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Luca Incurvati
University of Amsterdam
  1. Metalogic and the Overgeneration Argument.Salvatore Florio & Luca Incurvati - 2019 - Mind:1-33.
    A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part of the article, we examine the argument and locate its main source, namely, the alleged entanglement of second-order logic and mathematics. We then identify various reasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective on the matter. (...)
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  2.  37
    Weak Assertion.Luca Incurvati & Julian J. Schlöder - forthcoming - Philosophical Quarterly.
    We present an inferentialist account of the epistemic modal operator 'might'. Our starting point is the bilateralist programme. A bilateralist explains the operator 'not' in terms of the speech act of rejection; we explain the operator 'might' in terms of weak assertion, a speech act whose existence we argue for on the basis of linguistic evidence. We show that our account of 'might' provides a solution to certain well-known puzzles about the semantics of modal vocabulary whilst retaining classical logic. This (...)
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  3.  22
    Overgeneration in the Higher Infinite.Salvatore Florio & Luca Incurvati - manuscript
    The Overgeneration Argument is a prominent objection against the model-theoretic account of logical consequence for second-order languages. In previous work we have offered a reconstruction of this argument which locates its source in the conflict between the neutrality of second-order logic and its alleged entanglement with mathematics. Some cases of this conflict concern small large cardinals. In this article, we show that in these cases the conflict can be resolved by moving from a set-theoretic implementation of the model-theoretic account to (...)
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  4.  39
    Weak Rejection.Luca Incurvati & Julian J. Schlöder - 2017 - Australasian Journal of Philosophy 95 (4):741-760.
    ABSTRACTLinguistic evidence supports the claim that certain, weak rejections are less specific than assertions. On the basis of this evidence, it has been argued that rejected sentences cannot be premisses and conclusions in inferences. We give examples of inferences with weakly rejected sentences as premisses and conclusions. We then propose a logic of weak rejection which accounts for the relevant phenomena and is motivated by principles of coherence in dialogue. We give a semantics for which this logic is sound and (...)
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  5. Maximally Consistent Sets of Instances of Naive Comprehension.Luca Incurvati & Julien Murzi - 2017 - Mind 126 (502).
    Paul Horwich (1990) once suggested restricting the T-Schema to the maximally consistent set of its instances. But Vann McGee (1992) proved that there are multiple incompatible such sets, none of which, given minimal assumptions, is recursively axiomatizable. The analogous view for set theory---that Naïve Comprehension should be restricted according to consistency maxims---has recently been defended by Laurence Goldstein (2006; 2013). It can be traced back to W.V.O. Quine(1951), who held that Naïve Comprehension embodies the only really intuitive conception of set (...)
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