(e\) is \(F\)- neutral for \(h\) relative to \(k\) if and only if \(P(h\mid e \wedge k) = \bfrac{1}{2}.\)

The point of qualitative \(F\)-confirmation is thus straightforward: \(h\) is said to be (dis)confirmed by \(e\) (given \(k\)) if it is more likely than not to be true (false). (Sometimes a threshold higher than a probability \(\bfrac{1}{2}\) is identified, but this complication would add little for our present purposes.)

The ordinal notion of confirmation is of high theoretical significance because ordinal divergences, unlike purely quantitative differences, imply opposite comparative judgments for some evidence-hypothesis pairs. A refinement from the ordinal to a properly quantitative level is also be of interest, however, and much useful for tractability and applications. For example, one can have 0 as a convenient neutrality threshold for confirmation as firmness, provided that the following functional representation is adopted (see Peirce 1878 for an early occurrence):

(The base of the logarithm can be chosen at convenience, as long as it is strictly greater than 1.)

A quantitative requirement that is often put forward is the following stringent form of additivity:

Strict additivity (SA) For any \(h, e_{1},e_{2},k \in \bL\) and any \(P \in \bP\), \(\ \ \ C_{P}(h, e_{1} \wedge e_{2}\mid k) = C_{P}(h, e_{1}\mid k) + C_{P}(h, e_{2}\mid e_{1} \wedge k).\)

Although extraneous to \(F\)-confirmation, Strict Additivity will prove of use later on for the discussion of further variants of Bayesian confirmation theory.

Confirmation as firmness shares a number of structural properties with Hempelian confirmation. It satisfies the Special Consequence Condition, thus the Predictive Inference Condition too. It satisfies the Entailment Condition and, in virtue of (P1), extends it smoothly to the following ordinal counterpart:

• if, \(e_{1}\wedge k \vDash h\) and \(e_{2}\wedge k \not\vDash h\), then \(h\) is more confirmed by \(e_{1}\) than by \(e_{2}\) relative to \(k\), that is, \(C_{P}(h, e_{1}\mid k) \gt C_{P}(h, e_{2}\mid k);\)
• if, \(e_{1}\wedge k\vDash h\) and \(e_{2}\wedge k\vDash h,\) then \(h\) is equally confirmed by \(e_{1}\) and by \(e_{2}\) relative to \(k\), that is, \(C_{P}(h, e_{1}\mid k) = C_{P}(h, e_{2}\mid k).\)

According to (EC-Ord) not only is classical entailment retained as a case of confirmation, it also represents a limiting case: it is the strongest possible form of confirmation that a fixed hypothesis \(h\) can receive.

\(F\)-confirmation also satisfies Confirmation Complementarity and, moreover, extends it to its appealing ordinal counterpart (see Crupi, Festa, and Buttasi 2010, 85–86), that is:

Confirmation complementarity (ordinal extension) (CC-Ord) \(C_{P}(\neg h, e\mid k)\) is a strictly decreasing function of \(C_{P}(h, e\mid k)\), that is, for any \(h, h^*,e, e^*,k \in \bL\) and any \(P\in \bP,\) \(C_{P}(h, e\mid k)\gtreqless C_{P}(h^*,e^*\mid k)\) if and only if \(C_{P}(\neg h, e\mid k) \lesseqgtr C_{P}(\neg h^*,e^*\mid k).\)

(CC-Ord) neatly reflects Keynes’ (1921, 80) remark that “an argument is always as near to proving or disproving a proposition, as it is to disproving or proving its contradictory”. Indeed, quantitatively, the measure \(F(h, e\mid k)\) instantiates Confirmation Complementarity in a simple and elegant way, that is, it satisfies \(C_{P}(h, e\mid k) = -C_{P}(\neg h, e\mid k).\)

\(F\)-confirmation also implies another attractive quantitative result, alleviating the ailments of the irrelevant conjunction paradox. In the statement below, indicating this result, the irrelevance of \(q\) for hypothesis \(h\) and evidence \(e\) (relative to \(k\)) is meant to amount to the probabilistic independence of \(q\) from \(h, e\) and their conjunction (given \(k\)), that is, to \(P(h \wedge q\mid k) = P(h\mid k)P(q\mid k),\) \(P(e \wedge q\mid k) = P(e\mid k)P(q\mid k)\), and \(P(h \wedge e \wedge q\mid k) = P(h \wedge e\mid k)P(q\mid k)\), respectively.

Confirmation upon irrelevant conjunction (ordinal solution) (CIC) For any \(h, e, q, k \in \bL\) and any \(P \in \bP,\) if \(e\) confirms \(h\) relative to \(k\) and \(q\) is irrelevant for \(h\) and \(e\) relative to \(k\), then \(\ \ \ C_{P}(h, e\mid k) \gt C_{P}(h \wedge q, e\mid k).\)

So, even in case it is qualitatively preserved across the tacking of \(q\) onto \(h\), the positive confirmation afforded by \(e\) is at least bound to quantitatively decrease thereby.

Partly because of appealing formal features such as those mentioned so far, there is a long list of distinguished scholars advocating the firmness view of confirmation, from Keynes (1921) and Hosiasson-Lindenbaum (1940) onwards, most often coupled with some form of impermissive Bayesianism (see Hawthorne 2011 and Williamson 2011 for contemporary variations). In fact, \(F\)-confirmation fits most neatly a classical form of TE impermissivism à la Carnap, where one assumes that \(k = \top,\) that \(P\) is an “objective” initial probability based on essentially logical considerations, and that all the non-logical information available is collected in \(e\). The spirit of the Carnapian project never lost its appeal entirely (see, e.g., Festa 2003, Franklin 2001, Maher 2010, Paris 2011). However, the idea of a “logical” interpretation of \(P\) got stuck into difficulties that are often seen as insurmountable (e.g., Earman and Salmon 1992, 85–89; Gillies 2000, Ch. 3; Hájek 2019; Howson and Urbach 2006, 59–72; van Fraassen 1989, Ch. 12; Zabell 2011). And arguably, lacking some robust and effective impermissivist policy, the account of confirmation as firmness ends up loosing much of its philosophical momentum. The issues surrounding the ravens and blite paradoxes provide a useful illustration.

Consider again \(h = \forall x(raven(x) \rightarrow black(x))\), and the main analyses of “the observation that \(a\) is a black raven” encountered so far, that is:

• \(k = \top\) and \(e = raven(a) \wedge black(a)\), and
• \(k = raven(a)\) and \(e = black(a).\)

In both cases, whether \(e\) \(F\)-confirms \(h\) or not (relative to \(k\)) critically depends on \(P\): if the prior \(P(h\mid k)\) is low enough, \(e\) won’t do no matter what under either (i) or (ii); and if it is high enough, \(h\) will be \(F\)-confirmed either way. As a consequence, the \(F\)-confirmation view, by itself, does not offer any definite hint as to when, how, and why Nicod’s remarks apply or not.

For the purposes of our discussion, the following condition reveals another debatable aspect of the firmness explication of confirmation.

Consistency condition (Cons) For any \(h, h^*,e, k \in \bL\) and any \(P \in \bP\), if \(k \vDash \neg(h\wedge h^*)\) then \(e\) confirms \(h\) given \(k\) if and only if \(e\) disconfirms \(h^*\) given \(k\).

(Cons) says that evidence \(e\) can never confirm incompatible hypotheses. But consider, by way of illustration, a clinical case of an infectious disease of unknown origin, and suppose that \(e\) is the failure of antibiotic treatment. Arguably, there is nothing wrong in saying that, by discrediting bacteria as possible causes, the evidence confirms (viz. provides some support for) any of a number of alternative viral diagnoses. This judgment clashes with (Cons), though, which then seems an overly strong constraint.

Notably, (Cons) was defended by Hempel (1945) and, in fact, one can show that it follows from the conjunction of (qualitative) Confirmation Complementary and the Special Consequence Condition, and so from both Hempelian and \(F\)-confirmation. This is but one sign of how stringent the Special Consequence Condition is. Mainly because of the latter, both the Hempelian and the firmness views of confirmation must depart from the plausible HD idea that hypotheses are generally confirmed by their verified consequences (see Hempel 1945, 103–104). We will come back to this while discussing our next topic: a very different Bayesian explication of confirmation, based on the notion of probabilistic relevance .

We’ve seen that the firmness notion of probabilistic confirmation can be singled out through one ordinal constraint, (P2), in addition to the fundamental principles (P0)–(P1). The counterpart condition for the so-called relevance notion of probabilistic confirmation is the following:

(P3) Tautological evidence For any \(h_{1},h_{2},k\in \bL\) and any \(P\in \bP\), \(C_{P}(h_{1},\top \mid k) = C_{P}(h_{2},\top \mid k).\)

(P3) implies that any hypothesis is equally “confirmed” by empty evidence. We will say that \(C_{P}(h, e\mid k)\) represents the probabilistic relevance notion of confirmation, or relevance-confirmation, if and only if it satisfies (P0), (P1) and (P3). These conditions are sufficient to derive the following, purely qualitative principle, according to the definitional method in (QC) above (see Crupi and Tentori 2014, 82, and Crupi 2015).

• \(e\) relevance-confirms \(h\) relative to \(k\) if and only if \(P(h\mid e \wedge k)\gt P(h\mid k);\)
• \(e\) relevance-disconfirms \(h\) relative to \(k\) if and only if \(P(h\mid e \wedge k)\lt P(h\mid k);\)
• \(e\) is relevance-neutral for \(h\) relative to \(k\) if and only if \(P(h\mid e \wedge k) = P(h\mid k).\)

The point of relevance confirmation is that the credibility of a hypothesis can be changed in either a positive (confirmation in a strict sense) or negative way (disconfirmation) by the evidence concerned (given \(k\)). Confirmation (in the strict sense) thus reflects an increase from initial to final probability, whereas disconfirmation reflects a decrease (see Achinstein 2005 for some diverging views on this very idea).

The qualitative notions of confirmation as firmness and as relevance are demonstrably distinct. Unlike firmness, relevance confirmation can not be formalized by the final probability alone, or any increasing function thereof. To illustrate, the probability of an otherwise very rare disease \((h)\) can be quite low even after a relevant positive test result \((e)\); yet \(h\) is relevance-confirmed by \(e\) to the extent that its probability rises thereby. By the same token, the probability of the absence of the disease \((\neg h)\) can be quite high despite the positive test result \((e)\), yet \(\neg h\) is relevance-disconfirmed by \(e\) to the extent that its probability decreases thereby. Perhaps surprisingly, the distinction between firmness and relevance confirmation—“extremely fundamental” and yet “sometimes unnoticed”, as Salmon (1969, 48–49) put it—had to be stressed time and again to achieve theoretical clarity in philosophy (e.g., Popper 1954; Peijnenburg 2012) as well as in other domains concerned, such as artificial intelligence and the psychology of reasoning (see Horvitz and Heckerman 1986; Crupi, Fitelson, and Tentori 2008; Shogenji 2012).

The qualitative notion of relevance confirmation already has some interesting consequences. It implies, for instance, the following remarkable fact:

Complementary Evidence (CompE) For any \(h, e, k\in \bL\) and any \(P\in \bP,\) \(e\) confirms \(h\) relative to \(k\) if and only if \(\neg e\) disconfirms \(h\) relative to \(k.\)

The importance of (CompE) can be illustrated as follows. Consider the case of a father suspected of abusing his son. Suppose that the child does claim that s/he has been abused (label this evidence \(e\)). A forensic psychiatrist, when consulted, declares that this confirms guilt \((h)\). Alternatively, suppose that the child is asked and does not report having been abused \((\neg e).\) As pointed out by Dawes (2001), it may well happen that a forensic psychiatrist will nonetheless interpret this as evidence confirming guilt (suggesting that violence has prompted the child’s denial). One might want to argue that, other things being equal, this kind of “heads I win, tails you lose” judgment would be inconsistent, and thus in principle untenable. Whoever concurs with this line of argument (as Dawes 2001 himself did) is likely to be relying on the relevance notion of confirmation. In fact, no other notion of confirmation considered so far provides a general foundation for this judgment. \(F\)-confirmation, in particular, would not do, for it does allow that both \(e\) and \(\neg e\) confirm \(h\) (relative to \(k\)). This is because, mathematically, it is perfectly possible for both \(P(h\mid e \wedge k)\) and \(P(h\mid \neg e \wedge k)\) to be arbitrarily high above \(\bfrac{1}{2}.\) Condition (CompE), on the contrary, ensures that only one between the complementary statements \(e\) and \(\neg e\) can confirm hypothesis \(h\) (relative to \(k\)). (To be precise, HD-confirmation also satisfies condition CompE, yet it would fail the above example all the same, although for a different reason, that is, because the connection between \(h\) and \(e\) is plausibly one of probabilistic dependence but not of logical entailment.)

Remarks such as the foregoing have induced some contemporary Bayesian theorists to dismiss the notion of confirmation as firmness altogether, concluding with I.J. Good (1968, 134) that “if you had \(P(h\mid e \wedge k)\) close to unity, but less than \(P(h\mid k)\), you ought not to say that \(h\) was confirmed by \(e\)” (also see Salmon 1975, 13). Let us follow this suggestion and proceed to consider the ordinal (and quantitative) notions of relevance confirmation.

Just as with firmness, the ordinal analysis of relevance confirmation can be characterized axiomatically. With the relevance notion, however, a larger set of options arises. Consider the following principles.

(P4) Disjunction of alternative hypotheses For any \(e, h_{1},h_{2},k\in \bL\) and any \(P\in \bP,\) if \(k\vDash \neg (h_{1} \wedge h_{2})\), then \(C_{P}(h_{1},e\mid k) \gtreqless C_{P}(h_{1} \vee h_{2},e\mid k)\) if and only if \(P(h_{2}\mid e \wedge k)\gtreqless P(h_{2}\mid k).\)

(P5) Law of likelihood For any \(e, h_{1}, h_{2}, k\in \bL\) and any \(P\in \bP,\) \(C_{P}(h_{1}, e\mid k)\gtreqless C_{P}(h_{2}, e\mid k)\) if and only if \(P(e\mid h_{1} \wedge k)\gtreqless P(e\mid h_{2} \wedge k).\)

(P6) Modularity (for conditionally independent data) For any \(e_{1},e_{2},h, k\in \bL\) and any \(P\in \bP,\) if \(P(e_{1}\mid \pm h \wedge e_{2} \wedge k)=P(e_{1}\mid \pm h \wedge k),\) then \(C_{P}(h, e_{1}\mid e_{2} \wedge k) = C_{P}(h, e_{1}\mid k).\)

All the above conditions occur more or less widely in the literature (see Crupi, Chater, and Tentori 2013 and Crupi and Tentori 2016 for references and discussion). Interestingly, they’re all pairwise incompatible on the background of the Formality and the Final Probability principles (P0 and P1 above). Indeed, they sort out the relevance notion of confirmation into three distinct, classical families of measures, as follows (Crupi, Chater, and Tentori 2013; Crupi and Tentori 2016; Heckerman 1988; Sprenger and Hartmann 2020, Ch. 1):

• (P4) holds if and only if \(C_{P}(h, e\mid k)\) is a probability difference measure , that is, if there exists a strictly increasing function \(f\) such that, for any \(h, e, k\in \bL\) and any \(P\in \bP,\) \(C_{P}(h, e\mid k) = f[P(h\mid e \wedge k) - P(h\mid k)];\)
• (P5) holds if and only if \(C_{P}(h, e\mid k)\) is a probability ratio measure , that is, if there exists a strictly increasing function \(f\) such that, for any \(h, e, k\in \bL\) and any \(P\in \bP,\) \(C_{P}(h, e\mid k) =f[\frac{P(h\mid e \wedge k)}{P(h\mid k)}];\)
• (P6) holds if and only if \(C_{P}(h, e\mid k)\) is a likelihood ratio measure , that is, if there exists a strictly increasing function \(f\) such that, for any \(h, e, k\in \bL\) and any \(P\in \bP,\) \(C_{P}(h, e\mid k) =f[\frac{P(e\mid h \wedge k)}{P(e\mid \neg h \wedge k)}].\)

If a strictly additive behavior (SA above) is imposed, one functional form is singled out for the quantitative representation of confirmation corresponding to each of the clauses above:

• \(D_{P}(h, e\mid k) = P(h\mid e \wedge k) - P(h\mid k);\)
• \(R_{P}(h, e\mid k) = \log[\frac{P(h\mid e \wedge k)}{P(h\mid k)}];\)
• \(L_{P}(h, e\mid k) = \log[\frac{P(e\mid h \wedge k)}{P(e\mid \neg h \wedge k)}].\)

(The bases of the logarithms are assumed to be strictly greater than 1.)

