Inferentialism, Structure, and Conservativeness

Hjortland, Ole Thomassen; Standefer, Shawn

doi:10.4324/9781315103587-6

Cited by 6 publications

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“…In a nutshell, his argument is the following: since asserting, denying, and making an assumption are all speech acts, and speech acts cannot be iterated (as an example, in Rumfitt's vocabulary the expression + + p is forbidden), then Rumfitt cannot adopt assumptions in his system. 14 While I find his objection well-defended and convincing, in this paper I will focus on what seems to me an orthogonal issue. I will just treat + and − as two modalities, without discussing their nature, and try to address some well-known problems of this system.…”

Section: Introductionmentioning

confidence: 94%

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Bilateral Rules as Complex Rules

Ceragioli

2023

B Sect Log

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Proof-theoretic semantics is an inferentialist theory of meaning originally developed in a unilateral framework. Its extension to bilateral systems opens both opportunities and problems. The problems are caused especially by Coordination Principles (a kind of rule that is not present in unilateral systems) and mismatches between rules for assertion and rules for rejection. In this paper, a solution is proposed for two major issues: the availability of a reduction procedure for tonk and the existence of harmonious rules for the paradoxical zero-ary connective \(\bullet\). The solution is based on a reinterpretation of bilateral rules as complex rules, that is, rules that introduce or eliminate connectives in a subordinate position. Looking at bilateral rules from this perspective, the problems faced by bilateralism can be seen as special cases of general problems of complex systems, which have been already analyzed in the literature. In the end, a comparison with other proposed solutions underlines the need for further investigation in order to complete the picture of bilateral proof-theoretic semantics.

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Section: Introductionmentioning

confidence: 94%

“…For a recent analysis of the precise relation between normalization and validity in proof-theoretic semantics, see [38]. 7 Inter alia, see [14] for inferentialism and proof-theoretic semantics, and [34] for a bilateralist analysis of these calculi.…”

Section: Introductionmentioning

confidence: 99%

Bilateral Rules as Complex Rules

Ceragioli

2023

B Sect Log

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“…In recent years,these rules, and others, have been put into question and, therefore, their justification is now relevant and not so obvious anymore. However, Priest argues that this justification is not possible in purely proof-theoretic terms (although see [Hjortland and Standefer, 2018] for a possible response). While Priest does not further develop the objection, I deduce that the reason for the proof-theoretic characterization to be impossible is that structural rules do not depend on connectives nor, a fortiori, on the connectives' meaning.…”

Section: Proof-theoretic Vs Model-theoreticmentioning

confidence: 99%

Local Applications of Logics via Model-Theoretic Interpretations

Benito-Monsalvo

2022

LLP

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This paper analyses the notion of ‘interpretation’, which is often tied to the semantic approach to logic, where it is used when referring to truth-value assignments, for instance. There are, however, other uses of the notion that raise interesting problems. These are the cases in which interpreting a logic is closely related to its justification for a given application. The paper aims to present an understanding of interpretations that supports the model-theoretic characterization of validity to the detriment of the proof-theoretic one. This is done by making use of the hierarchy of ST-related logics. Finally, a localist conception of logic is defended as the natural view stemming from the model-theoretic approach.

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“…The notions of harmony and stability are notoriously difficult to pin down across different logics. See [52] for a recent discussion of the literature. What follows is not the account of harmony and stability, but rather one which fits naturally with the form of bilateralism adopted.…”

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confidence: 99%

Subatomic Inferences: An Inferentialist Semantics for Atomics, Predicates, and Names

Tanter¹

2021

The Review of Symbolic Logic

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Inferentialism is a theory in the philosophy of language which claims that the meanings of expressions are constituted by inferential roles or relations. Instead of a traditional model-theoretic semantics, it naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules with a proof system. Most work in proof-theoretic semantics has focused on logical constants, with comparatively little work on the semantics of non-logical vocabulary. Drawing on Robert Brandom’s notion of material inference and Greg Restall’s bilateralist interpretation of the multiple conclusion sequent calculus, I present a proof-theoretic semantics for atomic sentences and their constituent names and predicates. The resulting system has several interesting features: (1) the rules are harmonious and stable; (2) the rules create a structure analogous to familiar model-theoretic semantics; and (3) the semantics is compositional, in that the rules for atomic sentences are determined by those for their constituent names and predicates.

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Inferentialism, Structure, and Conservativeness

Cited by 6 publications

References 0 publications

Bilateral Rules as Complex Rules

Bilateral Rules as Complex Rules

Local Applications of Logics via Model-Theoretic Interpretations

Subatomic Inferences: An Inferentialist Semantics for Atomics, Predicates, and Names

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