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Peter Schroeder-Heister (2006). Validity Concepts in Proof-Theoretic Semantics.

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  1.  8
    The Harmony of Identity.Ansten Klev - forthcoming - Journal of Philosophical Logic:1-18.
    The standard natural deduction rules for the identity predicate have seemed to some not to be harmonious. Stephen Read has suggested an alternative introduction rule that restores harmony but presupposes second-order logic. Here it will be shown that the standard rules are in fact harmonious. To this end, natural deduction will be enriched with a theory of definitional identity. This leads to a novel conception of canonical derivation, on the basis of which the identity elimination rule can be justified in (...)
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  2.  14
    On Paradoxes in Normal Form.Mattia Petrolo & Paolo Pistone - forthcoming - Topoi:1-13.
    A proof-theoretic test for paradoxicality was famously proposed by Tennant: a paradox must yield a closed derivation of absurdity with no normal form. Drawing on the remark that all derivations of a given proposition can be transformed into derivations in normal form of a logically equivalent proposition, we investigate the possibility of paradoxes in normal form. We compare paradoxes à la Tennant and paradoxes in normal form from the viewpoint of the computational interpretation of proofs and from the viewpoint of (...)
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  3.  8
    The Seeming Interdependence Between the Concepts of Valid Inference and Proof.Dag Prawitz - forthcoming - Topoi:1-11.
    We may try to explain proofs as chains of valid inference, but the concept of validity needed in such an explanation cannot be the traditional one. For an inference to be legitimate in a proof it must have sufficient epistemic power, so that the proof really justifies its final conclusion. However, the epistemic concepts used to account for this power are in their turn usually explained in terms of the concept of proof. To get out of this circle we may (...)
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  4.  12
    Proof, Meaning and Paradox: Some Remarks.Luca Tranchini - forthcoming - Topoi:1-13.
    In the present paper, the Fregean conception of proof-theoretic semantics that I developed elsewhere will be revised so as to better reflect the different roles played by open and closed derivations. I will argue that such a conception can deliver a semantic analysis of languages containing paradoxical expressions provided some of its basic tenets are liberalized. In particular, the notion of function underlying the Brouwer–Heyting–Kolmogorov explanation of implication should be understood as admitting functions to be partial. As argued in previous (...)
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  5.  24
    The Fundamental Problem of General Proof Theory.Dag Prawitz - 2019 - Studia Logica 107 (1):11-29.
    I see the question what it is that makes an inference valid and thereby gives a proof its epistemic power as the most fundamental problem of general proof theory. It has been surprisingly neglected in logic and philosophy of mathematics with two exceptions: Gentzen’s remarks about what justifies the rules of his system of natural deduction and proposals in the intuitionistic tradition about what a proof is. They are reviewed in the paper and I discuss to what extent they succeed (...)
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  6.  21
    Boolos and the Metamathematics of Quine's Definitions of Logical Truth and Consequence.Günther Eder - 2016 - History and Philosophy of Logic 37 (2):170-193.
    The paper is concerned with Quine's substitutional account of logical truth. The critique of Quine's definition tends to focus on miscellaneous odds and ends, such as problems with identity. However, in an appendix to his influential article On Second Order Logic, George Boolos offered an ingenious argument that seems to diminish Quine's account of logical truth on a deeper level. In the article he shows that Quine's substitutional account of logical truth cannot be generalized properly to the general concept of (...)
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  7. Anything Goes.David Ripley - 2015 - Topoi 34 (1):25-36.
    This paper consider Prior's connective Tonk from a particular bilateralist perspective. I show that there is a natural perspective from which we can see Tonk and its ilk as perfectly well-defined pieces of vocabulary; there is no need for restrictions to bar things like Tonk.
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  8.  40
    Bolzano's Concept of Grounding (Abfolge) Against the Background of Normal Proofs.Antje Rumberg - 2013 - Review of Symbolic Logic 6 (3):424-459.
    In this paper, I provide a thorough discussion and reconstruction of Bernard Bolzano’s theory of grounding and a detailed investigation into the parallels between his concept of grounding and current notions of normal proofs. Grounding (Abfolge) is an objective ground-consequence relation among true propositions that is explanatory in nature. The grounding relation plays a crucial role in Bolzano’s proof-theory, and it is essential for his views on the ideal buildup of scientific theories. Occasionally, similarities have been pointed out between Bolzano’s (...)
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  9.  53
    Proof-Theoretic Semantics, Self-Contradiction, and the Format of Deductive Reasoning.Peter Schroeder-Heister - 2012 - Topoi 31 (1):77-85.
