Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality

Kürbis, Nils

doi:10.1007/s10992-013-9310-6

Cited by 14 publications

(10 citation statements)

References 40 publications

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“…1 The purpose of the present paper is not to contribute to their development or critique. In the light of its heritage and the vast literature ensuing its conception, an author is justified in taking for granted that inferentialist semantics for the logical constants 1 For a brief overview with a focus on Dummett and Prawitz, see Kürbis (2015a).…”

Section: Introductionmentioning

confidence: 99%

Normalisation and subformula property for a system of intuitionistic logic with general introduction and elimination rules

Kürbis

2021

Synthese

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This paper studies a formalisation of intuitionistic logic by Negri and von Plato which has general introduction and elimination rules. The philosophical importance of the system is expounded. Definitions of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system are formulated and corresponding reduction procedures for maximal formulas and permutative reduction procedures for maximal segments given. Alternatives to the main method used are also considered. It is shown that deductions in the system convert into normal form and that deductions in normal form have the subformula property.

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Section: Introductionmentioning

confidence: 99%

Normalisation and subformula property for a system of intuitionistic logic with general introduction and elimination rules

Kürbis

2021

Synthese

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“…I give formally precise definitions of harmony and stability in (Kürbis 2013), which work by specifying how to read off introduction from elimination rules and conversely.…”

Section: Negation According To Dummett and Prawitzmentioning

confidence: 99%

What is Wrong with Classical Negation?

Kürbis¹

2015

Grazer Philos Stud

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Penultimate draft, forthcoming in Grazer Philosophische Studien.Für die Negation liegen die Verhältnisse nicht so einfach. 1 Gentzen AbstractThe focus of this paper are Dummett's meaning-theoretical arguments against classical logic based on consideration about the meaning of negation. Using Dummettian principles, I shall outline three such arguments, of increasing strength, and show that they are unsuccessful by giving responses to each argument on behalf of the classical logician. What is crucial is that in responding to these arguments a classicist need not challenge any of the basic assumptions of Dummett's outlook on the theory of meaning. In particular, I shall grant Dummett his general bias towards verificationism, encapsulated in the slogan 'meaning is use'. The second general assumption I see no need to question is Dummett's particular breed of molecularism. Some of Dummett's assumptions will have to be given up, if classical logic is to be vindicated in his meaning-theoretical framework. A major result of this paper will be that the meaning of negation cannot be defined by rules of inference in the Dummettian framework. 2

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“…His ideas were subsequently developed by Prawitz [24] and Dummett [11] among others, with the latter coining the term harmony to denote the balance between the L/R rules for a logical constant that is indicative of its meaning-coherence. 4 However, the results of these procedures, including their many ulterior refinements, are highly sensitive to whether the underlying formal systems allow or not multiple conclusions [26,27,13,20,12,37]. 5 Classical 4 Dummett's preferred formalism is natural deduction, although he seems not to be having any qualms with sequent calculi beyond their (unspecific and potential) appeal to multiple conclusions.…”

Section: Introductionmentioning

confidence: 99%

Hopeful Monsters: A Note on Multiple Conclusions

Dicher

2018

Erkenn

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Arguments, the story goes, have one or more premises and only one conclusion. A contentious generalisation allows arguments with several disjunctively connected conclusions. Contentious as this generalisation may be, I will argue nevertheless that it is justified. My main claim is that multiple conclusions are epiphenomena of the logical connectives: some connectives determine, in a certain sense, multiple-conclusion derivations. Therefore, such derivations are completely natural and can safely be used in proof-theoretic semantics. Keywords multiple conclusions • defining rules • structure of derivations • logical inferentialism Delta: [.. . ] He seems engrossed in the production of monstrosities. But monstrosities never foster growth, either in world of nature or in the world of thought. Gamma: Geneticists can easily refute that. Have you not heard that mutations producing monstrosities play a considerable role in macro-evolution? They call such monstrous mutants 'hopeful monsters'. Lakatos, Proofs and refutations, pp. 21-22 1 Preamble An argument has one or more premises and one conclusion. Thus goes the orthodox stance. In this paper, I will defend the heretical claim that an argument may have

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Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality

Cited by 14 publications

References 40 publications

Normalisation and subformula property for a system of intuitionistic logic with general introduction and elimination rules

Normalisation and subformula property for a system of intuitionistic logic with general introduction and elimination rules

What is Wrong with Classical Negation?

Hopeful Monsters: A Note on Multiple Conclusions

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