Before discussing briefly this set of alternative quantitative measures of relevance confirmation, we will address one further related issue. It is a long-standing idea, going back to Carnap at least, that confirmation theory should yield an inductive logic that is analogous to classical deductive logic in some suitable sense, thus providing a theory of partial entailment, and partial refutation. Now, the deductive-logical notions of entailment and refutation (contradiction) exhibit the following well-known properties:

Contraposition of entailment Entailment is contrapositive, but not commutative. That is, it holds that \(e\) entails \(h\) \((e\vDash h)\) if and only if \(\neg h\) entails \(\neg e\) \((\neg h\vDash \neg e),\) while it does not hold that \(e\) entails \(h\) if and only if \(h\) entails \(e\) \((h\vDash e).\)

Commutativity of refutation Refutation, on the contrary, is commutative, but not contrapositive. That is, it holds that \(e\) refutes \(h\) \((e\vDash \neg h)\) if and only if \(h\) refutes \(e\) \((h\vDash \neg e)\), while it does not hold that \(e\) refutes \(h\) if and only if \(\neg h\) refutes \(\neg e\) \((\neg h \vDash \neg\neg e).\)

The confirmation-theoretic counterparts are fairly straightforward:

(P7) Contraposition of confirmation For any \(e, h, k\in \bL\) and any \(P\in \bP,\) if \(e\) relevance-confirms \(h\) relative to \(k,\) then \(C_{P}(h, e\mid k) = C_{P}(\neg e,\neg h\mid k).\)

(P8) Commutativity of disconfirmation For any \(e, h, k \in \bL\) and any \(P \in \bP,\) if \(e\) relevance-disconfirms \(h\) relative to \(k\), then \(C_{P}(h, e\mid k) = C_{P}(e, h\mid k).\)

The following can then be proven (Crupi and Tentori 2013):

Theorem 3 Given (P0) and (P1), (P7) and (P8) hold if and only if \(C_{P}(h, e\mid k)\) is a relative distance measure , that is, if there exists a strictly increasing function \(f\) such that, for any \(h, e, k\in \bL\) and any \(P\in \bP,\) \(C_{P}(h, e\mid k) = f[Z(h, e\mid k)],\) where:

\( Z(h,e\mid k)= \begin{cases} \dfrac{P(h\mid e \wedge k) - P(h\mid k)}{1-P(h\mid k)} & \mbox{if } P(h\mid e \wedge k) \ge P(h\mid k) \\ \\ \dfrac{P(h\mid e \wedge k) - P(h\mid k)}{P(h\mid k)} & \mbox{if } P(h\mid e \wedge k) \lt P(h\mid k) \end{cases} \)

So, despite some pessimistic suggestions (see, e.g., Hawthorne 2018, and the discussion in Crupi and Tentori 2013), a neat confirmation-theoretic generalization of logical entailment (and refutation) is possible after all. Interestingly, relative distance measures can be additive, but only for uniform pairs of arguments – both confirmatory or both disconfirmatory (see Milne 2014, p. 259). (Note: Crupi, Tentori, and Gonzalez 2007; Crupi, Festa, and Buttasi 2010; and Crupi and Tentori 2013, 2014, provide further discussions of the properties of relative distance measures and their intuitive motivations. Also see Mura 2008 for a related analysis.)

The plurality of alternative probabilistic measures of relevance confirmation has prompted some scholars to be skeptical or dismissive of the prospects for a quantitative theory of confirmation (see, e.g., Howson 2000, 184–185, and Kyburg and Teng 2001, 98 ff.). However, as we will see shortly, quantitative analyses of relevance confirmation have proved important for handling a number of puzzles and issues that plagued competing approaches. Moreover, various arguments in the philosophy of science and beyond have been shown to depend critically (and sometimes unwittingly) on the choice of one confirmation measure (or some of them) rather than others (see Festa and Cevolani 2017, Fitelson 1999, Brössel 2013, Glass 2013, Roche and Shogenji 2014, Rusconi et al . 2014, and van Enk 2014).

Recently, arguments have been offered by Huber (2008b) in favor of \(D\), by Park (2014), Pruss (2014), and Vassend (2015) in favor of \(L\) (also see Morey, Romeijn, and Rouder 2016 for an important connection with statistics), and by Crupi and Tentori (2010) in favor of \(Z\). Hájek and Joyce (2008, 123), on the other hand, have seen different measures as possibly capturing “distinct, complementary notions of evidential support” (also see Schlosshauer and Wheeler 2011, Sprenger and Hartmann 2020, Ch.1, and Steel 2007 for tempered forms of pluralism). The case of measure \(R\) deserves some more specific comments, however. Following Fitelson (2007), one could see \(R\) as conveying key tenets of so-called “likelihoodist” position about evidential reasoning (see Royall 1997 for a classical statement, and Chandler 2013 and Sober 1990 for consonant arguments and inclinations). There seems to be some consensus, however, that compelling objections can be raised against the adequacy of \(R\) as a proper measure of relevance confirmation (see, in particular, Crupi, Festa, and Buttasi 2010, 85–86; Eells and Fitelson 2002; Gillies 1986, 112; and compare Milne 1996 with Milne 2010, Other Internet Resources). In what follows, too, it will be convenient to restrict our discussion to \(D, L\) and \(Z\) as candidate measures. All the results to be presented below are invariant for whatever choice among these three options, and across ordinal equivalence with each of them (but those results do not always extend to measures ordinally equivalent to \(R\)).

Let us go back to a classical HD case, where the (consistent) conjunction \(h \wedge k\) (but not \(k\) alone) entails \(e.\) The following can be proven:

• if \(P(e\mid k)\lt 1,\) then \(e\) relevance-confirms \(h\) relative to \(k\) and \(C_{P}(h, e\mid k)\) is a decreasing function of \(P(e\mid k);\)
• if \(P(e\mid k) = 1,\) then \(e\) is relevance-neutral for \(h\) relative to \(k.\)

Formally, it is fairly simple to show that (SP) characterizes relevance confirmation (see, e.g., Crupi, Festa, and Buttasi 2010, 80; Hájek and Joyce 2008, 123), but the philosophical import of this result is nonetheless remarkable. For illustrative purposes, it is useful to assume the endorsement of the principle of total evidence (TE) as a default position for the Bayesian. This means that \(P\) is assumed to represent actual degrees of belief of a rational agent, that is, given all the background information available. Then, by clause (i) of (SP), we have that the occurrence of \(e\), a consequence of \(h \wedge k\) (but not of \(k\) alone), confirms \(h\) relative to \(k\) provided that \(e\) was initially uncertain to some degree (even given \(k\)). In other words: \(e\) must have been predicted on the basis of \(h \wedge k\). Moreover, again by (i), the confirmatory impact will be stronger the more surprising (unlikely) the evidence was unless \(h\) was conjoined to \(k\). So, under TE, relevance confirmation turns out to embed a squarely predictivist version of hypothetico-deductivism! As we know, this neutralizes the charge of underdetermination, yet it comes at the usual cost, namely, the old evidence problem. In fact, if TE is in force, then clause (ii) of (SP) implies that no statement that is known to be true (thus assigned probability 1) can ever have confirmatory import.

Interestingly, the Bayesian predictivist has an escape (neatly anticipated, and criticized, by Glymour 1980a, 91–92). Consider Einstein and Mercury once again. As effectively pointed out by Norton (2011a, 7), Einstein was extremely careful to emphasize that the precession phenomenon had been derived “ without having to posit any special [ auxiliary ] hypotheses at all ”. Why? Well, presumably because if one had allowed herself to arbitrarily devise ad hoc auxiliaries (within \(k\), in our notation) then one could have been pretty much certain in advance to find a way to get Mercury’s data right (remember: that’s the lesson of the underdetermination theorem). But getting those data right with auxiliaries \(k\) that were not thus adjusted—that would have been a natural consequence had the theory of general relativity been true and it would have been surprising otherwise . Arguably, this line of argument exploits much of the use-novelty idea within a predictivist framework. The crucial points are (i) that the evidence implied is not a verified empirical statement \(e\) but the logical fact that \(h \wedge k\) entails \(e\), and (ii) that the existence of this connection of entailment was not to be obviously anticipated at all, precisely because \(h \wedge k\) and \(e\) are such that the latter did not serve as a constraint to specify the former. On these conditions, it seems that \(h\) can be confirmed by this kind of “second-order” (logical) evidence in line with (SP) while TE is concurrently preserved .

At least two main problems arise, however. The first one is more technical in nature. Modelling rational uncertainty concerning logical facts (such as \(h \wedge k \vDash e\)) by probabilistic means is no trivial task. Garber (1983) put forward an influential proposal, but doubts have been raised that it might not be well-behaved (e.g., van Fraassen 1988; a careful survey with further references can be found in Eva and Hartmann forthcoming). Second, and more substantially, this solution of the old evidence problem can be charged of being an elusive change of the subject: for it was Mercury’s data , not anything else, that had to be recovered as having confirmed (and still confirming, some would add) Einstein’s theory. That’s the kind of judgment that confirmation theory must capture, and which remains unattainable for the predictivist Bayesian. (Earman 1992, 131 voiced this complaint forcefully. Hints for a possible rejoinder appear in Eells’s 1990 thorough discussion; see also Skyrms 1983.)

Bayesians that are unconvinced by the predictivist position are naturally led to dismiss TE and allow for the assignment of initial probabilities lower than 1 even to statements that were known all along. Of course, this brings the underdetermination problem back, for now \(k\) can still be concocted ad hoc to have known evidence \(e\) following from \(h \wedge k\) and moreover \(P(e\mid k)\lt 1\) is not prevented by TE anymore, thus potentially licencing arbitrary confirmation relations. Two moves can be combined to handle this problem. First, unlike HD, the Bayesian framework has the formal resources to characterize the auxiliaries themselves as more or less likely and thus their adoption as relatively safe or suspicious (the standard Bayesian treatment of auxiliary hypotheses is developed along these lines in Dorling 1979 and Howson and Urbach 2006, 92–102, and it is critically discussed in Rowbottom 2010, Strevens 2001, and Worrall 1993; also see Christensen 1997 for an important analysis of related issues). Second, one has to provide indications as to how TE should be relaxed. Non-TE Bayesians of the impermissivist strand often suggest that objective likelihood values concerning the outcome \(e\)—\(P(e\mid h \wedge k)\)—can be specified for the competing hypotheses at issue quite apart from the fact that \(e\) may have already occurred. Such values would typically be diverse for different hypotheses (thus mathematically implying \(P(e\mid k)\lt 1\)) and serve as a basis to capture formally the confirmatory impact of \(e\) (see Hawthorne 2005 for an argument along these lines). Permissivists, on the other hand, can not coherently rely on these considerations to articulate a non-TE position. They must invoke counterfactual degrees of belief instead, suggesting that \(P\) should be reconstructed as representing the beliefs that the agent would have, had she not known that \(e\) was true (see Howson 1991 for a statement and discussion, and Sprenger 2015 for an original recent variant; also see Jeffrey 1995 and Wagner 2001 for relevant technical results, and Steele and Werndl 2013 for an intriguing case-study from climate science).

The theory of Bayesian confirmation as relevance indicates when and why the HD idea works: if \(h \wedge k\) (but not \(k\)) entails \(e\), then \(h\) is relevance-confirmed by \(e\) (relative to \(k\)) because the latter increases the probability of the former— provided that \(P(e\mid k) \lt 1\). Admittedly, the meaning of the latter proviso partly depends on how one handles the problem of old evidence. Yet it seems legitimate to say that Bayesian relevance confirmation ( unlike the firmness view) retains a key point of ordinary scientific practice which is embedded in HD and yields further elements of clarification. Consider the following illustration.

Qualitative confirmation theories comply with the idea that \(h\) is confirmed both by \(e_{1} \wedge e_{2}\) and by \(e_{1} \wedge e_{2}^*.\) In the HD case, it is clear that \(h\) entails both conjunctions, given of course \(k\) stating that tigers, lions, and elephants are all mammals (an Hempelian account could also be given easily). Bayesian relevance confirmation unequivocally yields the same qualitative verdict. There is more, however. Presumably, one might also want to say that \(h\) is more strongly confirmed by \(e_{1} \wedge e_{2}\) than by \(e_{1} \wedge e_{2}^*,\) because the former offers a more varied and diverse body of positive evidence (interestingly, on experimental investigation, this pattern prevails in most people’s judgment, including children, see Lo et al. 2002). Indeed, the variety of evidence is a fairly central issue in the analysis of confirmation (see, e.g., Bovens and Hartmann 2002, Schlosshauer and Wheeler 2011, and Viale and Osherson 2000). In the illustrative case above, higher variety is readily captured by lower probability: it just seems a priori less likely that species as diverse as tigers and elephants share some unspecified genetic trait as compared to tigers and lions, that is, \(P(e_{1} \wedge e_{2}\mid k)\lt P(e_{1} \wedge e_{2}^*\mid k).\) By (SP) above, then, one immediately gets from the relevance confirmation view the sound implication that \(C_{P}(h, e_{1} \wedge e_{2}\mid k)\gt C_{P}(h, e_{1} \wedge e_{2}^*\mid k).\)

Principle (SP) is also of much use in the ravens problem. Posit \(h = \forall x(raven(x)\rightarrow black(x))\) once again. Just as HD, Bayesian relevance confirmation directly implies that \(e = black(a)\) confirms \(h\) given \(k = raven(a)\) and \(e^* =\neg raven(a)\) confirms \(h\) given \(k^* =\neg black(a)\) (provided, as we know, that \(P(e\mid k)\lt 1\) and \(P(e^*\mid k^*)\lt 1).\) That’s because \(h \wedge k\vDash e\) and \(h \wedge k^*\vDash e^*.\) But of course, to have \(h\) confirmed, sampling ravens and finding a black one is intuitively more significant than failing to find a raven while sampling the enormous set of the non-black objects. That is, it seems, because the latter is very likely to obtain anyway, whether or not \(h\) is true, so that \(P(e^*\mid k^*)\) is actually quite close to unity. Accordingly, (SP) implies that \(h\) is indeed more strongly confirmed by \(black(a)\) given \(raven(a)\) than it is by \(\neg raven(a)\) given \(\neg black(a)\)—that is, \(C_{P}(h, e\mid k)\gt C_{P}(h, e^*\mid k^*)\)—as long as the assumption \(P(e\mid k)\lt P(e^*\mid k^*)\) applies.

What then if the sampling in not constrained \((k = \top)\) and the evidence now amounts to the finding of a black raven, \(e = raven(a) \wedge black(a)\), versus a non-black non-raven, \(e^* =\neg black(a) \wedge \neg raven(a)\)? We’ve already seen that, for either Hempelian or HD-confirmation, \(e\) and \(e^*\) are on a par: both Hempel-confirm \(h\), none HD-confirms it. In the former case, the original Hempelian version of the ravens paradox immediately arises; in the latter, it is avoided, but at a cost: \(e\) is declared flatly irrelevant for \(h\)—a bit of a radical move. Can the Bayesian do any better? Quite so. Consider the following conditions:

• \(P[raven(a)\mid h] = P[raven(a)] \gt 0\)
• \(P[\neg raven(a) \wedge black(a)\mid h] = P[\neg raven(a) \wedge black(a)]\)

Roughly, (i) says that the size of the ravens population does not depend on their color (in fact, on \(h\)), and (ii) that the size of the population of black non -raven objects also does not depend on the color of ravens. Note that both (i) and (ii) seem fairly sound as far as our best understanding of our actual world is concerned. It is easy to show that, in relevance-confirmation terms, (i) and (ii) are sufficient to imply that \(e = raven(a) \wedge black(a)\), but not \(e^* = \neg raven(a) \wedge \neg black(a)\), confirms \(h\), that is \(C_{P}(h,e) \gt C_{P}(h,e^*) = 0\) (this observation is due to Mat Coakley). So the Bayesian relevance approach to confirmation can make a principled difference between \(e\) and \(e^*\) in both ordinal and qualitative terms. (A much broader analysis is provided by Fitelson and Hawthorne 2010, Hawthorne and Fitelson 2010 [Other Internet Resources]. Notably, their results include the full specification of the sufficient and necessary conditions for the main inequality \(C_{P}(h, e) \gt C_{P}(h, e^*)\).)

In general, Bayesian (relevance) confirmation theory implies that the evidential import of an instance of some generalization will often depend on the credence structure, and relies on its formal representation, \(P\), as a tool for more systematic analyses. Consider another instructive example. Assume that \(a\) denotes some company from some (otherwise unspecified) sector of the economy, and label the latter predicate \(S\). So, \(k = Sa\). You are informed that \(a\) increased revenues in 2019, represented as \(e = Ra\). Does this confirm \(h = \forall x(Sx \rightarrow Rx)\)? It does, at least to some degree, one would say. For an expansion of the whole sector (recall that you have no clue what this is) surely would account for the data. That’s a straightforward HD kind of reasoning (and a suitable Hempelian counterpart reconstruction would concur). But does \(e\) also confirm \(h^* = Sb \rightarrow Rb\) for some further company \(b\)? Well, another obvious account of the data \(e\) would be that company \(a\) has gained market shares at the expenses of some competitor, so that \(e\) might well seem to support \(\neg h^*,\) if anything (the revenues example is inspired by a remark in Blok, Medin, and Osherson 2007, 1362).

It can be shown that the Bayesian notion of relevance confirmation allows for this pattern of judgments, because (given \(k\)) evidence \(e\) above increases the probability of \(h\) but may well have the opposite effect on \(h^*\) (see Sober 1994 for important remarks along similar lines). Notably, \(h\) entails \(h^*\) by plain instantiation, and so contradicts \(\neg h^*\). As a consequence, the implication that \(C_{P}(h,e\mid k)\) is positive while \(C_{P}(h^*,e\mid k)\) is not clashes with each of the following, and proves them unduly restrictive: the Special Consequence Condition (SCC), the Predictive Inference Condition (PIC), and the Consistency Condition (Cons). Note that these principles were all evaded by HD-confirmation, but all implied by confirmation as firmness (see above).