    From the point of view of proof-theoretic semantics, it is argued that the sequent calculus with introduction rules on the assertion and on the assumption side represents deductive reasoning more appropriately than natural deduction. In taking consequence to be conceptually prior to truth, it can cope with non-well-founded phenomena such as contradictory reasoning. The fact that, in its typed variant, the sequent calculus has an explicit and separable substitution schema in form of the cut rule, is seen as a crucial (...)
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  10.  53
    Truth From a Proof-Theoretic Perspective.Luca Tranchini - 2012 - Topoi 31 (1):47-57.
    Validity, the central concept of the so-called ‘proof-theoretic semantics’ is described as correctly applying to the arguments that denote proofs. In terms of validity, I propose an anti-realist characterization of the notions of truth and correct assertion, at the core of which is the idea that valid arguments may fail to be recognized as such. The proposed account is compared with Dummett’s and Prawitz’s views on the matter.
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  11.  23
    Rules for Subatomic Derivation.Bartosz Więckowski - 2011 - Review of Symbolic Logic 4 (2):219-236.
    In proof-theoretic semantics the meaning of an atomic sentence is usually determined by a set of derivations in an atomic system which contain that sentence as a conclusion (see, in particular, Prawitz, 1971, 1973). The paper critically discusses this standard approach and suggests an alternative account which proceeds in terms of subatomic introduction and elimination rules for atomic sentences. A simple subatomic normal form theorem by which this account of the semantics of atomic sentences and the terms from which they (...)
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  12.  40
    Free Semantics.Ross Thomas Brady - 2010 - Journal of Philosophical Logic 39 (5):511 - 529.
    Free Semantics is based on normalized natural deduction for the weak relevant logic DW and its near neighbours. This is motivated by the fact that in the determination of validity in truth-functional semantics, natural deduction is normally used. Due to normalization, the logic is decidable and hence the semantics can also be used to construct counter-models for invalid formulae. The logic DW is motivated as an entailment logic just weaker than the logic MC of meaning containment. DW is the logic (...)
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  13. Proof-Theoretic Semantics for a Natural Language Fragment.Nissim Francez & Roy Dyckhoff - 2010 - Linguistics and Philosophy 33 (6):447-477.
    The paper presents a proof-theoretic semantics (PTS) for a fragment of natural language, providing an alternative to the traditional model-theoretic (Montagovian) semantics (MTS), whereby meanings are truth-condition (in arbitrary models). Instead, meanings are taken as derivability-conditions in a dedicated natural-deduction (ND) proof-system. This semantics is effective (algorithmically decidable), adhering to the meaning as use paradigm, not suffering from several of the criticisms formulated by philosophers of language against MTS as a theory of meaning. In particular, Dummett’s manifestation argument does not (...)
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  14.  90
    Radical Anti-Realism, Wittgenstein and the Length of Proofs.Mathieu Marion - 2009 - Synthese 171 (3):419 - 432.
    After sketching an argument for radical anti-realism that does not appeal to human limitations but polynomial-time computability in its definition of feasibility, I revisit an argument by Wittgenstein on the surveyability of proofs, and then examine the consequences of its application to the notion of canonical proof in contemporary proof-theoretical-semantics.
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  15.  56
    On Reduction Rules, Meaning-as-Use, and Proof-Theoretic Semantics.Ruy J. G. B. de Queiroz - 2008 - Studia Logica 90 (2):211-247.
    The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that we suggest an extension (...)
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  16.  62
    Some Problems for Proof-Theoretic Semantics.William R. Stirton - 2008 - Philosophical Quarterly 58 (231):278–298.
    Proof-theoretic semantics is an approach to logical semantics based on two ideas, of which the first is that the meaning of a logical connective can be explained by stipulating that some mode of inference, e.g., a natural deduction introduction or elimination rule, is permissible. The second idea is that the soundness of rules which are not stipulated outright may be deduced by some proof-theoretic argument from properties of the rules which are stipulated outright. I examine the first idea. My main (...)
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  17.  82
    Meaning and Dialogue Coherence: A Proof-Theoretic Investigation.Paul Piwek - 2007 - Journal of Logic, Language and Information 16 (4):403-421.
    This paper presents a novel proof-theoretic account of dialogue coherence. It focuses on an abstract class of cooperative information-oriented dialogues and describes how their structure can be accounted for in terms of a multi-agent hybrid inference system that combines natural deduction with information transfer and observation. We show how certain dialogue structures arise out of the interplay between the inferential roles of logical connectives (i.e., sentence semantics), a rule for transferring information between agents, and a rule for information flow between (...)
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