Fitch's Paradox and Level-Bridging Principles

San, Weng Kin

doi:10.5840/jphil202011711

Cited by 5 publications

(3 citation statements)

References 20 publications

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“…47 It is also worth mentioning that even if A→OA is not immediately implausible for some operator O (e.g., "is in principle justifiable"), a version of Fitch's (1963) paradox may arise that leads to a much more implausible conclusion ("is in fact justified"). See San (2020) for discussion of how versions of Fitch's paradox can arise very generally, without the need for a factive operator. the level-bridging principle is factivity itself.)…”

Section: Level-bridging Principlesmentioning

confidence: 99%

Epistemic characterizations of validity and level-bridging principles

Schechter

2023

Philos Stud

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How should we understand validity? A standard way to characterize validity is in terms of the preservation of truth (or truth in a model). But there are several problems facing such characterizations. An alternative approach is to characterize validity epistemically, for instance in terms of the preservation of an epistemic status. In this paper, I raise a problem for such views. First, I argue that if the relevant epistemic status is factive, such as being in a position to know or having conclusive evidence for, then the account runs into trouble if we endorse certain familiar logical principles. Second, I argue that if the relevant epistemic status is non-factive, such as is rationally committed to or has justification for believing, then a similar problem arises if we endorse the logical principles as well as a sufficiently strong epistemic "level-bridging" principle. Finally, I argue that an analogous problem arises for the most natural characterization of validity in terms of rational credence.* Forthcoming in Philosophical Studies. 1 On some views, including those inspired by Harman's (1986) emphasis on the distinction between inference and implication, validity concerns an abstract relation among propositions, not any kind of reasoning. So it is a mistake to think of inferences as valid or invalid. If that is right, then the issues raised here should be put in terms of whether a purported entailment is valid or invalid. This would only require minor changes in the discussion to follow.

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Section: Level-bridging Principlesmentioning

confidence: 99%

Epistemic characterizations of validity and level-bridging principles

Schechter

2023

Philos Stud

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“…This result is often attributed toFitch (1963) but was first noted byChurch (2009) in an anonymous referee report.22 In fact, the assumptions required for the collapse is much weaker than the ones assumed here. In particular, while the standard derivation of the Church-Fitch Theorem appeals to the factivity of K, this assumption can be weakened significantly (seeSan (2020)). 23 A popular variant of KK states that if one knows that ϕ, then one is in a position to know that one knows that ϕ.…”

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confidence: 99%

KK, Knowledge, Knowability

San

2023

Mind

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kk states that knowing entails knowing that one knows, and K¬K states that not knowing entails knowing that one does not know. In light of the arguments against kk and K¬K, one might consider modally qualified variants of those principles. According to weak kk, knowing entails the possibility of knowing that one knows. And according to weak K¬K, not knowing entails the possibility of knowing that one does not know. This paper shows that weak kk and weak K¬K are much stronger than they initially appear. Jointly, they entail kk and K¬K. And they are susceptible to variants of the standard arguments against kk and K¬K. This has interesting implications for the debate on positive introspection and for deeper issues concerning the structure and limits of knowability.

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“…San (2020) has proved a 'general collapse' theorem: a logic with (A-R), D K and some 'n-level bridging principle' (e.g., T K is a one-level bridging principle) with RN and RM K as rules entails a 'nth degree modal collapse'.5 If the K-operator means that some human at some time knows, then Marton has to cite scenarios in which no individual human being at some point in time is able to foresee that in the future no human beings are alive anymore.…”

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Anti-Realism and Modal-Epistemic Collapse: Reply to Marton

Heylen

2021

Erkenn

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Marton (2019) argues that that it follows from the standard antirealist theory of truth, which states that truth and possible knowledge are equivalent, that knowing possibilities is equivalent to the possibility of knowing, whereas these notions should be distinct. Moreover, he argues that the usual strategies of dealing with the Church-Fitch paradox of knowability are either not able to deal with his modal-epistemic collapse result or they only do so at a high price. Against this, I argue that Marton's paper does not present any seriously novel challenge to anti-realism not already found in the Church-Fitch result. Furthermore, Edgington (1985)'s reformulated antirealist theory of truth can deal with his modal-epistemic collapse argument at no cost.

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Fitch's Paradox and Level-Bridging Principles

Cited by 5 publications

References 20 publications

Epistemic characterizations of validity and level-bridging principles

Epistemic characterizations of validity and level-bridging principles

KK, Knowledge, Knowability

Anti-Realism and Modal-Epistemic Collapse: Reply to Marton

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