At the same time, the most compelling features of \(F\)-confirmation, which the HD model was unable to capture, are retained by confirmation as relevance. In fact, all our measures of relevance confirmation (\(D, L\), and \(Z\)) entail the ordinal extension of the Entailment Condition (EC) as well as \(C_{P}(h, e\mid k) = -C_{P}(\neg h, e\mid k)\) and thereby Confirmation Complementarity in all of its forms (qualitative, ordinal, and quantitative). Moreover, the Bayesian confirmation theorist of either the firmness or the relevance strand can avail herself of the same quantitative strategy of “damage control” for the main specific paradox of HD-confirmation, i.e., the irrelevant conjunction problem. (See statement (CIC) above, and Crupi and Tentori 2010, Fitelson 2002. Also see Chandler 2007 for criticism, and Moretti 2006 for a related debate.)

We’re left with one last issue to conclude our discussion, to wit, the blite paradox. Recall that \(blite\) is so defined:

As always heretofore, we posit \(h = \forall x(raven(x)\rightarrow black(x)),\) \(h^* = \forall x(raven(x)\rightarrow blite(x)).\) We then consider the set up where \(k = raven(a) \wedge ex_{t\le T}(a),\) \(e= black(a),\) and \(P(e\mid k)\lt 1.\) Various authors have noted that, with Bayesian relevance confirmation, one has that \(P(h\mid k)\gt P(h^*\mid k)\) is sufficient to imply that \(C_{P}(h, e\mid k)\gt C_{P}(h^*,e\mid k)\) (see Gaifman 1979, 127–128; Sober 1994, 229–230; and Fitelson 2008, 131). So, as long as the black hypothesis is perceived as initially more credible than its blite counterpart, the former will be more strongly confirmed than the latter. Of course, \(P(h\mid k)\gt P(h^*\mid k)\) is an entirely commonsensical assumption, yet these same authors have generally, and quite understandably, failed to see this result as philosophically illuminating. Lacking some interesting, non-question-begging story as to why that inequality should obtain, no solution of the paradox seems to emerge. More modestly, one could point out that a measure of relevance confirmation \(C_{P}(h, e\mid k)\) implies (i) and (ii) below.

• Necessarily (that is, for any \(P\in \bP\)), \(e\) confirms \(h\) relative to \(k\).
• \(e\) confirms that a raven will be black if examined after \(T\), that is, \((raven(b)\wedge \neg ex_{t\le T}(b)) \rightarrow black(b),\) relative to \(k\); and
• \(e\) does not confirm that a raven will be white if examined after \(T\), that is, \((raven(b)\wedge \neg ex_{t\le T}(b)) \rightarrow white(b),\) relative to \(k\).

Without a doubt, (i) and (ii) fall far short of a satisfactory solution of the blite paradox. Yet it seems at least a legitimate minimal requirement for a compelling solution (if any exists) that it implies both. It is then of interest to note that confirmation as firmness is inconsistent with (i), while Hempelian and HD-confirmation are inconsistent with (ii).

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How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• Hawthorne, J. and B. Fitelson, 2010, An Even Better Solution to the Paradox of the Ravens , manuscript available online (PDF).
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Carnap, Rudolf | epistemology: Bayesian | evidence | Hempel, Carl | induction: problem of | logic: inductive | probability, interpretations of | statistics, philosophy of

Acknowledgments

I would like to thank Gustavo Cevolani, Paul Dicken, and Jan Sprenger for useful comments on previous drafts of this entry, and Prof. Wonbae Choi for helping me correcting a mistake.

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Research Article

Why a Confirmation Strategy Dominates Psychological Science

* E-mail: [email protected]

Affiliation Department of Psychology, University of Utah; Salt Lake City, Utah, United States of America

Affiliation Owen Graduate School of Management, Vanderbilt University, Nashville, Tennessee, United States of America

• David M. Sanbonmatsu, 
• Steven S. Posavac, 
• Arwen A. Behrends, 
• Shannon M. Moore, 
• Bert N. Uchino

• Published: September 18, 2015
• https://doi.org/10.1371/journal.pone.0138197
• Reader Comments

Our research explored the incidence and appropriateness of the much-maligned confirmatory approach to testing scientific hypotheses. Psychological scientists completed a survey about their research goals and strategies. The most frequently reported goal is to test the non-absolute hypothesis that a particular relation exists in some conditions. As expected, few scientists reported testing universal hypotheses. Most indicated an inclination to use a confirmation strategy to test the non-absolute hypotheses that a particular relation sometimes occurs or sometimes does not occur, and a disconfirmation strategy to test the absolute hypotheses that a particular relation always occurs or never occurs. The confirmatory search that dominates the field was found to be associated with the testing of non-absolute hypotheses. Our analysis indicates that a confirmatory approach is the normatively correct test of the non-absolute hypotheses that are the starting point of most studies. It also suggests that the strategy of falsification that was once proposed by Popper is generally incorrect given the infrequency of tests of universal hypotheses.

Citation: Sanbonmatsu DM, Posavac SS, Behrends AA, Moore SM, Uchino BN (2015) Why a Confirmation Strategy Dominates Psychological Science. PLoS ONE 10(9): e0138197. https://doi.org/10.1371/journal.pone.0138197

Editor: Jelte M. Wicherts, Tilburg University, NETHERLANDS

Received: April 29, 2015; Accepted: August 26, 2015; Published: September 18, 2015

Copyright: © 2015 Sanbonmatsu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Data Availability: All relevant data are within the paper and its Supporting Information files.

Funding: The authors have no support or funding to report.

Competing interests: The authors have declared that no competing interests exist.

Introduction

One of the enduring legacies of Karl Popper’s [ 1 ] philosophy of science is his belief in the central role of falsification in scientific advancement [ 2 , 3 ]. According to Popper, scientific theories can never be conclusively verified. Although evidence may be gathered which is consistent with a theory, the possibility always remains that instances will be uncovered that prove it to be false. In contrast, scientific generalizations can be conclusively falsified by a single disconfirming observation. Thus, science progresses primarily through falsification. Negative evidence permits the rejection of erroneous theories and allows the promotion of more viable alternatives.

Popper’s [ 1 ] provocative analysis of how science progresses is unsettling, because it is largely inconsistent with what psychological scientists do and have always done. Rather than following a strategy of falsification, most researchers attempt to provide confirming evidence for their hypotheses. Evidence of the approach taken by most psychological scientists was provided by Uchino, Thoman, and Byerly [ 4 ], who analyzed papers published in the Journal of Personality and Social Psychology over a 23 year period. An examination of the studies reported in a large sample of the journal’s papers showed that the vast majority (76.7%) took a confirmatory approach involving the testing of a favored hypothesis. Almost all of the reported studies (91.3%) supported an existing theory. Only 21.6% discussed alternative hypotheses and only 11.4% mentioned testing competing hypotheses. Thus, a strategy of falsification and its epistemological cousin, the crucial testing of alternative theories [ 5 – 7 ], appear to be atypical of psychology. This suggests that someone must be wrong; either scientists are going about their business incorrectly or Popper was mistaken about how science progresses.

Everyday Hypothesis Testing

The approach taken by psychological scientists is similar to how people generally test their ideas. Research has shown that in the selective testing of hypotheses [ 8 ], people typically engage in a positive or confirmatory search for instances of the presumed relation between variables [ 9 , 10 ]. They may also assimilate the gathered evidence in a manner that is consistent with the hypothesis or expectations [ 8 , 11 ]. Nevertheless, the search for confirming evidence does not necessarily lead to verification. Instead, the hypothesis is often falsified if instances are discovered that do not hold true in the predicted conditions [ 12 , 13 ].

Although confirmation appears to be the default strategy in the everyday testing of hypotheses [ 14 ], there are important conditions in which a disconfirmatory approach predominates. Sanbonmatsu, Posavac, Vanous, and Ho [ 15 ] have shown that the search for evidence depends heavily on the hypothesized frequency of the test relation. Hypotheses specify in general terms the proportion of instances that are characterized by a particular pattern, relation, or effect. At the broadest level, hypotheses presume that a phenomenon is either present or absent. Additionally, they are either absolute in presuming that a particular relation is always present or always absent, or non-absolute in presuming that a relation is sometimes present or sometimes absent. The informativeness of confirming vs. disconfirming evidence depends on the hypothesized frequency of the test relation [ 14 ]. Broadly speaking, the diagnosticity of a piece of information or datum can be defined in terms of the degree to which it distinguishes the test hypothesis from its complement [ 12 ]. A datum is informative to the extent that the probability of the datum when the hypothesis is true differs from the probability of the datum when the hypothesis is not true. In tests of absolute or universal hypotheses, disconfirmations have considerably greater diagnostic value than confirmations. A confirming observation is probable or possible not only when an absolute hypothesis is true but also when it is false. In contrast, a disconfirming instance is not possible when an absolute hypothesis is true. This, of course, is in keeping with Popper’s [ 1 ] analysis of the utility of falsification in science. In contrast, confirmations are much more diagnostic than disconfirmations in tests of non-absolute hypotheses presuming that a test relation occurs in some instances. A disconfirming observation is probable not only when the non-absolute hypothesis is false but also when it is true. In contrast, a confirming observation is not possible when a non-absolute hypothesis is false.

Sanbonmatsu, et al. [ 15 ] investigated whether the likelihood of a confirmatory vs. disconfirmatory search varies as a function of the hypothesized frequency of the test relation. Across three studies, they found that participants tended to seek evidence disconfirming the hypotheses that a phenomenon always occurs or never occurs, and evidence confirming the non-absolute hypothesis that a phenomenon sometimes occurs. For example, participants in one study were given the task of testing whether a statement about a set of integers from 1 to 10 was true. Some tested the absolute hypothesis that all of the numbers were even or the absolute hypothesis that none of the numbers were even, while others tested the non-absolute hypothesis that some of the numbers were even. They generated individual numbers, one possible number at a time, to test whether they were members of the set. As expected, participants tended to take a disconfirmatory approach to testing absolute hypotheses. For example, they tested odd numbers such as 3 to assess the hypothesis that all of the numbers were even. In contrast, participants typically took a confirmatory approach to test the hypothesis that some of the numbers were even. That is, they tested whether even numbers such as 2 belonged to the set. The findings were in line with previous research showing that people seek the most diagnostic evidence in the testing of hypotheses [ 16 , 17 ]. More generally, the results were consistent with the conception of people as able and flexible thinkers who utilize different test strategies as a function of the context [ 18 ].

The findings of the Sanbonmatsu, et al. [ 15 ] study raise questions about why a confirmation strategy dominates psychological science. If scientists think as well as research participants and, hence, are sensitive to the diagnosticity of evidence in the testing of hypotheses, why do they generally take a confirmatory approach in their studies?

Is Science Absolute?

Popper [ 1 ] assumed that scientific theories are universal; he believed they postulate that a phenomenon holds true in all conditions or instances. Of course, if theories are absolute, the most informative approach is the strategy of falsification that he prescribed. Again, when a phenomenon is hypothesized to always occur, a single negative observation is sufficient to reject the hypothesis while positive observations are inconclusive.

However, the ideas that are generated and tested in science may not always be absolute. To the contrary, we believe that most scientific hypotheses and theories predict that a particular relation between variables exists in some instances. For example, water turns to ice in some atmospheric conditions. Smoking contributes to lung cancer in some smokers. Anxiety sometimes undermines task performance. If the testing of non-absolute hypotheses is the most prevalent goal, the confirmatory approach that dominates psychological science [ 4 ] may be normatively correct. Note that when scientists hypothesize that a relation exists in some conditions, they presume that the relation exists uniformly in some conditions. That is, they believe there is invariance or regularity in nature [ 19 ] such that an effect that occurs in a particular context always occurs in that context (or nearly identical contexts).

An Empirical Investigation of Scientific Goals and Strategies

The nature of the goals and approaches characterizing psychological research is an empirical question that is best addressed through systematic study. Unfortunately, most prior accounts of this important aspect of the scientific enterprise have been speculative and based heavily on informal observation. In our investigation, psychological scientists completed a survey about their research practices. They began by reporting the research goals guiding their studies. We were particularly interested in the prevalence of tests of absolute vs. non-absolute hypotheses. The scientists were also asked about the general approach they take in the early stages of research aimed at establishing a phenomenon and in the later stages aimed at determining the causes and scope. Finally, the scientists indicated the strategies they use to test different research goals. We were interested in whether they tend to take a disconfirmatory approach to test absolute hypotheses and a more confirmatory approach to test non-absolute hypotheses.

Participants

The University of Utah Institutional Review Board approved the procedures and consent process for this study (IRB protocol #77072 “Research goals and strategies”). The survey was preceded by a consent cover letter that described the purpose and procedures of the study. Participants were informed that “by proceeding and responding to the questionnaire, you are giving your consent to participate.”

We expected large differences (an effect size of .50) in the approach taken to test different types of hypotheses based on our previous work examining the impact of quantifiers on information search [ 15 ]. A power analysis adopting an alpha of .05 (2-tailed) and power of 80% indicated that a sample of at least 33 scientists was needed to demonstrate within-subjects differences. Because participation was solicited en masse, we had limited control over the exact number of respondents.

Scientists at 6 research universities working as faculty in psychology departments or psychology programs, or who were trained as psychologists were recruited to participate in the study. At the end of the survey, respondents indicated the field of psychology in which they were trained. Their diverse psychological backgrounds are presented in Table 1 . Altogether, 17 female and 26 male scientists responded to the survey. The survey data are available in S1 Dataset .

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https://doi.org/10.1371/journal.pone.0138197.t001

Potential respondents were solicited for participation in a study of “research goals and strategies” via email. They were presented with the following study description:

This research is concerned with the goals and approaches that guide scientific research. There has been a great deal of philosophizing about the strategies that scientists use to test their theories and hypotheses. However, there has been a paucity of empirical research on this topic. The main purpose of this study is to examine the type of hypotheses that guide scientific research and the strategies used by scientists to test them.

The survey was administered online using Qualtrics. The first set of questions on the survey began with the following instructions:

Research often begins with a hypothesis about the relation between two or more variables. For example, many studies begin with the hypothesis that a variable X is significantly correlated with a variable Y. In particular, the presumption may be that a variable X has the property Y or that changes in variable X cause changes in a variable Y.

Scientific studies may be driven by a number of different hypothesis testing goals. Please indicate the extent to which each of the following goals guides your research.

Participants were presented with four possible research goals:

The goal is to test the hypothesis that a particular relation exists in all conditions. That is, the goal is to show that a particular relation always occurs or is always present in nature.

The goal is to test the hypothesis that a particular relation exists in some conditions. That is, the goal is to show that a particular relation occurs sometimes or is present some of the time in nature.

The goal is to test the hypothesis that a particular relation does not exist in some conditions. That is, the goal is to show that a particular relation does not occur sometimes or is not present some of the time in nature.

The goal is to test the hypothesis that a particular relation does no t exist under any conditions. That is, the goal is to show that a particular relation never occurs or is never present in nature.

The scientists’ task was to indicate the extent to which each goal guided their research on a scale containing the following four possible responses: a . Primary goal of my studies; b . Frequent goal of my studies; c . Infrequent goal of my studies; d . Not a goal of my studies .

The scientists were then asked about the approach they take to achieve their research goals. The first question was “Which of the following approaches do you typically take in your studies?” Two response alternatives were presented:

• a. I usually take a confirmatory approach in which I try to show that a particular relation occurs or exists in at least one set of conditions.
• b. I usually take a disconfirmatory approach in which I try to show that a particular relation does not occur or exist in at least one set of conditions.

They were then asked “In which of these phases of a research program are you more apt to take a confirmatory approach in which you attempt to verify that a particular relation exists in at least one set of conditions?” This was followed by the question “In which of these phases of a research program are you more apt to take a disconfirmatory approach in which you attempt to verify that a particular relation does not exist in at least one set of conditions? In both questions, the following two alternatives were presented:

• a. The early phases of a research program aimed at establishing that a particular relation or phenomenon occurs or exists.
• b. The later phases of a research program aimed at delineating the generality of a phenomenon and explaining a phenomenon.

The final set of questions presented psychological scientists with four different hypothesis testing goals:

Imagine you have been given the task of testing the hypothesis is that a particular relation always exists in nature. That is, you need conduct a study to test the hypothesis that a particular relation always occurs or is present in all conditions.

Imagine you have been given the task of testing the hypothesis is that a particular relation sometimes exists in nature. That is, you need conduct a study to test the hypothesis that a particular relation occurs sometimes or is present in some conditions.

Imagine you have been given the task of testing the hypothesis is that a particular relation sometimes does not exist in nature. That is, you need conduct a study to test the hypothesis that a particular relation does not occur sometimes or is not present in some conditions.

Imagine you have been given the task of testing the hypothesis is that a particular relation never exists in nature. That is, you need conduct a study to test the hypothesis that a particular relation does not occur or is not present in any conditions.

For each hypothesis, they were asked “If you were to conduct a study to test the truth or falsity of this hypothesis, which of the following research approaches would you more apt to take?” The following two alternatives were presented:

• a. I would attempt to provide a demonstration of the presumed relation. That is, I would conduct a study to show that the presumed relation occurs or is present in at least one set of conditions.
• b. I would attempt to provide a demonstration of the presumed relation not occurring. That is, I would conduct a study to show that the presumed relation does not occur or is not present in at least one set of conditions.

