Abstract
This paper aims at elucidating the connection between explanatory considerations and epistemic justification stipulated by explanationism which take epistemic justification to be definable in terms of best explanations. By relying on the notion of truthlikeness, this paper argues that it is rational for a subject to expect the best explanation she has for her evidence to be more truthlike than any of the other potential explanations available to her by virtue of containing a class of propositions that, given her evidence, she is justified in believing. Based on this elucidation of the connection between explanatory considerations and epistemic justification, an explanationist account of the evidential support relation is then offered.
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Notes
It is common to distinguish propositional justification from doxastic justification. Propositional justification requires only that the content of a subject’s beliefs be supported by the evidence she has at a certain time. Doxastic justification, in contrast, requires that, in addition to that support, her beliefs be properly based on the evidence she has. This paper’s primary focus is propositional justification.
A first version of McCain’s (2013, 2014) account of the evidential support relation was challenged by two varieties of cases due to Byerly (2013) and Byerly and Martin (2014). To accommodate these cases, McCain (2015) offered an amended version of his account. Byerly and Martin (2016) then raised further objections against McCain’s second account to which he (2017) recently reacted.
e represents S’s overall evidence at t.
Note that, irrespective of cases such as the Animal Case, conceiving explanations as theories is also a quite natural way to delimitate their semantical content. If an explanation states that \( p_{i} \) is true and states that This case represents a problem for Explanationism\( p_{j} \) is true, then it is quite natural to consider that it also states that \( p_{i} \wedge p_{j} \) is true.
According to Hempel (1965), explanations consist of deductive (or inductive) arguments in which the explained event is derived from certain laws and initial conditions. Kitcher (1989) and Friedman (1974) before him, while preserving Hempel’s initial idea, conceive explanations as patterns of derivations of different events which provide a unifying systemization of initially dissimilar phenomena. Salmon (1984), on the other hand, abandons the Hempelian conception of explanations as arguments and takes explaining to be fundamentally a matter of showing how the explained event fits into the causal patterns found in the world. Alternative causal models of explanations have been proposed by Woodward (2003) and Strevens (2008).
Kuipers (2004) and Niiniluoto (2004, 2005) both worked on the relation between theories’ expected degree of truthlikeness and abductive inferences in order to formulate rules of abductive inference that conform to our intuitions regarding the ways subjects should revise their beliefs. The rule formulated by Kuipers prescribes one to infer that the best explanation available to a subject is more truthlike than any other potential explanation available to this subject and relies, therefore, on the same plausible connection that I just stressed between explanatory considerations and the relative truthlikeness of potential explanations.
The present paper focuses exclusively on definitions of comparative truthlikeness and not on definitions of quantitative truthlikeness and measures of expected quantitative truthlikeness that have been offered, inter alia, by Niiniluoto (2011) and Cevolani and Schurz (2017). The reason for this focus is that the truthlikeness hypothesis relies on a comparative notion of truthlikeness and, therefore, to see how this hypothesis can help to answer the main question that this paper aims at addressing, a definition of comparative truthlikeness is required.
This result is due to the fact that if the falsity-content of a theory \( {\text{H}} \) is not empty, \( {\text{H}} \)’s truth-content cannot be increased without thereby increasing its falsity-content. By adding a true proposition \( p_{i} \) to \( {\text{C}}\left( {\text{H}} \right) \) one, thereby, adds a false proposition \( p_{i} \wedge p_{j} \) to \( {\text{C}}\left( {\text{H}} \right) \) where \( p_{j} \) is a false consequence of \( {\text{H}} \) already contained in \( {\text{C}}\left( {\text{H}} \right) \).
Schurz and Weingartner (2010, pp. 425–426) propose as conventions to write all members \( {\text{E}}\left( {\text{H}} \right) \) in their negation normal form—namely by writing them only with the logical operators “\( \wedge , \vee , \neg \)”, by putting all negations in front of propositional variables and by eliminating all double negations and associative brackets—and that all disjunctions of literals (propositional variables or their negation) in \( {\text{E}}\left( {\text{H}} \right) \) be written as clauses—that is, as disjunctions of literals in distinct and alphabetically ordered propositional variables.
Note that, according to this definition, a proposition \( p \) such that \( p \) \( \in {\text{C}}\left( {\text{H}} \right) \) can be an elementary consequence of \( {\text{H}} \) without being a relevant consequence of \( {\text{H}} \). Likewise, \( p \) can be a relevant consequence of \( {\text{H}} \) without being an elementary consequence of \( {\text{H}} \).
SW-Truthlikeness is formulated in terms of entailments of classes of relevant elements instead of inclusions because classes of relevant elements are not themselves closed under logical consequence.
To say that \( {\text{E}}\left( {{\text{H}}_{i} } \right)_{T} \) exceeds \( {\text{E}}\left( {{\text{H}}_{j} } \right)_{T} \) means that some members of \( {\text{E}}\left( {{\text{H}}_{i} } \right)_{T} \) are not deducible from \( {\text{E}}\left( {{\text{H}}_{j} } \right)_{T} \) but that all members of \( {\text{E}}\left( {{\text{H}}_{j} } \right)_{T} \) are deducible from \( {\text{E}}\left( {{\text{H}}_{i} } \right)_{T} \). Thus, \( {\text{E}}\left( {{\text{H}}_{i} } \right)_{T} \) exceeds \( {\text{E}}\left( {{\text{H}}_{j} } \right)_{T} \) just in case all true relevant elements of \( {\text{H}}_{j} \) are part of \( {\text{H}}_{i} \)’s semantic content but some of \( {\text{H}}_{i} \)’s true relevant elements are not part of \( {\text{H}}_{j} \)’s semantic content. The same holds for \( {\text{E}}\left( {{\text{H}}_{i} } \right)_{F} \) and \( {\text{E}}\left( {{\text{H}}_{j} } \right)_{F} \).
As a theory’s class of relevant elements represents its entire semantic content, condition (ii) guarantees that \( p \) is part of \( {\text{H}}_{i} \)’s semantic content but is not part of the semantic content of at least one other potential explanation of e available to S at t.
Byerly and Martin (2014, p. 783) offer a case in which, according to McCain’s account of the evidential support relation which is equivalent to the version of Explanationism considered in Sect. 2, a subject is justified in believing that \( p \) while \( p \) is not probable conditional on her overall evidence. Based on this case, they argue that McCain’s account is too permissive as, intuitively, the subject involved in that case is not justified in believing that \( p \). See Belkoniene (2017) for a more detailed discussion of that case.
The first case offered by Gettier involves the formation of a lucky true belief concerning an existential proposition that is inferred from a non-quantified proposition. While Schurz and Weingartner’s definition of a theory’s relevant consequences’ class does not deal with quantified propositions, Gemes’s definition, for instance, which is developed for higher-order logics, typically excludes such consequences from the class of \( {\text{H}} \)’s relevant consequences.
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Acknowledgements
Thanks are due to Professors Gianfranco Soldati, Fabian Dorsch (1974–2017), Lara Buchak and two anonymous referees from this journal for their insightful comments on earlier drafts of this paper. This publication was made possible through the support of a grant from the Swiss National Science Foundation.
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Belkoniene, M. Why Explanatory Considerations Matter. Erkenn 86, 473–491 (2021). https://doi.org/10.1007/s10670-019-00114-5
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DOI: https://doi.org/10.1007/s10670-019-00114-5