Conceptions of truth in intuitionism

Raatikainen, Panu

doi:10.1080/014453401625669

Cited by 53 publications

(7 citation statements)

References 29 publications

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“…It is worth noting that Brouwer's and Heyting's attempts to identify truth with a notion of proof have failed, as [32] shows, because the result is a concept of truth that goes against some basic intuitions about truth. The notion of constructive provability is stronger than truth in the sense that if we have a constructive proof of α, we know that α is true, but the converse may not hold.…”

Section: Paraconsistency and The Nature Of Logicmentioning

confidence: 96%

Contradiction and (in)Consistency

Carnielli

Coniglio

2016

Paraconsistent Logic: Consistency, Contradiction and Negation

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Section: Paraconsistency and The Nature Of Logicmentioning

confidence: 96%

Contradiction and (in)Consistency

Carnielli

Coniglio

2016

Paraconsistent Logic: Consistency, Contradiction and Negation

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“…We will now discuss both of these matters before turning to an in-depth analysis of the views of the verificationists and the technical exposition of the system we will use to represent them. 3 Cf., e.g., Raatikainen (2004) for discussion of this point. 4 Our closest anticipators in proposing such a resolution to the Paradox are Cozzo (1994) and Hand (2003Hand ( , 2008.…”

Section: An Approach To the Paradoxmentioning

confidence: 99%

From the Knowability Paradox to the existence of proofs

Dean

Kurokawa

2009

Synthese

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The Knowability Paradox purports to show that the controversial but not patently absurd hypothesis that all truths are knowable entails the implausible conclusion that all truths are known. The notoriety of this argument owes to the negative light it appears to cast on the view that there can be no verification-transcendent truths. We argue that it is overly simplistic to formalize the views of contemporary verificationists like Dummett, Prawitz or Martin-Löf using the sort of propositional modal operators which are employed in the original derivation of the Paradox. Instead we propose that the central tenet of verificationism is most accurately formulated as follows: if ϕ is true, then there exists a proof of ϕ. Building on the work of Artemov (Bull Symb Log 7(1): 1-36, 2001), a system of explicit modal logic with proof quantifiers is introduced to reason about such statements. When the original reasoning of the Paradox is developed in this setting, we reach not a contradiction, but rather the conclusion that there must exist non-constructed proofs. This outcome is evaluated relative to the controversy between Dummett and Prawitz about proof existence and bivalence.

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“…The identification of an intuitionistic notion of provability with truth was not successful. As is shown by Raatikainen (2004), in the works of Brouwer and Heyting we find some attempts to formulate an explanation of the notion of truth in terms of provability, but all of them produce counterintuitive results.…”

Section: Epistemological Contradiction and The Nature Of Logicmentioning

confidence: 99%

Towards a Philosophical Understanding of the Logics of Formal Inconsistency

Carnielli

Rodrigues

2015

Manuscrito

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In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we show that mbC, a logic of formal inconsistency based on classical logic, may be enhanced in order to express the basic ideas of an intuitive interpretation of contradictions as conflicting evidence.

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Conceptions of truth in intuitionism

Cited by 53 publications

References 29 publications

Contradiction and (in)Consistency

Contradiction and (in)Consistency

From the Knowability Paradox to the existence of proofs

Towards a Philosophical Understanding of the Logics of Formal Inconsistency

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