Thus, the scientists were asked whether they would attempt to demonstrate the presence of a particular relation or the absence of a particular relation. The survey ended with questions about the respondent’s gender and psychological training. Note that participants had the option of not responding to any of the survey questions.

Research Goals

A one way within-subjects analysis of variance (ANOVA) indicated that the four possible goals varied significantly in the extent to which they guided research, F (1,45) = 26.35, p < .001. The means (see Table 2 ) suggest that the scientists’ studies are guided most commonly by the goal of demonstrating that a relation sometimes occurs or exists; a total of 95.7% of the scientists indicated that it is the primary goal (12 or 26.1%) or a frequent goal of their studies (32 or 69.6%). Research appears to be infrequently guided by the goal of testing the absolute hypotheses that a relation always occurs or never occurs; 41.3% (19) indicated that demonstrating that a relation always exists is “not a goal of my studies” and 76.1% (35) indicated that demonstrating that a relation never exists is “not a goal of my studies”.

https://doi.org/10.1371/journal.pone.0138197.t002

A planned comparison indicated that scientists were more likely to investigate the hypothesis that a relation sometimes exists than the hypothesis that a relation always exists, t (45) = 11.45, p < .001, d = 2.47, 95% CI: 1.24 to 1.76. They were also more likely to test the hypothesis that a relation sometimes does not exist than the hypothesis that a relation never exists, t (45) = 10.77, p < .001, d = 1.85, 95% CI: 0.95 to 1.39. Further analyses verified that the scientists were much more apt to test non-absolute hypotheses (that a relation sometimes exists or sometimes does not exist) than absolute hypotheses (that a relation always exists or never exists), M = 2.18 vs M = 3.51, t (45) = 14.74, p < .001, d = 2.93, 95% CI: 1.15 to 1.52. They were also more likely to attempt to demonstrate the presence of a relation (i.e., that a relation always or sometimes exists) than the absence of a relation (i.e., that a relation sometimes does not exist or never exists), M = 2.53 vs M = 3.16, t (45) = 6.54, p < .001, d = 1.34, 95% CI: -0.81 to -0.43. Finally, the scientists’ studies are guided more by the goal of demonstrating that a particular relation sometimes exists than the goal of demonstrating that a particular relation sometimes does not exist, t (45) = 6.52, p < .001, d = 1.23, 95% CI: -1.02 to -0.54.

Research Approach

The scientists indicated whether they generally engage in a confirmatory or disconfirmatory search in their studies, and then reported the phases of research in which their approach tended to be confirmatory and disconfirmatory. When asked about their general research approach, 95.7% (44) of the participants indicated “I usually take a confirmatory approach in which I try to show that a particular relation occurs or exists in at least one set of conditions” while only 4.3% (2) indicated “I usually take a disconfirmatory approach in which I try to show that a particular relation does not occur or exist in at least one set of conditions.” A binomial test indicated that participants are more likely to engage in a confirmatory search than would be expected by chance, p < .001.

When asked about when they are most apt to take a confirmatory approach, 82.6% (38) of the participants indicated that they are most likely to attempt to confirm the test relation in “The early phases of a research program aimed at establishing that a particular relation or phenomenon occurs or exists” while only 17.4% (8) of the scientists are most apt to attempt to confirm a test relation in the “The later phases of a research program aimed at delineating the generality of a phenomenon and explaining a phenomenon.” A binomial test suggested that more participants take a confirmatory approach in the early phases of a research program than in the later phases, p < .001.

When asked about the research phase in which they were most apt to take a disconfirmatory approach, only 14.3% (6) indicated that they are most likely to attempt to disconfirm a test relation in the early phases aimed at establishing the existence or occurrence of a phenomenon while the vast majority (36 or 85.7%) of the scientists are most apt to attempt to disconfirm a test relation in the later phases aimed at delineating the generality of a phenomenon and explaining a phenomenon.” A binomial test indicated that more participants reported taking a disconfirmatory approach in the later phases of a research program vs. the early phases than would be expected by chance, p < .001.

A correlational analysis explored the relation between the research goals and strategies of the scientists. The goal of demonstrating that a particular relation sometimes exists was positively correlated with a confirmatory rather a disconfirmatory approach, r (45) = .30, p = .042. This correlation was actually quite surprising given the near absence of variability in both measures. The type of approach taken was not correlated with the goals of demonstrating that a relation always exists, r (45) = .07, p = .653, sometimes does not exist, r (45) = -.162, p = .281, or never exists, r (45) = .114, p = .449. The findings suggest that scientists are more likely to take a confirmatory approach in their studies if their goal is to demonstrate that particular phenomena sometimes exist in nature.

Testing Research Hypotheses

The final set of questions examined how the research approach of scientists varies as a function of their goals. We were interested specifically in whether the tendency to engage in a confirmatory vs. disconfirmatory search depends on the type of hypothesis under investigation. When the test hypothesis is that a relation sometimes or always exists, a confirmatory approach entails an attempt to demonstrate the presence of the hypothesized relation. However, two of the research hypotheses concerned the absence of a relation–the possibility that a particular relation does not occur sometimes or does not occur at all. A confirmation of the absence of a relation is a demonstration of the relation not occurring while a disconfirmation of the absence of a relation is a demonstration of the relation occurring. Thus, when the test hypothesis was that a relation sometimes does not occur or never occurs, a response of “I would attempt to show that the presumed relation does not occur. . .” was coded as a confirmatory approach while a response of “I would attempt to show that the presumed relation occurs…” was coded as a disconfirmatory approach.

Table 3 presents the approach the scientists are inclined to take to test the different types of hypotheses. A series of binomial tests were used to determine whether the scientists are more inclined to engage in a confirmatory or disconfirmatory search in testing each of the different types of hypotheses. Participants are much more likely to utilize a disconfirmatory search than a confirmatory search to test the absolute hypothesis that a test relation always occurs, p < .001. More than 80% indicated they would attempt to disconfirm the hypothesis that a possible relation is always present. They are much more inclined to take a confirmatory rather than a disconfirmatory approach to test the non-absolute hypotheses that a test relation sometimes occurs, p < .001, or sometimes does not occur, p < .002. In fact, more than 90% reported they would attempt to confirm the hypothesis that a relation is sometimes present and almost 75% reported they would attempt to confirm the hypothesis that a relation is sometimes not present. Finally, they are almost all inclined to take a disconfirmatory approach to test the absolute hypothesis that a test relation never occurs, p < .001. More than 95% indicated they would seek to disconfirm the hypothesis that a possible relation is never present.

https://doi.org/10.1371/journal.pone.0138197.t003

A planned comparison revealed that participants are much more likely to take a confirmatory approach to test the hypothesis that a particular relation sometimes occurs than to test the hypothesis that a particular relation always occurs, Χ 2 (1, N = 86) = 45.09, p < .0001. They are also much more likely to use a confirmatory strategy in testing the hypothesis that a particular relation sometimes does not occur than in testing the hypothesis that a particular relation never occurs, Χ 2 (1, N = 86) = 43.78, p < .0001. Further analyses revealed that a confirmatory approach is much more likely to be used in testing non-absolute hypotheses (that a particular relation sometimes occurs or sometimes does not occur) than in testing absolute hypotheses (that a particular relation always occurs or never occurs), Χ 2 (1, N = 172) = 86.83, p < .0001. Finally, a confirmatory approach is more likely to be taken in tests of hypotheses about the presence of a test relation (that a relation always or sometimes occurs) than in tests of hypotheses about the absence of a relation (that a relation never occurs or sometimes does not occur), Χ 2 (1, N = 172) = 3.94, p = .047.

Many books and articles have speculated about hypothesis testing in science. Our study took a more empirical approach to this important topic by surveying psychological scientists about their goals and strategies. The most commonly reported aim is to test the non-absolute hypothesis that a particular relation between variables occurs or exists sometimes. As expected, few scientists reported testing universal hypotheses. They also indicated that they are more likely to strive to establish the presence than the absence of a phenomenon. Following Uchino et al. [ 4 ], scientists reported they generally use a confirmation strategy, especially in the early phases of a research program. When they do use a disconfirmation strategy, it tends to be in the later phases aimed at explicating the scope and causes of a phenomenon.

Researchers appear to be aware that the diagnosticity of different search strategies depends on the hypothesis under investigation. They are highly inclined to engage in a confirmatory search to test the non-absolute hypotheses that a phenomenon sometimes occurs or sometimes does not occur, and a disconfirmatory approach to test the absolute hypotheses that a phenomenon always or never occurs. This along with the correlational evidence showing the linkage between the testing of non-absolute hypotheses and confirmation suggests that psychological scientists generally take a confirmatory approach because their most common goal is to demonstrate that a particular phenomenon sometimes exists in nature.

In order to increase participation, we purposely limited the number of questions on the survey and made responding easy with a multiple choice response format. Obviously, this diminished the richness of the data that were obtained from our sample of scientists. We were not able to examine the relative prevalence of other basic research aims such as description and replication that often drive investigations and more nuanced research strategies. Future research will need to take a much more open ended approach to ascertain the diverse goals and approaches characterizing the scientific enterprise.

Yet another limitation of our study is that self-reports were used to explicate the research goals and strategies of psychological scientists. People, of course, are not always aware of what they do or why they do what they do [ 20 ]. Moreover, self-reports may be biased by a host of factors including self-presentation concerns, acquiescence, reactance, and memory lapses [ 21 ]. As a consequence, there is often a significant gap between self-reports and actual behavior. Our concern is diminished by the belief that scientists tend to have a clear sense of their aims and approaches because of the frequency with which they are required to articulate their thoughts and activities in presentations, forums, articles, and grant proposals. Our confidence is also increased by the fact that the research approach reported by our sample of scientists was entirely consistent with the archival findings of Uchino, et al [ 4 ].

The sample in our study was far from representative of psychological scientists across the globe. The individuals who were solicited for participation were affiliated with six different research institutions exclusively in the United States, with only one developmental psychologist responding. Thus, caution should be exercised in generalizing to all psychologists.

Although our sample was limited to psychological scientists, the goals and strategies that were reported may be typical of all fields of science. We believe that in most scientific investigations, a confirmatory approach is used to test the non-absolute hypothesis that a phenomenon exists in some conditions. The approaches of other disciplines and the generality of our findings are topics that will need to be examined in future studies.

The Limits of Falsification

Popper’s [ 1 ] logic of falsification was more than a prescription for how scientists should proceed. He regarded it as a description of how science actually works and progresses. However, numerous philosophers and scientists have argued that scientific theories are based more on corroborations than falsifications [ 3 ]. Moreover, disconfirmations are commonly discounted or dismissed because of possible “misassumptions” [ 22 ] such as insensitive measures, improper operationalizations, and weak manipulations. Even reliable falsifications rarely lead to the rejection of hypotheses. Instead, theories are typically modified to accommodate disconfirming findings [ 23 , 24 ]. This was recognized by Popper [ 1 ] who believed that such ad-hoc adjustments were symptomatic of weak theory. In his view, the best (and most scientific) theories are those that are readily falsifiable. Because of the problems with simple or naïve falsification, he later proposed a more conventional and sophisticated form of “falsification” in which the weight of the evidence gathered by a field serves as the basis for the decision to reject or refute one theory in favor of another [ 1 ]. Nevertheless, he remained adamantly opposed to the idea of the confirmation of a theory throughout his career [ 25 , 26 ]. It is his conceptions of simple falsification that guide much of contemporary thinking in psychological science [ 27 , 28 ].

Our study adds to the literature on falsification by suggesting that the disconfirmation strategy once prescribed by Popper is actually normatively incorrect for the hypotheses that are most frequently investigated. In tests of the non-absolute hypotheses that dominate psychological science, falsifying evidence is relatively non-diagnostic. In contrast, the confirmatory approach that is typical of the field appears to be the most informative test of the non-absolute hypotheses that phenomena occur in some conditions.

Our analysis does not suggest that confirmation is more diagnostic than disconfirmation or vice versa; rather the informativeness of a search depends on the hypothesis under investigation. In this vein, it is worth noting that a confirmation of the non-absolute proposition that some instances are characterized by a test relation and a disconfirmation of the absolute proposition that no instances are characterized by a test relation are equivalent in their meaningfulness. Confirming that a relation sometimes exists by disconfirming the absolute proposition that a relation does not exist, of course, is precisely what is done in null hypothesis testing.

Our findings and analyses are largely mute regarding the controversy surrounding null hypothesis significance testing in psychological science. Our research does not speak to the criteria that should be used in tests or the statistical meaningfulness of the rejection of the null. Nevertheless, there is one issue that our study does address very sharply. Meehl [ 27 ] and later Dar [ 28 ] argue that null hypothesis testing falls short because confirmations are much less critical to theory development than the refutations afforded by other approaches. We believe that this particular criticism is misguided because of the limited diagnosticity of disconfirmations for tests of non-absolute hypotheses and because of the other problems associated with falsification discussed above.

Can Scientific Hypotheses be Verified?

One of the most influential ideas proposed by Popper [ 1 ] is that theories can never be conclusively verified. Our analysis suggests, quite fittingly, that this belief is correct sometimes. Universal generalizations can never be verified because an instance may be uncovered that is inconsistent with predictions. However, non-absolute hypotheses that a phenomenon occurs sometimes can be verified with a single confirming instance. The meaningfulness of such validation, of course, is more of a philosophical than an empirical question. Philosophers undoubtedly will have much to say about the informativeness (or uninformativeness) of confirmations of non-absolute hypotheses.

Although a study may confirm that a hypothesized relation sometimes exists, the results are specific to a particular time, context, sample, and set of procedures. Nevertheless, scientists assume that phenomena are relatively general and present in conditions beyond those examined in a study. After initial confirmation, they commonly investigate the scope of an observed relation. Although hypotheses can only be tentatively verified given the logical limitations of inductive inference, some philosophers have argued that each successive confirmation provides grounds for an increase in the probability of the hypothesis being “correct” [ 29 – 31 ]. Although intuitive, the probabilistic approach is primarily aimed at scoring the evidence for universal hypotheses and has met with both mathematical and philosophical problems [ 32 ].

An important category of non-absolute scientific generalizations which have been discussed extensively by philosophers are ceteris paribus laws [ 33 – 35 ]. These are laws that are presumed to hold true if there are no interferences or disturbing factors (ceteris paribus is Latin for "all other things being equal”). Many of the non-absolute hypotheses that are investigated in psychological science are not candidates for ceteris paribus laws because they are not presumed to be general. That is, the hypothesized relation is not expected to normally or typically occur in most instances. Often psychological scientists begin an investigation of a possible effect or relation without a clear sense of its scope. Following an initial demonstration, studies commonly attempt to determine not only the conditions in which a phenomenon is present but also the conditions in which it is absent. As our survey suggests, a disconfirmatory approach is much more frequent in the later stages of research. Often studies reveal that a phenomenon is limited largely to a narrow set of conditions. Some philosophers [ 36 ] distinguish “exclusive” ceteris paribus laws that refer specifically to effects or relations that occur only when particular factors are present.

Our findings and analysis suggest that science is a very different enterprise than that envisioned by Popper [ 1 ]. Research more often begins with tests of non-absolute hypotheses of limited scope than tests of universal laws. Because most hypotheses are non-absolute, they are not readily subject to the falsification that he initially postulated as the foundation of scientific advancement. Researchers much more commonly strive to confirm their ideas than falsify them. This approach is logically justifiable for tests of the non-absolute hypotheses that are investigated in most studies in psychological science. The ad hoc theorizing that Popper decried typifies science because theories are works in progress that are developed through the assimilation of new data.

Supporting Information

S1 dataset. survey data..

https://doi.org/10.1371/journal.pone.0138197.s001

Acknowledgments

The authors thank the editor and two reviewers for their thoughtful and constructive comments on an earlier version of this paper.

Author Contributions

Conceived and designed the experiments: DMS SSP BNU. Performed the experiments: AAB DMS. Analyzed the data: SMM DMS. Contributed reagents/materials/analysis tools: DMS SSP BNU. Wrote the paper: DMS SSP BNU SMM.

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Hypothesis-generating and confirmatory studies, Bonferroni correction, and pre-specification of trial endpoints

A p-value presents the outcome of a statistically tested null hypothesis. It indicates how incompatible observed data are with a statistical model defined by a null hypothesis. This hypothesis can, for example, be that 2 parameters have identical values, or that they differ by a specified amount. A low p-value shows that it is unlikely (a high p-value that it is not unlikely) that the observed data are consistent with the null hypothesis. Many null hypotheses are tested in order to generate study hypotheses for further research, others to confirm an already established study hypothesis. The difference between generating and confirming a hypothesis is crucial for the interpretation of the results. Presenting an outcome from a hypothesis-generating study as if it had been produced in a confirmatory study is misleading and represents methodological ignorance or scientific misconduct.

