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Göran Sundholm (2012). “Inference Versus Consequence” Revisited: Inference, Consequence, Conditional, Implication.

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  1.  21
    Mathematical Inference and Logical Inference.Yacin Hamami - forthcoming - Review of Symbolic Logic:1-40.
    The deviation of mathematical proof—proof in mathematical practice—from the ideal of formal proof—proof in formal logic—has led many philosophers of mathematics to reconsider the commonly accepted view according to which the notion of formal proof provides an accurate descriptive account of mathematical proof. This, in turn, has motivated a search for alternative accounts of mathematical proof purporting to be more faithful to the reality of mathematical practice. Yet, in order to develop and evaluate such alternative accounts, it appears as a (...)
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  2.  7
    Inference as Doxastic Agency. Part I: The Basics of Justification Stit Logic.Grigory K. Olkhovikov & Heinrich Wansing - forthcoming - Studia Logica:1-28.
    In this paper we consider logical inference as an activity that results in proofs and hence produces knowledge. We suggest to merge the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. The general idea is to understand proving that A as seeing to it that a proof of A is available. We introduce a semantics of various notions of proving as an activity and present a number of valid principles that (...)
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  3.  6
    The Neglect of Epistemic Considerations in Logic: The Case of Epistemic Assumptions.Göran Sundholm - forthcoming - Topoi:1-9.
    The two different layers of logical theory—epistemological and ontological—are considered and explained. Special attention is given to epistemic assumptions of the kind that a judgement is granted as known, and their role in validating rules of inference, namely to aid the inferential preservation of epistemic matters from premise judgements to conclusion judgement, while ordinary Natural Deduction assumptions serve to establish the holding of consequence from antecedent propositions to succedent proposition.
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    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.  2
    Unfolding Parallel Reasoning in Islamic Jurisprudence.Shahid Rahman & Muhammad Iqbal - 2018 - Arabic Sciences and Philosophy 28 (1):67-132.
  6.  26
    Frege on Judgement and the Judging Agent.Maria van der Schaar - 2018 - Mind 127 (505):225-250.
    How is Frege able to claim that the notion of judgement is essential to his logic without introducing a form of psychologism? I argue first that Frege’s logical notion of judgement is to be distinguished from an empirical notion of judgement, that it cannot be understood as an abstract, idealized notion, and that there are doubts concerning a transcendental reading of Frege’s writings. Then, I explain that the logical notion of judgement has to be understood from a first-person perspective, to (...)
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  7.  19
    Reprint Of: A More General General Proof Theory.Heinrich Wansing - 2017 - Journal of Applied Logic 25:23-46.
    In this paper it is suggested to generalize our understanding of general (structural) proof theory and to consider it as a general theory of two kinds of derivations, namely proofs and dual proofs. The proposal is substantiated by (i) considerations on assertion, denial, and bi-lateralism, (ii) remarks on compositionality in proof-theoretic semantics, and (iii) comments on falsification and co-implication. The main formal result of the paper is a normal form theorem for the natural deduction proof system N2Int of the bi-intuitionistic (...)
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  8.  16
    Nineteenth Century British Logic on Hypotheticals, Conditionals, and Implication.Francine F. Abeles - 2014 - History and Philosophy of Logic 35 (1):1-14.
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