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  1. Does Anti-Exceptionalism About Logic Entail That Logic is A Posteriori?Stephen Biggs & Jessica Wilson - 2022 - Synthese 1 (1):1--17.
    The debate between exceptionalists and anti-exceptionalists about logic is often framed as concerning whether the justification of logical theories is a priori or a posteriori (for short: whether logic is a priori or a posteriori). As we substantiate (S1), this framing more deeply encodes the usual anti-exceptionalist thesis that logical theories, like scientific theories, are abductively justified, coupled with the common supposition that abduction is an a posteriori mode of inference, in the sense that the epistemic value of abduction is (...)
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  2. Mathematicians Are Certain but Open to New Ideas: Mark Wilson: Innovation and Certainty. Cambridge Elements in the Philosophy of Mathematics. Cambridge: Cambridge University Press, 2020, 74 Pp, $20 PB. [REVIEW]Mark Zelcer - 2022 - Metascience 31 (1):45-48.
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  3. Wittgenstein, Peirce, and Paradoxes of Mathematical Proof.Sergiy Koshkin - 2021 - Analytic Philosophy 62 (3):252-274.
    Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on rule-following skepticism. We argue, with the help of C. S. Peirce's distinction between corollarial and theorematic proofs, that his intuitions are better explained by resistance to what we call conceptual omniscience, treating meaning as fixed content specified in advance. We interpret the distinction in the context of modern epistemic logic (...)
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  4. Why Did Weyl Think That Dedekind’s Norm of Belief in Mathematics is Perverse?Iulian D. Toader - 2016 - In Early Analytic Philosophy – New Perspectives on the Tradition. The Western Ontario Series in Philosophy of Science, vol. 80,. pp. 445-451.
    This paper argues that Weyl's criticism of Dedekind’s principle that "In science, what is provable ought not to be believed without proof." challenges not only a logicist norm of belief in mathematics, but also a realist view about whether there is a fact of the matter as to what norms of belief are correct.
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  5. Mathematics as a Quasi-Empirical Science.Gianluigi Oliveri - 2004 - Foundations of Science 11 (1-2):41-79.
    The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call ‘set theory’ is not one theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T1, ..., Tn in which Ti+1, for 1 ≤ i < n, supersedes Ti. This thesis has a great philosophical significance because it implies that there is a sense in which mathematical theories, (...)
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  6. Paradigm Transitions in Mathematics.Claire L. Parkinson - 1987 - Philosophia Mathematica (2):127-150.
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