Hypothesis-generating studies differ methodologically from confirmatory studies. A generated hypothesis must be confirmed in a new study. An experiment is usually required for confirmation as an observational study cannot provide unequivocal results. For example, selection and confounding bias can be prevented by randomization and blinding in a clinical trial, but not in an observational study. Confirmatory studies, but not hypothesis-generating studies, also require control of the inflation in the false-positive error risk that is caused by testing multiple null hypotheses. The phenomenon is known as a multiplicity or mass-significance effect. A method for correcting the significance level for the multiplicity effect has been devised by the Italian mathematician Carlo Emilio Bonferroni. The correction (Bender and Lange 2001 ) is often misused in hypothesis-generating studies, often ignored when designing confirmatory studies (which results in underpowered studies), and often inadequately used in laboratory studies, for example when an investigator corrects the significance level for comparing 3 experimental groups by lowering it to 0.05/3 = 0. 017 and believes that this solves the problem of testing 50 null hypotheses, which would have required a corrected significance level of 0.05/50 = 0.001.

In a confirmatory study, it is mandatory to show that the tested hypothesis has been pre-specified. A study protocol or statistical analysis plan should therefore be enclosed with the study report when submitted to a scientific journal for publication. Since 2005 the ICMJE (International Committee of Medical Journal Editors) and the WHO also require registration of clinical trials and their endpoints in a publicly accessible register before enrollment of the first participant. Changing endpoints in a randomized trial after its initiation can in some cases be acceptable, but this is never a trivial problem (Evans 2007 ) and must always be described to the reader. Many authors do not understand the importance of pre-specification and desist from registering their trial, use vague or ambiguous endpoint definitions, redefine the primary endpoint during the analysis, switch primary and secondary outcomes, or present completely new endpoints without mentioning this to the reader. Such publications are simply not credible, but are nevertheless surprisingly common (Ramagopalan et al. 2014 ) even in high impact factor journals (Goldacre et al. 2019 ). A serious editorial evaluation of manuscripts presenting confirmatory results should always include a verification of the endpoint’s pre-specification.

Hypothesis-generating studies are much more common than confirmatory, because the latter are logistically more complex, more laborious, more time-consuming, more expensive, and require more methodological expertise. However, the result of a hypothesis-generating study is just a hypothesis. A hypothesis cannot be generated and confirmed in the same study, and it cannot be confirmed with a new hypothesis-generating study. Confirmatory studies are essential for scientific progress.

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• Evans S. When and how can endpoints be changed after initiation of a randomized clinical trial? PLoS Clin Trials 2007; 2 : e18. [ PMC free article ] [ PubMed ] [ Google Scholar ]
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The Curious Case of Confirmation Bias

The concept of confirmation bias has passed its sell-by date..

Posted May 5, 2019 | Reviewed by Devon Frye

Confirmation bias is the tendency to search for data that can confirm our beliefs, as opposed to looking for data that might challenge those beliefs. The bias degrades our judgments when our initial beliefs are wrong because we might fail to discover what is really happening until it is too late.

To demonstrate confirmation bias, Pines (2006) provides a hypothetical example (which I have slightly modified) of an overworked Emergency Department physician who sees a patient at 2:45 a.m.—a 51-year-old man who has come in several times in recent weeks complaining of an aching back. The staff suspects that the man is seeking prescriptions for pain medication . The physician, believing this is just one more such visit, does a cursory examination and confirms that all of the man's vital signs are fine—consistent with what was expected. The physician does give the man a new prescription for a pain reliever and sends the man home—but because he was only looking for what he expected, he missed the subtle problem that required immediate surgery.

The concept of confirmation bias appears to rest on three claims:

• First, firm evidence, going back 60 years, has demonstrated that people are prone to confirmation bias.
• Second, confirmation bias is clearly a dysfunctional tendency.
• Third, methods of debiasing are needed to help us to overcome confirmation bias.

The purpose of this essay is to look closely at these claims and explain why each one of them is wrong.

Claim #1: Firm evidence has demonstrated that people are prone to confirmation bias.

Confirmation bias was first described by Peter Wason (1960), who asked participants in an experiment to guess at a rule about number triples. The participants were told that the sequence 2-4-6 fit that rule. They could generate their own triples and they would get feedback on whether or not their triple fit the rule. When they had collected enough evidence, they were to announce their guess about what the rule was.

Wason found that the participants tested only positive examples—triples that fit their theory of what the rule was. The actual rule was any three ascending numbers, such as 2, 3, 47. However, given the 2-4-6 starting point, many participants generated triples that were even numbers, ascending and also increasing by two. Participants didn’t try sequences that might falsify their theory (e.g., 6-4-5). They were simply trying to confirm their beliefs.

At least, that’s the popular story. Reviewing the original Wason data reveals a different story. Wason’s data on the number triples (e.g., 2-4-6) showed that six of the 29 participants correctly guessed the rule on the very first trial, and several of these six did use probes that falsified a belief.

Most of the other participants in that study seemed to take the task lightly because it seemed so simple—but after getting feedback that their first guess was wrong, they realized that there was only one right answer and they'd have to do more analysis. Almost half of the remaining 23 participants immediately shaped up—10 guessed correctly on the second trial, with many of these also making use of negative probes (falsifications).

Therefore, the impression found in the literature is highly misleading. The impression is that in this Wason study—the paradigm case of confirmation bias—the participants showed a confirmation effect. But when you look at all the data, most of the participants were not trapped by confirmation bias. Only 13 of the 29 participants failed to solve the problem in the first two trials. (By the fifth trial, 23 of the 29 had solved the problem.)

The takeaway should have been that most people do test their beliefs. However, Wason chose to headline the bad news. The abstract to his paper states that “The results show that those [13] subjects, who reached two or more incorrect solutions, were unable, or unwilling, to test their hypotheses.” (p. 129).

Since then, several studies have obtained results that challenge the common beliefs about confirmation bias. These studies showed that most people actually are thoughtful enough to prefer genuinely diagnostic tests when given that option (Kunda, 1999; Trope & Bassok, 1982; Devine et al., 1990).

In the cognitive interviews I have conducted, I have seen some people trying to falsify their beliefs. One fireground commander, responding to a fire in a four-story apartment building, saw that the fire was in a laundry chute and seemed to be just beginning. He believed that he and his crew had arrived before the fire had a chance to spread up the chute—so he ordered an immediate attempt to suppress it from above, sending his crew to the 2nd and 3rd floors.

But he also worried that he might be wrong, so he circled the building. When he noticed smoke coming out of the eaves above the top floor, he realized that he was wrong. The fire must have already reached the 4th floor and the smoke was spreading down the hall and out the eaves. He immediately told his crew to stop trying to extinguish the fire and instead to shift to search and rescue for the inhabitants. All of them were successfully rescued, even though the building was severely damaged.

Another difficulty with Claim #1 is that confirmation bias tends to disappear when we add context. In a second study, Wason (1968) used a four-card problem to demonstrate confirmation bias. For example: Four cards are shown, each of which has a number on one side and a color on the other. The visible faces show 3, 8, red and brown. Participants are asked, "Which two cards should you turn over to test the claim that if a card has an even number on one face, then its opposite face is red?” (This is a slight variant of Wason’s original task; see the top part of the figure next to this paragraph.)

Most people turn over cards two and three. Card two, showing an “8,” is a useful test because of the opposite face is not red, the claim is disproved. But turning over card three, “red,” is a useless test because the claim is not that only cards with even numbers on one side have a red opposite face. Selecting card three illustrates confirmation bias.

However, Griggs and Cox (1982) applied some context to the four-card problem—they situated the task in a tavern with a barkeeper intent on following the law about underage drinking. Now the question took the form, “Which two of these cards should you turn over to test the claim that in this bar, 'If you are drinking alcohol then you must be over 19'?" Griggs and Cox found that 73 percent of the participants now chose “16,” and the beer—meaning the confirmation bias effect seen in Wason's version had mostly vanished. (See the bottom part of the figure above.)

Therefore, the first claim about the evidence for confirmation bias does not seem warranted.

Claim #2: Confirmation bias is clearly a dysfunctional tendency.

Advocates for confirmation bias would argue that the bias can still get in the way of good decision making . They would assert that even if the data don’t really support the claim that people fall prey to confirmation bias, we should still, as a safeguard, warn decision-makers against the tendency to support their pre-existing beliefs.

But that ploy, to discourage decision-makers from seeking to confirm their pre-existing beliefs, won’t work because confirmation attempts often do make good sense. Klayman and Ha (1987) explained that under high levels of uncertainty, positive tests are more informative than negative tests (i.e., falsifications). Klayman and Ha refer to a “positive test strategy” as having clear benefits.

As a result of this work, many researchers in the judgment and decisionmaking community have reconsidered their view that the confirmation tendency is a bias and needs to be overcome. Confirmation bias seems to be losing its force within the scientific community, even as it echoes in various applied communities.

Think about it: Of course we use our initial beliefs and frames to guide our explorations. How else would we search for information? Sometimes we can be tricked, in a cleverly designed study. Sometimes we trick ourselves when our initial belief is wrong. The use of our initial beliefs, gained through experience, isn’t perfect. However, it is not clear that there are better ways of proceeding in ambiguous and uncertain settings.

We seem to have a category error here—people referring to the original Wason data on the triples and the four cards (even though these data are problematic) and then stretching the concept of confirmation bias to cover all kinds of semi-related or even unrelated problems, usually with hindsight: If someone makes a mistake, then the researchers hunt for some aspect of confirmation bias. As David Woods observed, "The focus on confirmation bias commits hindsight bias."

For all these reasons, the second claim that the confirmation tendency is dysfunctional doesn’t seem warranted. We are able to make powerful use of our experience to identify a likely initial hypothesis and then use that hypothesis to guide the way we search for more data.

How would we search for data without using our experience? We wouldn’t engage in random search because that strategy seems highly inefficient. And I don’t think we would always try to search for data that could disprove our initial hypothesis, because that strategy won’t help us make sense of confusing situations. Even scientists do not often try to falsify their hypotheses, so there’s no reason to set this strategy up as an ideal for practitioners.

The confirmation bias advocates seem to be ignoring the important and difficult process of hypothesis generation, particularly under ambiguous and changing conditions. These are the kinds of conditions favoring the positive test strategy that Klayman and Ha studied.

Claim #3: Methods of debiasing are needed to help us to overcome confirmation bias.

For example, Lilienfeld et al. (2009) asserted that “research on combating extreme confirmation bias should be among psychological science’s most pressing priorities.” (p. 390). Many if not most decision researchers would still encourage us to try to debias decision-makers.

Unfortunately, that’s been tried and has gotten nowhere. Attempts to re-program people have failed. Lilienfeld et al. admitted that “psychologists have made far more progress in cataloguing cognitive biases… than in finding ways to correct or prevent them.” (p. 391). Arkes (1981) concluded that psychoeducational methods by themselves are “absolutely worthless.” (p. 326). The few successes have been small and it is likely that many failures go unreported. One researcher whose work has been very influential in the heuristics and biases community has admitted to me that debiasing efforts don’t work.

And let’s imagine that, despite the evidence, a debiasing tactic was developed that was effective. How would we use that tactic? Would it prevent us from formulating an initial hypothesis without gathering all relevant information? Would it prevent us from speculating when faced with ambiguous situations? Would it require us to seek falsifying evidence before searching for any supporting evidence? Even the advocates acknowledge that confirmation tendencies are generally adaptive. So how would a debiasing method enable us to know when to employ a confirmation strategy and when to stifle it?

Making this a little more dramatic, if we could surgically excise the confirmation tendency, how many decision researchers would sign up for that procedure? After all, I am not aware of any evidence that debiasing the confirmation tendency improves decision quality or makes people more successful and effective. I am not aware of data showing that a falsification strategy has any value. The Confirmation Surgery procedure would eliminate confirmation bias but would leave the patients forever searching for evidence to disconfirm any beliefs that might come to their minds to explain situations. The result seems more like a nightmare than a cure.

One might still argue that there are situations in which we would want to identify several hypotheses, as a way of avoiding confirmation bias. For example, physicians are well-advised to do differential diagnosis, identifying the possible causes for a medical condition. However, that’s just good practice. There’s no need to invoke a cognitive bias. There’s no need to try to debias people.

For these reasons, I suggest that the third claim about the need for debiasing methods is not warranted.

What about the problem of implicit racial biases? That topic is not really the same as confirmation bias, but I suspect some readers will be making this connection, especially given all of the effort to set up programs to overcome implicit racial biases. My first reaction is that the word “bias” is ambiguous. “Bias” can mean a prejudice , but this essay uses “bias” to mean a dysfunctional cognitive heuristic, with no consideration of prejudice, racial or otherwise. My second reaction is to point the reader to the weakened consensus on implicit bias and the concession made by Greenwald and Banaji (the researchers who originated the concept of implicit bias) that the Implicit Association Test doesn’t predict biased behavior and shouldn’t be used to classify individuals as likely to engage in discriminatory behavior.

Conclusions

Where does that leave us?

Fischhoff and Beyth-Marom (1983) complained about this expansion: “Confirmation bias, in particular, has proven to be a catch-all phrase incorporating biases in both information search and interpretation. Because of its excess and conflicting meanings, the term might best be retired.” (p. 257).

I have mixed feelings. I agree with Fischhoff and Beyth-Marom that over the years, the concept of confirmation bias has been stretched—or expanded—beyond Wason’s initial formation so that today it can refer to the following tendencies:

• Search: to search only for confirming evidence (Wason’s original definition)
• Preference: to prefer evidence that supports our beliefs
• Recall: to best remember information in keeping with our beliefs
• Interpretation: to interpret evidence in a way that supports our beliefs
• Framing: to use mistaken beliefs to misunderstand what is happening in a situation
• Testing: to ignore opportunities to test our beliefs
• Discarding: to explain away data that don’t fit with our beliefs

I see this expansion as a useful evolution, particularly the last three issues of framing, testing, and discarding. These are problems I have seen repeatedly. With this expansion, researchers will perhaps be more successful in finding ways to counter confirmation bias and improve judgments.

Nevertheless, I am skeptical. I don’t think the expansion will be effective because researchers will still be going down blind alleys. Decision researchers may try to prevent people from speculating at the outset even though rapid speculation is valuable for guiding exploration. Decision researchers may try to discourage people from seeking confirming evidence, even though the positive test strategy is so useful. The whole orientation of correcting a bias seems misguided. Instead of appreciating the strength of our sensemaking orientation and trying to reduce the occasional errors that might arise, the confirmation bias approach typically tries to eliminate errors by inhibiting our tendencies to speculate and explore.

Fortunately, there seems to be a better way to address the problems of being captured by our initial beliefs, failing to test those beliefs, and explaining away inconvenient data—the concept of fixation . This concept is consistent with what we know of naturalistic decision making, whereas confirmation bias is not. Fixation doesn’t carry the baggage of confirmation bias in terms of the three unwarranted claims discussed in this essay. Fixation directly gets at a crucial problem of failing to revise a mistaken belief.

And best of all, the concept of fixation provides a novel strategy for overcoming the problems of being captured by initial beliefs, failing to test those beliefs, and explaining away data that are inconsistent with those beliefs.

My next essay will discuss fixation and describe that strategy.

Arkes, H. (1981). Impediments to accurate clinical judgment and possible ways to minimize their impact. Journal of Consulting and Clinical Psychology, 49, 323-330.

Devine, P. G. Hirt, E.R.; Gehrke, E.M. (1990), Diagnostic and confirmation strategies in trait hypothesis testing. Journal of Personality and Social Psychology, 58 , 952–63.

Fischhoff, B. & Beyth-Marom, R. (1983). Hypothesis evaluation from a Bayesian perspective. Psychological Review, 90 , 239-260.

Griggs, R.A., & Cox, J.R. (1982). The elusive thematic-materials effect in Wason’s selection task. British Journal of Psychology, 73, 407-420.

Klayman, J., & Ha, Y-W. (1987). Confirmation, disconfirmation, and information in hypothesis testing. Psychological Review, 94 , 211-228.

Klein, G. (1998). Sources of power: How people make decisions . Cambridge, MA: MIT Press.

Kunda, Z. (1999). Social cognition: Making sense of people .Cambridge, MA: MIT Press.

Lilienfeld, S.O., Ammirati, R., & Landfield, K. (2009). Giving debiasing away: Can psychological research on correcting cognitive errors promote human welfare? Perspectives on Psychological Science, 4 , 390-398.

Oswald, M.E., & Grossjean, S. (2004). Confirmation bias. In R.F. Rudiger (Ed.) Cognitive illusions: A handbook on fallacies and biases in thinking, judgement and memory. Hove, UK: Psychology Press.

Pines, J.M. (2006). Confirmation bias in emergency medicine .Academic Emergency Medicine, 13 , 90-94.

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Wason, P.C. (1960). On the failure to eliminate hypotheses in a conceptual task. The Quarterly Journal of Experimental Psychology, 12 , 129-140.

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Gary Klein, Ph.D., is a senior scientist at MacroCognition LLC. His most recent book is Seeing What Others Don't: The remarkable ways we gain insights.

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What Is a Confirmed Hypothesis?

The Real Difference Between Reliability and Validity

A hypothesis is a provisional idea or explanation requiring evaluation. It is a key component of the scientific method. Every scientific study, whether experimental or descriptive, begins with a hypothesis that the study is designed to test -- that is, depending on the results of the study, the hypothesis will be either confirmed or disconfirmed.

Unknown Outcome

Every well-designed study is designed to test something that we do not already know or which is reasonably subject to investigation. Though hypotheses are often “best guesses” about the outcome of a study, the outcome itself should not be something already known by the researcher. Outcomes that the researcher already knows are called “consequences” and should be taken into consideration when forming a study’s hypothesis. A consequence cannot in any real sense be confirmed, since it’s something that is already known.

