The Justification of the Logical Laws Revisited

Contu, Patrizio

doi:10.1007/s11229-004-6270-y

Cited by 3 publications

(4 citation statements)

References 2 publications

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“…This embedding, however, is not faithful; obviously IEL ⊢ ¬¬(A → KA) but in none of the classical logics just mentioned is it the case that ⊢ A → KA. 18 This makes more precise the claim above that IEL offers a more general framework than the classical epistemic one; classical epistemic reasoning is sound in IEL, but the intuitionistic epistemic language is rather more expressive. 19…”

Section: Axiomsmentioning

confidence: 92%

“…Verifications, hence, are not necessarily generalizations of the notion of 'canonical proof' found in philosophical verificationism, see e.g [18,22,27,29,30,. 31,33,66,71,75,77,78,85,86,88,90].…”

mentioning

confidence: 99%

“…Verifications, hence, are not necessarily generalizations of the notion of 'canonical proof' found in philosophical verificationism, see e.g.,Contu (2006);Dummett (1973Dummett ( , 1963Dummett ( , 1977Dummett ( , 1991; Martin-Löf (1998);Prawitz (1980Prawitz ( , 1998dPrawitz ( , 2005Prawitz ( , 2006; Schroeder-Heister (2006);Sundholm (2002);Tennant (1997);Usberti (2006);van Dalen & Troelstra (1988b). A verification does not have to be canonical or even a means for acquiring a canonical verification, consider the examples in Section 2.3.2.…”

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confidence: 99%

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Intuitionistic Epistemic Logic

Artëmov

Protopopescu

2016

The Review of Symbolic Logic

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We outline an intuitionistic view of knowledge which maintains the original Brouwer-Heyting-Kolmogorov semantics for intuitionism and is consistent with the wellknown approach that intuitionistic knowledge be regarded as the result of verification. We argue that on this view co-reflection A → KA is valid and the factivity of knowledge holds in the form KA → ¬¬A 'known propositions cannot be false'.We show that the traditional form of factivity KA → A is a distinctly classical principle which, like tertium non datur A ∨ ¬A, does not hold intuitionistically, but, along with the whole of classical epistemic logic, is intuitionistically valid in its double negation form ¬¬(KA → A).Within the intuitionistic epistemic framework the knowability paradox is resolved in a constructive manner. We argue that this paradox is the result of an unwarranted classical reading of constructive principles and as such does not have the consequences for constructive foundations traditionally attributed it.

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Section: Axiomsmentioning

confidence: 92%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Intuitionistic Epistemic Logic

Artëmov

Protopopescu

2016

The Review of Symbolic Logic

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“…Leech (2015) argues that the laws of logic are laws of thought: they are constitutive norms of thoughts: ‘…there are norms for thought, evaluability in light of which is constitutive of a mental activity being thought or reasoning. These norms are the basic, most fundamental laws of logic’ (Ibid., 26) (also see Contu, 2006; Martin‐Löf, 1985).…”

Section: Predicaments Of Logical Exceptionalismmentioning

confidence: 99%

Logical exceptionalism: Development and predicaments

Chen

2024

Theoria

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This paper examines the conceptions of logic from Leibniz, Hume, Kant, Frege, Wittgenstein and Ayer, and regards the six philosophers as the representatives of logical exceptionalism. From their standpoints, this paper refines the tenets of logical exceptionalism as follows: logic is exceptional to all other sciences because of four reasons: (i) logic is formal, neutral to any domain and any entities, and general; (ii) logical truths are made true by the meanings of logical constants they contain or by logicians' rational insight to consequence relations; (iii) logical truths are analytical, a prior and necessary, so not‐revisable; and (iv) logical laws are normative for how to correctly think. However, logical exceptionalism has encountered difficult open problems: What are logical constants? How to justify basic laws of logic? How are logical laws accessible to us? How to explain the reasonability of rival logics and select from them? How to explain the universal applicability of logical laws? How to explain the normativity of logical laws for correct thinking? This paper concludes that logical anti‐exceptionalism is more hopeful to successfully answer these questions than logical exceptionalism.

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Steps Towards a Proof-Theoretical Semantics

Moriconi

2012

Topoi

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The aim of this paper is to reconsider several proposals that have been put forward in order to develop a Proof-Theoretical Semantics, from the by now classical neo-verificationist approach provided by D. Prawitz and M. Dummett in the Seventies, to an alternative, more recent approach mainly due to the work of P. Schroeder-Heister and L. Hallnäs, based on clausal definitions. Some other intermediate proposals are very briefly sketched. Particular attention will be given to the role played by the so-called Fundamental Assumption. We claim that whereas, in the neo-verificationist proposal, the condition expressed by that Assumption is necessary to ensure the completeness of the justification procedure (from the outside, so to speak), within the definitional framework it is a built-in feature of the proposal. The latter approach, therefore, appears as an alternative solution to the problem which prompted the neo-verificationists to introduce the Fundamental Assumption

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The Justification of the Logical Laws Revisited

Cited by 3 publications

References 2 publications

Intuitionistic Epistemic Logic

Intuitionistic Epistemic Logic

Logical exceptionalism: Development and predicaments

Steps Towards a Proof-Theoretical Semantics

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