Fitch and intuitionistic knowability

Percival, Philip

doi:10.1093/analys/50.3.182

Cited by 19 publications

(11 citation statements)

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“…Besides (2), Philip Percival points out two more untoward intuitionistic consequences of weak verificationism: 8uð:Ku $ :uÞ and 8u:ð:Ku^:K:uÞ: SeePercival (1990).…”

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confidence: 99%

Knowability and bivalence: intuitionistic solutions to the Paradox of Knowability

Murzi

2009

Philos Stud

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In this paper, I focus on some intuitionistic solutions to the Paradox of Knowability. I first consider the relatively little discussed idea that, on an intuitionistic interpretation of the conditional, there is no paradox to start with. I show that this proposal only works if proofs are thought of as tokens, and suggest that anti-realists themselves have good reasons for thinking of proofs as types. In then turn to more standard intuitionistic treatments, as proposed by Timothy Williamson and, most recently, Michael Dummett. Intuitionists can either point out the intuitionistc invalidity of the inference from the claim that all truths are knowable to the insane conclusion that all truths are known, or they can outright demur from asserting the existence of forever-unknown truths, perhaps questioning-as Dummett now suggests-the applicability of the Principle of Bivalence to a certain class of empirical statements. I argue that if intuitionists reject strict finitism-the view that all truths are knowable by beings just like us-the prospects for either proposal look bleak.

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“…Besides (2), Philip Percival points out two more untoward intuitionistic consequences of weak verificationism: 8uð:Ku $ :uÞ and 8u:ð:Ku^:K:uÞ: SeePercival (1990).…”

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confidence: 99%

Knowability and bivalence: intuitionistic solutions to the Paradox of Knowability

Murzi

2009

Philos Stud

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“…In this kind of logic, those operators are interpreted usually as "metaphysical" (see e.g. [18], p. 182, [34], p. 273) or "ontic" (see [35], p. 100) possibility and necessity. As a result of combinations possibility operator with epistemic ones: S, D, E and C, we obtain suitable kinds of group knowability.…”

Section: On the Various Kinds Of Group Knowabilitymentioning

confidence: 99%

“…14 We leave open many questions concerning strategies of syntactic restrictions, and now we discuss another strategy. One of the first reactions to Fitch's paradox was change a propositional basis for modal epistemic logic from classical to intuitionistic (see [29], [18] and papers from Topoi no. 13,1994).…”

Section: Towards Combined Strategiesmentioning

confidence: 99%

“…It seems that anti-realists are especially interested just in feasible knowability and distributed one which gives them some additional advantages. 18 As a result of Def D , in modal epistemic logic without PK D , we obtain relations between notions of distributed knowledge, feasible distributed knowability, "ontic" possibility and truth, which are accepted by anti-realists as well as by realists (if both positions accept a modal and epistemic axiom T):…”

Section: Is Distributed Knowability Factive?mentioning

confidence: 99%

“…This definition, or rather a general schemata of definition for all kinds of knowability, was proposed by Andrzej Pietruszczak in a private communication 18. Note that recently R. T. Cook points out some problems connected with factivity of knowability (see[3]).…”

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confidence: 99%

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Distributed Knowability and Fitch’s Paradox

Palczewski

2007

Stud Logica

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Recently predominant forms of anti-realism claim that all truths are knowable. We argue that in a logical explanation of the notion of knowability more attention should be paid to its epistemic part. Especially very useful in such explanation are notions of group knowledge. In this paper we examine mainly the notion of distributed knowability and show its effectiveness in the case of Fitch's paradox. Proposed approach raised some philosophical questions to which we try to find responses. We also show how we can combine our point of view on Fitch's paradox with the others. Next we give an answer to the question: is distributed knowability factive? At the end, we present some details concerning a construction of anti-realist modal epistemic logic.

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The Knowability Paradox in the Light of a Logic for Pragmatics

Carrara¹,

Chiffi

2014

Recent Trends in Philosophical Logic

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The Knowability Paradox is a logical argument showing that if all truths are knowable in principle, then all truths are, in fact, known. Many strategies have been suggested in order to avoid the paradoxical conclusion. A family of solutionscalled logical revision -has been proposed to solve the paradox, revising the logic underneath, with an intuitionistic revision included. In this paper, we focus on socalled revisionary solutions to the paradox -solutions that put the blame on the underlying logic. Specifically, we analyse a possibile translation of the paradox into a modified intuitionistic fragment of a logic for pragmatics (KILP) inspired by Dalla Pozza and Garola in 1995. Our aim is to understand if KILP is a candidate for the logical revision of the paradox and to compare it with the standard intuitionistic solution to the paradox.

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Fitch and intuitionistic knowability

Cited by 19 publications

References 1 publication

Knowability and bivalence: intuitionistic solutions to the Paradox of Knowability

Knowability and bivalence: intuitionistic solutions to the Paradox of Knowability

Distributed Knowability and Fitch’s Paradox

The Knowability Paradox in the Light of a Logic for Pragmatics

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