Reducing the Question to Variables

As a first step in creating a hypothesis, researchers reduce the question that they're investigating to variables -- that is, measurable values. If a given question cannot be reduced to variables, it most likely is not a question answerable by scientific study. In an experimental study, which is one that attempts to show that one thing causes or affects another, these variables are directional -- the hypothesis will claim that if there is a certain change in one variable, there will be a corresponding change in another, but not necessarily the other way around. In a descriptive study, which attempts to show correlation but not necessarily causation between two or more things, there is no directionality to the variables.

Falsifiability

Falsifiability refers to the idea that there must be some set of conditions that could occur that would show that a given hypothesis is false. For example, if a hypothesis states, “If mice eat twice as many calories, they will show weight gain,” there is a set of conditions under which the hypothesis would be false -- the mice eat twice as many calories but do not show weight gain. If there is no such set of conditions, then the hypothesis has been poorly designed -- because it cannot be disconfirmed, it cannot in any real sense be confirmed.

Confirmation

If a well-designed study delivers the results predicted by the hypothesis, then that hypothesis is confirmed. Note, however, that there is a difference between a confirmed hypothesis and a “proven” hypothesis. Scientific studies can support a given hypothesis, but they do not claim to absolutely prove hypotheses -- there could always be some other explanation for why a given study obtained the results it did. Generally speaking, however, the more often a study or experiment obtains the same results, the more heavily supported -- and thus, more likely to be correct -- a given hypothesis is.

Related Articles

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What Is Experimental Research Design?

What Components Are Necessary for an Experiment to Be Valid?

What Makes an Experiment Testable?

Qualitative and Quantitative Research Methods

The Disadvantages of Qualitative & Quantitative Research

What Must Happen for Scientific Theories to Be Accepted as Valid?

Types of Primary Data

• LiveScience.com: What Is a Scientific Hypothesis?

Based in Chicago, Adam Jefferys has been writing since 2007. He teaches college writing and literature, and has tutored students in ESL. He holds a Masters of Fine Arts in creative writing, and is currently completing a PhD in English Studies.

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Implications

confirmation bias

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confirmation bias , people’s tendency to process information by looking for, or interpreting, information that is consistent with their existing beliefs. This biased approach to decision making is largely unintentional, and it results in a person ignoring information that is inconsistent with their beliefs. These beliefs can include a person’s expectations in a given situation and their predictions about a particular outcome. People are especially likely to process information to support their own beliefs when an issue is highly important or self-relevant.

Confirmation bias is one example of how humans sometimes process information in an illogical, biased manner. The manner in which a person knows and understands the world is often affected by factors that are simply unknown to that person. Philosophers note that people have difficulty processing information in a rational , unbiased manner once they have developed an opinion about an issue. Humans are better able to rationally process information, giving equal weight to multiple viewpoints, if they are emotionally distant from the issue (although a low level of confirmation bias can still occur when an individual has no vested interests).

(Read Steven Pinker’s Britannica entry on rationality.)

One explanation for why people are susceptible to confirmation bias is that it is an efficient way to process information. Humans are incessantly bombarded with information and cannot possibly take the time to carefully process each piece of information to form an unbiased conclusion. Human decision making and information processing is often biased because people are limited to interpreting information from their own viewpoint. People need to process information quickly to protect themselves from harm. It is adaptive for humans to rely on instinctive, automatic behaviours that keep them out of harm’s way.

Another reason why people show confirmation bias is to protect their self-esteem . People like to feel good about themselves, and discovering that a belief that they highly value is incorrect makes them feel bad about themselves. Therefore, people will seek information that supports their existing beliefs. Another closely related motive is wanting to be correct. People want to feel that they are intelligent, but information that suggests that they are wrong or that they made a poor decision suggests they are lacking intelligence—and thus confirmation bias will encourage them to disregard this information.

Research has shown that confirmation bias is strong and widespread and that it occurs in several contexts . In the context of decision making , once an individual makes a decision, they will look for information that supports it. Information that conflicts with a person’s decision may cause discomfort, and the person will therefore ignore it or give it little consideration. People give special treatment to information that supports their personal beliefs. In studies examining my-side bias , people were able to generate and remember more reasons supporting their side of a controversial issue than the opposing side. Only when a researcher directly asked people to generate arguments against their own beliefs were they able to do so. It is not that people are incapable of generating arguments that are counter to their beliefs, but, rather, people are not motivated to do so.

Confirmation bias also surfaces in people’s tendency to look for positive instances. When seeking information to support their hypotheses or expectations, people tend to look for positive evidence that confirms that a hypothesis is true rather than information that would prove the view is false (if it is false).

Confirmation bias also operates in impression formation. If people are told what to expect from a person they are about to meet, such as that the person is warm, friendly, and outgoing, people will look for information that supports their expectations. When interacting with people whom perceivers think have certain personalities, the perceivers will ask questions of those people that are biased toward supporting the perceivers’ beliefs. For example, if Maria expects her roommate to be friendly and outgoing, Maria may ask her if she likes to go to parties rather than asking if she often studies in the library.

Confirmation bias is important because it may lead people to hold strongly to false beliefs or to give more weight to information that supports their beliefs than is warranted by the evidence. People may be overconfident in their beliefs because they have accumulated evidence to support them, when in reality they have overlooked or ignored a great deal of evidence refuting their beliefs—evidence which, if they had considered it, should lead them to question their beliefs. These factors may lead to risky decision making and lead people to overlook warning signs and other important information. In this manner, confirmation bias is often a component of black swan events , which are high-impact events that are unexpected but, in retrospect , appear to be inevitable.

Confirmation bias has important implications in the real world, including in medicine, law, and interpersonal relationships. Research has shown that medical doctors are just as likely to have confirmation biases as everyone else. Doctors often have a preliminary hunch regarding the diagnosis of a medical condition early in the treatment process. This hunch can interfere with the doctor’s ability to assess information that may indicate an alternative diagnosis is more likely. Another related outcome is how patients react to diagnoses . Patients are more likely to agree with a diagnosis that supports their preferred outcome than a diagnosis that goes against their preferred outcome. Both of these examples demonstrate that confirmation bias has implications for individuals’ health and well-being.

In the context of law, judges and jurors sometimes form an opinion about a defendant’s guilt or innocence before all of the evidence is known. Once a judge or juror forms an opinion, confirmation bias will interfere with their ability to process new information that emerges during a trial, which may lead to unjust verdicts.

In interpersonal relations, confirmation bias can be problematic because it may lead a person to form inaccurate and biased impressions of others. This may result in miscommunication and conflict in intergroup settings. In addition, when someone treats a person according to their expectations, that person may unintentionally change their behavior to conform to the other person’s expectations, thereby providing further support for the perceiver’s confirmation bias.

Confirmation Bias In Psychology: Definition & Examples

Julia Simkus

Editor at Simply Psychology

BA (Hons) Psychology, Princeton University

Julia Simkus is a graduate of Princeton University with a Bachelor of Arts in Psychology. She is currently studying for a Master's Degree in Counseling for Mental Health and Wellness in September 2023. Julia's research has been published in peer reviewed journals.

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Saul McLeod, PhD

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Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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Confirmation Bias is the tendency to look for information that supports, rather than rejects, one’s preconceptions, typically by interpreting evidence to confirm existing beliefs while rejecting or ignoring any conflicting data (American Psychological Association).

One of the early demonstrations of confirmation bias appeared in an experiment by Peter Watson (1960) in which the subjects were to find the experimenter’s rule for sequencing numbers.

Its results showed that the subjects chose responses that supported their hypotheses while rejecting contradictory evidence, and even though their hypotheses were incorrect, they became confident in them quickly (Gray, 2010, p. 356).

Though such evidence of confirmation bias has appeared in psychological literature throughout history, the term ‘confirmation bias’ was first used in a 1977 paper detailing an experimental study on the topic (Mynatt, Doherty, & Tweney, 1977).

Biased Search for Information

This type of confirmation bias explains people’s search for evidence in a one-sided way to support their hypotheses or theories.

Experiments have shown that people provide tests/questions designed to yield “yes” if their favored hypothesis is true and ignore alternative hypotheses that are likely to give the same result.

This is also known as the congruence heuristic (Baron, 2000, p.162-64). Though the preference for affirmative questions itself may not be biased, there are experiments that have shown that congruence bias does exist.

For Example:

If you were to search “Are cats better than dogs?” in Google, all you would get are sites listing the reasons why cats are better.

However, if you were to search “Are dogs better than cats?” google will only provide you with sites that believe dogs are better than cats.

This shows that phrasing questions in a one-sided way (i.e., affirmative manner) will assist you in obtaining evidence consistent with your hypothesis.

Biased Interpretation

This type of bias explains that people interpret evidence concerning their existing beliefs by evaluating confirming evidence differently than evidence that challenges their preconceptions.

Various experiments have shown that people tend not to change their beliefs on complex issues even after being provided with research because of the way they interpret the evidence.

Additionally, people accept “confirming” evidence more easily and critically evaluate the “disconfirming” evidence (this is known as disconfirmation bias) (Taber & Lodge, 2006).

When provided with the same evidence, people’s interpretations could still be biased.

For example:

Biased interpretation is shown in an experiment conducted by Stanford University on the topic of capital punishment. It included participants who were in support of and others who were against capital punishment.

All subjects were provided with the same two studies.

After reading the detailed descriptions of the studies, participants still held their initial beliefs and supported their reasoning by providing “confirming” evidence from the studies and rejecting any contradictory evidence or considering it inferior to the “confirming” evidence (Lord, Ross, & Lepper, 1979).

Biased Memory

To confirm their current beliefs, people may remember/recall information selectively. Psychological theories vary in defining memory bias.

Some theories state that information confirming prior beliefs is stored in the memory while contradictory evidence is not (i.e., Schema theory). Some others claim that striking information is remembered best (i.e., humor effect).

Memory confirmation bias also serves a role in stereotype maintenance. Experiments have shown that the mental association between expectancy-confirming information and the group label strongly affects recall and recognition memory.

Though a certain stereotype about a social group might not be true for an individual, people tend to remember the stereotype-consistent information better than any disconfirming evidence (Fyock & Stangor, 1994).

In one experimental study, participants were asked to read a woman’s profile (detailing her extroverted and introverted skills) and assess her for either a job of a librarian or real-estate salesperson.

Those assessing her as a salesperson better recalled extroverted traits, while the other group recalled more examples of introversion (Snyder & Cantor, 1979).

These experiments, along with others, have offered an insight into selective memory and provided evidence for biased memory, proving that one searches for and better remembers confirming evidence.

Social Media

Information we are presented on social media is not only reflective of what the users want to see but also of the designers’ beliefs and values. Today, people are exposed to an overwhelming number of news sources, each varying in their credibility.

To form conclusions, people tend to read the news that aligns with their perspectives. For instance, new channels provide information (even the same news) differently from each other on complex issues (i.e., racism, political parties, etc.), with some using sensational headlines/pictures and one-sided information.

Due to the biased coverage of topics, people only utilize certain channels/sites to obtain their information to make biased conclusions.

Religious Faith

People also tend to search for and interpret evidence with respect to their religious beliefs (if any).

For instance, on the topics of abortion and transgender rights, people whose religions are against such things will interpret this information differently than others and will look for evidence to validate what they believe.

Similarly, those who religiously reject the theory of evolution will either gather information disproving evolution or hold no official stance on the topic.

Also, irreligious people might perceive events that are considered “miracles” and “test of faiths” by religious people to be a reinforcement of their lack of faith in a religion.

when Does The Confirmation Bias Occur?

There are several explanations why humans possess confirmation bias, including this tendency being an efficient way to process information, protect self-esteem, and minimize cognitive dissonance.

Information Processing

Confirmation bias serves as an efficient way to process information because of the limitless information humans are exposed to.

To form an unbiased decision, one would have to critically evaluate every piece of information present, which is unfeasible. Therefore, people only tend to look for information desired to form their conclusions (Casad, 2019).

Protect Self-esteem

People are susceptible to confirmation bias to protect their self-esteem (to know that their beliefs are accurate).

To make themselves feel confident, they tend to look for information that supports their existing beliefs (Casad, 2019).

Minimize Cognitive Dissonance

Cognitive dissonance also explains why confirmation bias is adaptive.

Cognitive dissonance is a mental conflict that occurs when a person holds two contradictory beliefs and causes psychological stress/unease in a person.

To minimize this dissonance, people adapt to confirmation bias by avoiding information that is contradictory to their views and seeking evidence confirming their beliefs.

Challenge avoidance and reinforcement seeking to affect people’s thoughts/reactions differently since exposure to disconfirming information results in negative emotions, something that is nonexistent when seeking reinforcing evidence (“The Confirmation Bias: Why People See What They Want to See”).

Implications

Confirmation bias consistently shapes the way we look for and interpret information that influences our decisions in this society, ranging from homes to global platforms. This bias prevents people from gathering information objectively.

During the election campaign, people tend to look for information confirming their perspectives on different candidates while ignoring any information contradictory to their views.

This subjective manner of obtaining information can lead to overconfidence in a candidate, and misinterpretation/overlooking of important information, thus influencing their voting decision and, eventually country’s leadership (Cherry, 2020).

Recruitment and Selection

Confirmation bias also affects employment diversity because preconceived ideas about different social groups can introduce discrimination (though it might be unconscious) and impact the recruitment process (Agarwal, 2018).

Existing beliefs of a certain group being more competent than the other is the reason why particular races and gender are represented the most in companies today. This bias can hamper the company’s attempt at diversifying its employees.

Mitigating Confirmation Bias

Change in intrapersonal thought:.

To avoid being susceptible to confirmation bias, start questioning your research methods, and sources used to obtain their information.

Expanding the types of sources used in searching for information could provide different aspects of a particular topic and offer levels of credibility.

• Read entire articles rather than forming conclusions based on the headlines and pictures. – Search for credible evidence presented in the article.
• Analyze if the statements being asserted are backed up by trustworthy evidence (tracking the source of evidence could prove its credibility). – Encourage yourself and others to gather information in a conscious manner.

Alternative hypothesis:

Confirmation bias occurs when people tend to look for information that confirms their beliefs/hypotheses, but this bias can be reduced by taking into alternative hypotheses and their consequences.

Considering the possibility of beliefs/hypotheses other than one’s own could help you gather information in a more dynamic manner (rather than a one-sided way).

Related Cognitive Biases

There are many cognitive biases that characterize as subtypes of confirmation bias. Following are two of the subtypes:

Backfire Effect

The backfire effect occurs when people’s preexisting beliefs strengthen when challenged by contradictory evidence (Silverman, 2011).

• Therefore, disproving a misconception can actually strengthen a person’s belief in that misconception.

One piece of disconfirming evidence does not change people’s views, but a constant flow of credible refutations could correct misinformation/misconceptions.

This effect is considered a subtype of confirmation bias because it explains people’s reactions to new information based on their preexisting hypotheses.

A study by Brendan Nyhan and Jason Reifler (two researchers on political misinformation) explored the effects of different types of statements on people’s beliefs.

While examining two statements, “I am not a Muslim, Obama says.” and “I am a Christian, Obama says,” they concluded that the latter statement is more persuasive and resulted in people’s change of beliefs, thus affirming statements are more effective at correcting incorrect views (Silverman, 2011).

Halo Effect

The halo effect occurs when people use impressions from a single trait to form conclusions about other unrelated attributes. It is heavily influenced by the first impression.

Research on this effect was pioneered by American psychologist Edward Thorndike who, in 1920, described ways officers rated their soldiers on different traits based on first impressions (Neugaard, 2019).

Experiments have shown that when positive attributes are presented first, a person is judged more favorably than when negative traits are shown first. This is a subtype of confirmation bias because it allows us to structure our thinking about other information using only initial evidence.

Learning Check

When does the confirmation bias occur.

• When an individual only researches information that is consistent with personal beliefs.
• When an individual only makes a decision after all perspectives have been evaluated.
• When an individual becomes more confident in one’s judgments after researching alternative perspectives.
• When an individual believes that the odds of an event occurring increase if the event hasn’t occurred recently.

The correct answer is A. Confirmation bias occurs when an individual only researches information consistent with personal beliefs. This bias leads people to favor information that confirms their preconceptions or hypotheses, regardless of whether the information is true.

Take-home Messages

• Confirmation bias is the tendency of people to favor information that confirms their existing beliefs or hypotheses.
• Confirmation bias happens when a person gives more weight to evidence that confirms their beliefs and undervalues evidence that could disprove it.
• People display this bias when they gather or recall information selectively or when they interpret it in a biased way.
• The effect is stronger for emotionally charged issues and for deeply entrenched beliefs.

Agarwal, P., Dr. (2018, October 19). Here Is How Bias Can Affect Recruitment In Your Organisation. https://www.forbes.com/sites/pragyaagarwaleurope/2018/10/19/how-can-bias-during-interviewsaffect-recruitment-in-your-organisation

American Psychological Association. (n.d.). APA Dictionary of Psychology. https://dictionary.apa.org/confirmation-bias

Baron, J. (2000). Thinking and Deciding (Third ed.). Cambridge University Press.

Casad, B. (2019, October 09). Confirmation bias . https://www.britannica.com/science/confirmation-bias

Cherry, K. (2020, February 19). Why Do We Favor Information That Confirms Our Existing Beliefs? https://www.verywellmind.com/what-is-a-confirmation-bias-2795024

Fyock, J., & Stangor, C. (1994). The role of memory biases in stereotype maintenance. The British journal of social psychology, 33 (3), 331–343.

Gray, P. O. (2010). Psychology . New York: Worth Publishers.

Lord, C. G., Ross, L., & Lepper, M. R. (1979). Biased assimilation and attitude polarization: The effects of prior theories on subsequently considered evidence. Journal of Personality and Social Psychology, 37 (11), 2098–2109.

Mynatt, C. R., Doherty, M. E., & Tweney, R. D. (1977). Confirmation bias in a simulated research environment: An experimental study of scientific inference. Quarterly Journal of Experimental Psychology, 29 (1), 85-95.

Neugaard, B. (2019, October 09). Halo effect. https://www.britannica.com/science/halo-effect

Silverman, C. (2011, June 17). The Backfire Effect . https://archives.cjr.org/behind_the_news/the_backfire_effect.php

Snyder, M., & Cantor, N. (1979). Testing hypotheses about other people: The use of historical knowledge. Journal of Experimental Social Psychology, 15 (4), 330–342.

Further Information

• What Is Confirmation Bias and When Do People Actually Have It?
• Confirmation Bias: A Ubiquitous Phenomenon in Many Guises
• The importance of making assumptions: why confirmation is not necessarily a bias
• Decision Making Is Caused By Information Processing And Emotion: A Synthesis Of Two Approaches To Explain The Phenomenon Of Confirmation Bias

Confirmation bias occurs when individuals selectively collect, interpret, or remember information that confirms their existing beliefs or ideas, while ignoring or discounting evidence that contradicts these beliefs.

This bias can happen unconsciously and can influence decision-making and reasoning in various contexts, such as research, politics, or everyday decision-making.

What is confirmation bias in psychology?

Confirmation bias in psychology is the tendency to favor information that confirms existing beliefs or values. People exhibiting this bias are likely to seek out, interpret, remember, and give more weight to evidence that supports their views, while ignoring, dismissing, or undervaluing the relevance of evidence that contradicts them.

This can lead to faulty decision-making because one-sided information doesn’t provide a full picture.

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The Bayes’ factor: the coherent measure for hypothesis confirmation

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Franco Taroni, Paolo Garbolino, Silvia Bozza, Colin Aitken, The Bayes’ factor: the coherent measure for hypothesis confirmation, Law, Probability and Risk , Volume 20, Issue 1, March 2021, Pages 15–36, https://doi.org/10.1093/lpr/mgab007

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What have been called ‘Bayesian confirmation measures’ or ‘evidential support measures’ offer a numerical expression for the impact of a piece of evidence on a judicial hypothesis of interest. The Bayes’ factor, sometimes simply called the ‘likelihood ratio’, represents the best measure of the value of the evidence. It satisfies a number of necessary conditions on normative logical adequacy. It is shown that the same cannot be said for alternative expressions put forward by some legal and forensic quarters. A list of desiderata are given that support the choice of the Bayes’ factor as the best measure for quantification of the value of evidence.

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• What Is Confirmation Bias? | Definition & Examples

What Is Confirmation Bias? | Definition & Examples

Published on September 19, 2022 by Kassiani Nikolopoulou . Revised on March 10, 2023.

Confirmation bias is the tendency to seek out and prefer information that supports our preexisting beliefs. As a result, we tend to ignore any information that contradicts those beliefs.

Confirmation bias is often unintentional but can still lead to poor decision-making in (psychology) research and in legal or real-life contexts.

Table of contents

What is confirmation bias, types of confirmation bias, confirmation bias examples, how to avoid confirmation bias, other types of research bias, frequently asked questions about confirmation bias.

Confirmation bias is a type of cognitive bias , or an error in thinking. Processing all the facts available to us costs us time and energy, so our brains tend to pick the information that agrees most with our preexisting opinions and knowledge. This leads to faster decision-making. Mental “shortcuts” like this are called heuristics.

When confronted with new information that confirms what we already believe, we are more likely to:

• Accept it as true and accurate
• Overlook any flaws or inconsistencies
• Incorporate it into our belief system
• Recall it later, using it to support our belief during a discussion

On the other hand, if the new information contradicts what we already believe, we respond differently. We are more likely to:

• Become defensive about it
• Focus on criticizing any flaw, while that same flaw would be ignored if the information confirmed our beliefs
• Forget this information quickly, not recalling reading or hearing about it later on

There are three main ways that people display confirmation bias:

• Selective search
• Selective interpretation
• Selective recall

Biased search for information

This type of bias occurs when only positive evidence is sought, or evidence that supports your expectations or hypotheses. Evidence that could prove them wrong is systematically disregarded.

If you reverse the question and type “are cats better than dogs?”, you will get results in support of cats.

This will happen with any two variables : the search engine “assumes” that you think variable A is better than variable B, and shows you the results that agree with your opinion first.

Biased interpretation of information

Confirmation bias is not limited to the type of information we search for. Even if two people are presented with the same information, it is possible that they will interpret it differently.

The reader who doubts climate change may interpret the article as evidence that climate change is natural and has happened at other points in history. Any arguments raised in the article about the negative impact of fossil fuels will be dismissed.

On the other hand, the reader who is concerned about climate change will view the information as evidence that climate change is a threat and that something must be done about it. Appeals to cut down fossil fuel emissions will be viewed favorably.

Biased recall of information

Confirmation bias also affects what type of information we are able to recall.

A week after encountering the story, the reader who is concerned about climate change is more likely to recall these arguments in a discussion with friends. On the contrary, a climate change doubter likely won’t be able to recall the points made in the article.

Confirmation bias has serious implications for our ability to seek objective facts. It can lead individuals to “cherry-pick” bits of information that reinforce any prejudices or stereotypes.

An overworked physician, believing this is just drug-seeking behavior, examines him hastily in the hall. The physician confirms that all of the man’s vital signs are fine: consistent with what was expected.

The man is discharged. Because the physician was only looking for what was already expected, she missed the signs that the man was actually having a problem with his kidneys.

Confirmation bias can lead to poor decision-making in various contexts, including interpersonal relationships, medical diagnoses, or applications of the law.

Due to this, you unconsciously seek information to support your hypothesis during the data collection phase, rather than remaining open to results that could disprove it. At the end of your research, you conclude that memory games do indeed delay memory loss.

Although confirmation bias cannot be entirely eliminated, there are steps you can take to avoid it:

• First and foremost, accept that you have biases that impact your decision-making. Even though we like to think that we are objective, it is our nature to use mental shortcuts. This allows us to make judgments quickly and efficiently, but it also makes us disregard information that contradicts our views.
• Do your research thoroughly when searching for information. Actively consider all the evidence available, rather than just the evidence confirming your opinion or belief. Only use credible sources that can pass the CRAAP test .
• Make sure you read entire articles, not just the headline, prior to drawing any conclusions. Analyze the article to see if there is reliable evidence to support the argument being made. When in doubt, do further research to check if the information presented is trustworthy.

Cognitive bias

• Confirmation bias
• Baader–Meinhof phenomenon

Selection bias

• Sampling bias
• Ascertainment bias
• Attrition bias
• Self-selection bias
• Survivorship bias
• Nonresponse bias
• Undercoverage bias
• Hawthorne effect
• Observer bias
• Omitted variable bias
• Publication bias
• Pygmalion effect
• Recall bias
• Social desirability bias
• Placebo effect

Reliability and validity are both about how well a method measures something:

• Reliability refers to the  consistency of a measure (whether the results can be reproduced under the same conditions).
• Validity   refers to the  accuracy of a measure (whether the results really do represent what they are supposed to measure).

If you are doing experimental research, you also have to consider the internal and external validity of your experiment.

Research bias affects the validity and reliability of your research findings , leading to false conclusions and a misinterpretation of the truth. This can have serious implications in areas like medical research where, for example, a new form of treatment may be evaluated.

It can sometimes be hard to distinguish accurate from inaccurate sources , especially online. Published articles are not always credible and can reflect a biased viewpoint without providing evidence to support their conclusions.

Information literacy is important because it helps you to be aware of such unreliable content and to evaluate sources effectively, both in an academic context and more generally.

Confirmation bias is the tendency to search, interpret, and recall information in a way that aligns with our pre-existing values, opinions, or beliefs. It refers to the ability to recollect information best when it amplifies what we already believe. Relatedly, we tend to forget information that contradicts our opinions.

Although selective recall is a component of confirmation bias, it should not be confused with recall bias.

On the other hand, recall bias refers to the differences in the ability between study participants to recall past events when self-reporting is used. This difference in accuracy or completeness of recollection is not related to beliefs or opinions. Rather, recall bias relates to other factors, such as the length of the recall period, age, and the characteristics of the disease under investigation.

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What Is Confirmation Bias?

Cherrypicking the Facts to Support an Existing Belief

Verywell / Daniel Fishel 

• Tips for Overcoming It

Confirmation bias is a type of cognitive bias that favors information that confirms your previously existing beliefs or biases .

For example, imagine that Mary believes left-handed people are more creative than right-handed people. Whenever Mary encounters a left-handed, creative person, she will place greater importance on this "evidence" because it supports what she already believes. Mary might even seek proof that further backs up this belief while discounting examples that don't support the idea.

Confirmation biases affect not only how we gather information but also how we interpret and recall it. For example, people who support or oppose a particular issue will not only seek information to support it, but they will also interpret news stories in a way that upholds their existing ideas. They will also remember details in a way that reinforces these attitudes .

History of Confirmation Bias

The idea behind the confirmation bias has been observed by philosophers and writers since ancient times. In the 1960s, cognitive psychologist Peter Wason conducted several experiments known as Wason's rule discovery task. He demonstrated that people tend to seek information that confirms their existing beliefs.

Signs of Confirmation Bias

When it comes to confirmation bias, there are often signs that a person is inadvertently or consciously falling victim to it. Unfortunately, it can also be very subtle and difficult to spot. Some of these signs that might help you identify when you or someone else is experiencing this bias include:

• Only seeking out information that confirms your beliefs and ignoring or discredit information that doesn't support them.
• Looking for evidence that confirms what you already think is true, rather than considering all of the evidence available.
• Relying on stereotypes or personal biases when assessing information.
• Selectively remembering information that supports your views while forgetting or discounting information that doesn't.
• Having a strong emotional reaction to information (positive or negative) that confirms your beliefs, while remaining relatively unaffected by information that doesn't.

Types of Confirmation Bias

There are a few different types of confirmation bias that can occur. Some of the most common include the following:

• Biased attention : This is when we selectively focus on information that confirms our views while ignoring or discounting data that doesn't.
• Biased interpretation : This is when we consciously interpret information in a way that confirms our beliefs.
• Biased memory : This is when we selectively remember information that supports our views while forgetting or discounting information that doesn't.

Examples of the Confirmation Bias

It can be helpful to consider a few examples of how confirmation bias works in everyday life to get a better idea of the effects and impact it may have.

Interpretations of Current Issues

One of the most common examples of confirmation bias is how we seek out or interpret news stories. We are more likely to believe a story if it confirms our pre-existing views, even if the evidence presented is shaky or inconclusive. For example, if we support a particular political candidate, we are more likely to believe news stories that paint them in a positive light while discounting or ignoring those that are critical.

Consider the debate over gun control:

• Let's say Sally is in support of gun control. She seeks out news stories and opinion pieces that reaffirm the need for limitations on gun ownership. When she hears stories about shootings in the media, she interprets them in a way that supports her existing beliefs.
• Henry, on the other hand, is adamantly opposed to gun control. He seeks out news sources that are aligned with his position. When he comes across news stories about shootings, he interprets them in a way that supports his current point of view.

These two people have very different opinions on the same subject, and their interpretations are based on their beliefs. Even if they read the same story, their bias shapes how they perceive the details, further confirming their beliefs.

Personal Relationships

Another example of confirmation bias can be seen in the way we choose friends and partners. We are more likely to be attracted to and befriend people who share our same beliefs and values, and less likely to associate with those who don't. This can lead to an echo chamber effect, where we only ever hear information that confirms our views and never have our opinions challenged.

Decision-Making

The confirmation bias can often lead to bad decision-making . For example, if we are convinced that a particular investment is good, we may ignore warning signs that it might not be. Or, if we are set on getting a job with a particular company, we may not consider other opportunities that may be better suited for us.

Impact of the Confirmation Bias

The confirmation bias happens due to the natural way the brain works, so eliminating it is impossible. While it is often discussed as a negative tendency that impairs logic and decisions, it isn't always bad. The confirmation bias can significantly impact our lives, both positively and negatively. On the positive side, it can help us stay confident in our beliefs and values and give us a sense of certainty and security. 

Unfortunately, this type of bias can prevent us from looking at situations objectively. It can also influence our decisions and lead to poor or faulty choices.

During an election season, for example, people tend to seek positive information that paints their favored candidates in a good light. They will also look for information that casts the opposing candidate in a negative light.

By not seeking objective facts, interpreting information in a way that only supports their existing beliefs, and remembering details that uphold these beliefs, they often miss important information. These details and facts might have influenced their decision on which candidate to support.

How to Overcome the Confirmation Bias

There are a few different ways that we can try to overcome confirmation bias:

• Be aware of the signs that you may be falling victim to it. This includes being aware of your personal biases and how they might be influencing your decision-making.
• Consider all the evidence available, rather than just the evidence confirming your views.
• Seek out different perspectives, especially from those who hold opposing views.
• Be willing to change your mind in light of new evidence, even if it means updating or even changing your current beliefs.

Confirmation Bias: The Takeaway

Unfortunately, all humans are prone to confirmation bias. Even if you believe you are very open-minded and consider the facts before coming to conclusions, some bias likely shapes your opinion. Combating this natural tendency is difficult.

However, knowing about confirmation bias and accepting its existence can help you recognize it. Be curious about opposing views and listen to what others have to say and why. This can help you see issues and beliefs from other perspectives.

American Psychological Association. Confirmation bias . APA Dictionary of Psychology.

Wason PC. On the failure to eliminate hypotheses in a conceptual task . Quarterly Journal of Experimental Psychology . 1960;12(3):129-140. doi:10.1080/17470216008416717

Satya-Murti S, Lockhart J. Recognizing and reducing cognitive bias in clinical and forensic neurology . Neurol Clin Pract . 2015 Oct;5(5):389-396. doi:10.1212/CPJ.0000000000000181

Allahverdyan AE, Galstyan A. Opinion dynamics with confirmation bias . PLoS One . 2014;9(7):e99557. doi:10.1371/journal.pone.0099557

Frost P, Casey B, Griffin K, Raymundo L, Farrell C, Carrigan R. The influence of confirmation bias on memory and source monitoring. J Gen Psychol . 2015;142(4):238-52. doi:10.1080/00221309.2015.1084987

Suzuki M, Yamamoto Y. Characterizing the influence of confirmation bias on web search behavior . Front Psychol . 2021;12:771948. doi:10.3389/fpsyg.2021.771948

Poletiek FH. Hypothesis-Testing Behavior . Psychology Press, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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Expert Commentary

Confirmation bias in journalism: What it is and strategies to avoid it

A behavioral scientist explains why it's important for journalists to recognize and reduce the influence of cognitive bias in their work.

Republish this article

This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License .

by Carey Morewedge, The Journalist's Resource June 6, 2022

This <a target="_blank" href="https://journalistsresource.org/home/confirmation-bias-strategies-to-avoid-it/">article</a> first appeared on <a target="_blank" href="https://journalistsresource.org">The Journalist's Resource</a> and is republished here under a Creative Commons license.<img src="https://journalistsresource.org/wp-content/uploads/2020/11/cropped-jr-favicon-150x150.png" style="width:1em;height:1em;margin-left:10px;">

When we ask a question, test a hypothesis or question a belief, we often exhibit confirmation bias. We are more likely to search for evidence that confirms than disconfirms the question, hypothesis or belief we are testing. We also interpret evidence in ways that confirm rather than disconfirm that question, hypothesis or belief, and we are more likely to perceive confirming evidence to be more important than disconfirming evidence. Confirmation bias influences the questions we explore in both our professional and personal lives, whether our investigation is on behalf of an audience of millions or an audience of one.

In journalism, confirmation bias can influence a reporter’s assessment of whether a story is worth pitching and an editor’s decision to greenlight a story pitch. If the pitch is accepted, it can determine the questions the reporter decides to ask — or declines to ask — while investigating the story. It can affect an editor’s choice to assign certain stories to one reporter versus another. And it can leave journalists susceptible to deliberate misinformation campaigns.  

As a behavioral scientist, my research examines the causes and consequences of cognitive biases and develops interventions to reduce them. I have found that susceptibility to cognitive biases is not an immutable property of the mind. It can be reduced with training that targets specific biases . Debiasing training interventions teach people about biases like confirmation bias. They can also give examples, feedback and practice and offer actionable strategies to reduce each bias, which can improve professional judgments and decisions, from intelligence analysis to management .

Many of the same cognitive biases apply to journalism . I believe debiasing training can help journalists recognize and reduce the influence of cognitive biases in their own judgments and decisions, and see it in the actions and statements of the people they cover in their stories. Take for example this audio clip in which Pulitzer Prize-winning New York Times reporter Azmat Khan discusses how confirmation bias affected decisions about U.S. air strikes in the Middle East.

Confirmation bias in coverage of the Iraq War

In 2002, during the buildup to the United States’ invasion of Iraq, major newspapers including The Washington Post, The New York Times, The Los Angeles Times, The Guardian, The Daily Telegraph and The Christian Science Monitor ran a total of 80 front-page articles on weapons of mass destruction, between Oct. 11 and 31 alone. Many exhibited confirmation bias, as revealed by a 2004 analysis by Susan Moeller, a professor of media and international affairs and director of the International Center for Media and the Public Agenda at the University of Maryland . By contrast to earlier careful distinctions made by these papers between terrorism and the acquisition of WMD during 1998 tensions between India and Pakistan, Moeller found that these articles broadly accepted the linkages between terrorism and WMD made by the Bush administration and its assertions that war with Iraq would prevent terrorists from gaining access to WMD. The articles tended to lead with the White House’s perspective. Alternative perspectives and disconfirming evidence tended to be placed farther down in the story or buried .  

How does confirmation bias work?

Confirmation bias often takes the form of positive test strategy . When testing a hypothesis, belief or question, there are usually four kinds of evidence to consider: evidence for and against that hypothesis, belief or question, and evidence for and against alternative hypotheses or its negative (i.e., that the hypothesis being tested is wrong). We exhibit confirmation bias when we search for and prioritize evidence that would confirm our main hypothesis and disconfirm its alternatives or negative and when we ignore or brush off evidence that refutes our main hypothesis and confirms its alternatives or negative.

Consider a reporter investigating whether SARS-CoV-2 was manufactured and leaked from a laboratory in Wuhan, China , rather than had a zoonotic origin . The journalist might be more likely to report on or feature the physical proximity of the Wuhan Institute of Virology to the Huanan Market, where live animals were sold and most of the earliest cases were found, research on bat Coronaviruses conducted at the Institute , or mention Chinese government attempts to deny that live animals were sold at the market or the potentially erroneous first case reported 30 km from the Huanan Market. That journalist might be less likely to emphasize that most early cases were tied to the Huanan Market, that similar infections were found in raccoon dogs sold there and in nearby animal markets, that the structure of SARS-CoV-2 is not optimized for human transmission , and the profound impact that SARS-CoV-2 has had on the Chinese economy. 

We are prone to confirmation bias when intrinsic or extrinsic factors prompt us to focus on or test a particular hypothesis. Confirmation bias can be induced by our own values and motives (e.g., values, fears, politics, economic incentives), and by the way in which a problem or a question is framed .

Confirmation bias in the laboratory

Empirical evidence for confirmation bias in information search dates back to Peter Wason’s research from the 1960s on the psychology of how people test rules. The most famous example is his Card Selection task (sometimes called the four-card task). Research participants are shown four cards and are asked which two cards they should turn to test a rule. You can try it out right here.

Which two cards would you turn to test the rule, “ All cards with an even number on one side have a vowel on the other side ”?

Most of us choose cards 2 and A , and both cards have the potential to confirm the hypothesis. If you turned over the 2 and found a vowel, that would confirm your hypothesis. If you turned over the A and found an even number, that would confirm your hypothesis. However, we would need to turn over the 2 and B cards to test whether this set of cards disconfirm the rule. Only if an even number is paired with a consonant is the rule violated. If you turned over the 2 and found a Z, for instance, or turned over the B and found a 4, then you would know the rule was wrong. 

Another way we exhibit confirmation bias is in the kinds of questions we choose to ask, research shows. Many questions can only provide evidence that supports the hypothesis they test (e.g., “What makes you the right person for this job?”). We tend to be unbalanced in the number of questions we ask that would confirm or disconfirm our hypotheses.

In a classic 1978 paper , psychologists Mark Snyder and William Swann asked 58 undergraduate women at the University of Minnesota to test whether another participant fit a personality profile. Half tested whether their partner was an extravert. The other half tested whether their partner was an introvert.

To perform this test, each participant was shown a list of 26 questions and told to pick the 12 questions that would help them best test the hypothesis about their partner’s personality. The full list of questions fell into three categories. Eleven questions were the kind people usually ask of people they know are extraverts (“What kind of situations do you seek out if you want to meet new people?”). Ten questions were the kind people usually ask of people they know are introverts (“In what situations do you wish you could be more outgoing?”). The last five questions were irrelevant to extraversion and introversion (e.g., “What kind of charities do you like to contribute to?”). 

Participants testing for evidence of extraversion were 52% more likely than participants testing for evidence of introversion to ask questions that would confirm extraversion. By contrast, participants testing for evidence of introversion were 115% more likely than participants testing for evidence of extraversion to ask questions that would confirm introversion.

Evidence that confirmation bias influences how we interpret and weigh information comes from research on framing effects in decision making. Framing effects occur when the way you consider a decision (e.g., by choosing versus rejecting one of two options), changes which option you choose. Imagine you are a judge deciding a child custody case between two parents getting a divorce, Parents A and B. Parent A gets along well with the child and is average in terms of income, health, working hours, and other characteristics typical of adults in the United States, whereas the characteristics of Parent B are more extreme. Parent B earns and travels for work more, has an active social life, minor health problems, and is very close with the child. How you decide between these two parents might depend on the frame through which you ask the question.

In 1993, psychologist Eldar Shafir showed 170 Princeton University undergraduates the information above and asked them to make a decision . He asked half to whom they would award custody. A majority (64%) awarded custody to Parent B. He asked the other half of participants to whom they would deny custody. A majority (55%) also denied custody to Parent B! How did the frame lead more participants to both award and deny custody to Parent B? The way the question was framed (award versus deny) led participants to change the way they interpreted and weighed the evidence. Participants who chose a parent in the “award frame” focused on positive features of the parents, which favored parent B. Participants who rejected a parent in the “deny frame” focused on negative features of the parents, which favored Parent A.

Confirmation bias in the newsroom

Investigative journalism can be influenced by confirmation bias at many stages. Confirmation bias can influence which stories editors and journalists decide are likely to be worth reporting. It can influence which journalists are assigned to stories (those who share the cognitive biases of their editor and, therefore, also believe the stories to be important and newsworthy). Most important, it can influence how they collect evidence and transform that evidence into information for the public. Confirmation bias can influence what data is gathered and featured, which sources are interviewed and deemed credible, how evidence and quotes are interpreted and analyzed, which aspects of the story are featured prominently, which are downplayed and which are removed.

Whether a news organization decided to report on the SARS-CoV-2 lab leak hypothesis , for instance, was a decision made by its editors who greenlight the stories and the journalist(s) who reported it . Journalists made decisions about what evidence they deemed credible and worth reporting to the public, which sources to interview, trust and quote , and how to contrast evidence for a lab leak against evidence for zoonotic or other origins (if those alternatives were present at all).

Tips to reduce confirmation bias

Confirmation bias can be reduced with interventions that range from simple decision strategies to more intensive training interventions. A simple strategy one can apply immediately is when testing a hypothesis, make sure to test if alternatives or its negative are true (a “ consider-the-opposite ” strategy). Our justice system assumes that a person is innocent until proven guilty, but many jurors, investigators, judges and the public do not. Most presume guilt . Asking ourselves to explicitly consider whether an accused person is innocent can increase our propensity to consider evidence that challenges their criminal case.

When reporting on a story, remember that people’s default is to adopt a positive test strategy. Remember to examine the neglected diagonal — evidence disconfirming the main hypothesis and confirming its alternatives.

New research by my collaborators and me finds that even one-shot debiasing training interventions can help people recognize confirmation bias and reduce its influence on their own judgments and decisions, in the short and long term.

In a 2015 study, we brought 278 Pittsburghers into the laboratory. Each participant completed a pretest consisting of three tests of their susceptibility to confirmation bias and two other biases (i.e., bias blind spot and correspondence bias ). One-third of the participants then watched a 30-minute training video developed by IARPA (the Intelligence Advanced Research Projects Activity). In the video, a narrator defines biases, actors demonstrate in skits how a bias might influence a judgment or decision, and then strategies are reviewed to reduce the bias. You can watch it here:

The other two-thirds of participants played a 90-minute “ serious” detective game . The game elicited each of the three biases during game play. At the end of each level, experts described the three biases and gave examples of how they influence professional judgments and decisions. Participants then received personalized feedback on the biases they exhibited during game play and strategies to mitigate the biases. They also practiced implementing those strategies.

After completing one of these two interventions, all participants completed a post-test that included scales measuring how the interventions influenced their susceptibility to each of the three biases. Two months later, participants completed a third round of bias scales online, which tested whether the intervention produced a lasting change.

This project was a long shot. Most decision scientists think that cognitive biases are like visual illusions — that we can learn that they exist, but we can’t do much to prevent or reduce them . What we found was striking. Whether participants watched the video or played the game, participants exhibited large reductions in their susceptibility to all three cognitive biases both immediately and even two months later. 

In a 2019 paper with Anne-Laure Sellier and Irene Scopelliti — the Cartier-chaired professor of creativity and marketing at HEC Paris and a professor of marketing and behavioral science in the Bayes Business School at City, University of London, respectively — I found that debiasing training can improve decision making outside the laboratory, when people are not reminded of cognitive biases and do not know that their decisions are being observed. We conducted a naturalistic experiment in which 318 students enrolled in Masters degree programs at HEC Paris played our serious game once across a 20-day period.

We surreptitiously measured the extent to which the game influenced their susceptibility to confirmation bias by inserting a business case based on a real-world event, with which we measured their susceptibility to confirmation bias, into their courses.  Students did not know that the course and game were connected.

Business cases are essentially a role playing game or simulation of a problem that business leaders might face. Students are presented with the problem and evidence (e.g., data, opinions of different employees and managers). They then conduct an analysis and decide their best course of action under those circumstances.

We found that students who played the debiasing training game before doing the case were 19% less likely to make an inferior hypothesis-confirming decision in the case (than participants who played the debiasing training game after doing the case.

These experiments give us hope that debiasing training can work. There is still much exciting work to be done to see when and how debiasing training interventions reduce cognitive biases and which features of these and other interventions are most effective. 

Cognitive biases like confirmation bias can help us save time and energy when our initial hypotheses are correct, but they can also create catastrophic mistakes . Learning to understand, spot and correct them — especially when the stakes are high — is a valuable skill for all journalists.   

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Carey Morewedge

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How did life begin on earth a lightning strike of an idea..

Yahya Chaudhry

Harvard Correspondent

Researchers mimic early conditions on barren planet to test hypothesis of ancient electrochemistry

About four billion years ago, Earth resembled the set of a summer sci-fi blockbuster. The planet’s surface was a harsh and barren landscape, recovering from hellish asteroid strikes, teeming with volcanic eruptions, and lacking enough nutrients to sustain even the simplest forms of life.

The atmosphere was composed predominantly of inert gases like nitrogen and carbon dioxide, meaning they did not easily engage in chemical reactions necessary to form the complex organic molecules that are the building blocks of life. Scientists have long sought to discover the key factors that enabled the planet’s chemistry to change enough to form and sustain life.

Now, new research zeroes in on how lightning strikes may have served as a vital spark, transforming the atmosphere of early Earth into a hotbed of chemical activity. In the study, published in Proceedings of the National Academy of Sciences , a team of Harvard scientists identified lightning-induced plasma electrochemistry as a potential source of reactive carbon and nitrogen compounds necessary for the emergence and survival of early life.

“The origin of life is one of the great unanswered questions facing chemistry,” said George M. Whitesides, senior author and the Woodford L. and Ann A. Flowers University Research Professor in the Department of Chemistry and Chemical Biology. How the fundamental building blocks of “nucleic acids, proteins, and metabolites emerged spontaneously remains unanswered.”

One of the most popular answers to this question is summarized in the so-called RNA World hypothesis, Whitesides said. That is the idea that available forms of the elements, such as water, soluble electrolytes, and common gases, formed the first biomolecules. In their study, the researchers found that lightning could provide accessible forms of nitrogen and carbon that led to the emergence and survival of biomolecules.

A plasma vessel used to mimic cloud-to-ground lightning and its resulting electrochemical reactions. The setup uses two electrodes, with one in the gas phase and the other submerged in water enriched with inorganic salts.

Credit: Haihui Joy Jiang

Researchers designed a plasma electrochemical setup that allowed them to mimic conditions of the early Earth and study the role lightning strikes might have had on its chemistry. They were able to generate high-energy sparks between gas and liquid phases — akin to the cloud-to-ground lightning strikes that would have been common billions of years ago.

The scientists discovered that their simulated lightning strikes could transform stable gases like carbon dioxide and nitrogen into highly reactive compounds. They found that carbon dioxide could be reduced to carbon monoxide and formic acid, while nitrogen could be converted into nitrate, nitrite, and ammonium ions.

These reactions occurred most efficiently at the interfaces between gas, liquid, and solid phases — regions where lightning strikes would naturally concentrate these products. This suggests that lightning strikes could have locally generated high concentrations of these vital molecules, providing diverse raw materials for the earliest forms of life to develop and thrive.

“Given what we’ve shown about interfacial lightning strikes, we are introducing different subsets of molecules, different concentrations, and different plausible pathways to life in the origin of life community,” said Thomas C. Underwood, co-lead author and Whitesides Lab postdoctoral fellow. “As opposed to saying that there’s one mechanism to create chemically reactive molecules and one key intermediate, we suggest that there is likely more than one reactive molecule that might have contributed to the pathway to life.”

The findings align with previous research suggesting that other energy sources, such as ultraviolet radiation, deep-sea vents, volcanoes, and asteroid impacts, could have also contributed to the formation of biologically relevant molecules. However, the unique advantage of cloud-to-ground lightning is its ability to drive high-voltage electrochemistry across different interfaces, connecting the atmosphere, oceans, and land.

The research adds a significant piece to the puzzle of life’s origins. By demonstrating how lightning could have contributed to the availability of essential nutrients, the study opens new avenues for understanding the chemical pathways that led to the emergence of life on Earth. As the research team continues to explore these reactions, they hope to uncover more about the early conditions that made life possible and to improve modern applications.

“Building on our work, we are now experimentally looking at how plasma electrochemical reactions may influence nitrogen isotopes in products, which has a potential geological relevance,” said co-lead author Haihui Joy Jiang, a former Whitesides lab postdoctoral fellow. “We are also interested in this research from an energy-efficiency and environmentally friendly perspective on chemical production. We are studying plasma as a tool to develop new methods of making chemicals and to drive green chemical processes, such as producing fertilizer used today.”

Harvard co-authors included Professor Dimitar D. Sasselov in the Department of Astronomy and Professor James G. Anderson in the Department of Chemistry and Chemical Biology, Department of Earth and Planetary Sciences, and the Harvard John A. Paulson School of Engineering and Applied Sciences.

The study not only sheds light on the past but also has implications for the search for life on other planets. Processes the researchers described could potentially contribute to the emergence of life beyond Earth.

“Lightning has been observed on Jupiter and Saturn; plasmas and plasma-induced chemistry can exist beyond our solar system,” Jiang said. “Moving forward, our setup is useful for mimicking environmental conditions of different planets, as well as exploring reaction pathways triggered by lightning and its analogs.”

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A pilot study on proteomic predictors of mortality in stable copd.

1. Introduction

2. materials and methods, 2.1. study design and ethics, 2.2. study population, 2.3. biological sample obtention, 2.4. liquid chromatography–tandem mass spectrometry (lc–ms/ms), 2.5. immune-based multiplexing, 2.6. data analysis, 2.6.1. calculation of the sample size, 2.6.2. descriptive statistics and comparisons between groups, 2.7. functional classification of proteins and network analysis, 2.8. generation of predictive models, 3.1. general characteristics of the patients, 3.2. proteomic profile, 3.3. prediction of death and days of survival ( table 4 and table 5 ), 3.3.1. conventional approach.

3.3.2. AI Free Choice of Proteins

4. discussion, 4.1. previous studies, 4.2. interpretation of novel findings, 4.2.1. differentially abundant proteins, 4.2.2. prediction of death and days of survival, 4.3. strengths and potential limitations, 5. conclusions, supplementary materials, author contributions, institutional review board statement, informed consent statement, data availability statement, acknowledgments, conflicts of interest.

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Enríquez-Rodríguez, C.J.; Casadevall, C.; Faner, R.; Pascual-Guardia, S.; Castro-Acosta, A.; López-Campos, J.L.; Peces-Barba, G.; Seijo, L.; Caguana-Vélez, O.A.; Monsó, E.; et al. A Pilot Study on Proteomic Predictors of Mortality in Stable COPD. Cells 2024 , 13 , 1351. https://doi.org/10.3390/cells13161351

Enríquez-Rodríguez CJ, Casadevall C, Faner R, Pascual-Guardia S, Castro-Acosta A, López-Campos JL, Peces-Barba G, Seijo L, Caguana-Vélez OA, Monsó E, et al. A Pilot Study on Proteomic Predictors of Mortality in Stable COPD. Cells . 2024; 13(16):1351. https://doi.org/10.3390/cells13161351

Enríquez-Rodríguez, Cesar Jessé, Carme Casadevall, Rosa Faner, Sergi Pascual-Guardia, Ady Castro-Acosta, José Luis López-Campos, Germán Peces-Barba, Luis Seijo, Oswaldo Antonio Caguana-Vélez, Eduard Monsó, and et al. 2024. "A Pilot Study on Proteomic Predictors of Mortality in Stable COPD" Cells 13, no. 16: 1351. https://doi.org/10.3390/cells13161351

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