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Profile: Luca Incurvati (University of Amsterdam)
  1. Luca Incurvati (forthcoming). On the Concept of Finitism. Synthese.
    At the most general level, the concept of finitism is typically characterized by saying that finitistic mathematics is that part of mathematics which does not appeal to completed infinite totalities and is endowed with some epistemological property that makes it secure or privileged. This paper argues that this characterization can in fact be sharpened in various ways, giving rise to different conceptions of finitism. The paper investigates these conceptions and shows that they sanction different portions of mathematics as finitistic.
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  2. Luca Incurvati & Julien Murzi (forthcoming). Maximally Consistent Sets of Instances of Naive Comprehension. Mind.
    Paul Horwich (1990) once suggested restricting the T-Schema to the maximal 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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  3. Luca Incurvati (2014). The Graph Conception of Set. Journal of Philosophical Logic 43 (1):181-208.
    The non-well-founded set theories described by Aczel (1988) have received attention from category theorists and computer scientists, but have been largely ignored by philosophers. At the root of this neglect might lie the impression that these theories do not embody a conception of set, but are rather of mere technical interest. This paper attempts to dispel this impression. I present a conception of set which may be taken as lying behind a non-well-founded set theory. I argue that the axiom AFA (...)
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  4. Luca Incurvati (2013). The Reference Book By John Hawthorne and David Manley. [REVIEW] Analysis 73 (3):582-585.
  5. Luca Incurvati (2012). How to Be a Minimalist About Sets. Philosophical Studies 159 (1):69-87.
    According to the iterative conception of set, sets can be arranged in a cumulative hierarchy divided into levels. But why should we think this to be the case? The standard answer in the philosophical literature is that sets are somehow constituted by their members. In the first part of the paper, I present a number of problems for this answer, paying special attention to the view that sets are metaphysically dependent upon their members. In the second part of the paper, (...)
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  6. Luca Incurvati (2012). The Evolution of Logic, by W. D. Hart. [REVIEW] Mind 121 (483):822-825.
  7. Luca Incurvati & Peter Smith (2012). Review of P. Maddy, Defending the Axioms: On the Philosophical Foundations of Set Theory. [REVIEW] Mind 121 (481):195-200.
  8. Luca Incurvati & Peter Smith (2012). Is 'No' a Force-Indicator? Sometimes, Possibly. Analysis 72 (2):225-231.
    Some bilateralists have suggested that some of our negative answers to yes-or-no questions are cases of rejection. Mark Textor (2011. Is ‘no’ a force-indicator? No! Analysis 71: 448–56) has recently argued that this suggestion falls prey to a version of the Frege-Geach problem. This note reviews Textor's objection and shows why it fails. We conclude with some brief remarks concerning where we think that future attacks on bilateralism should be directed.
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  9. Luca Incurvati & Peter Smith (2010). Rejection and Valuations. Analysis 70 (1):3 - 10.
    Timothy Smiley's wonderful paper 'Rejection' (Analysis 1996) is still perhaps not as well known or well understood as it should be. This note first gives a quick presentation of themes from that paper, though done in our own way, and then considers a putative line of objection - recently advanced by Julien Murzi and Ole Hjortland (Analysis 2009) - to one of Smiley's key claims. Along the way, we consider the prospects for an intuitionistic approach to some of the issues (...)
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  10. Luca Incurvati (2009). Does Truth Equal Provability in the Maximal Theory? Analysis 69 (2):233-239.
    According to the received view, formalism – interpreted as the thesis that mathematical truth does not outrun the consequences of our maximal mathematical theory – has been refuted by Goedel's theorem. In support of this claim, proponents of the received view usually invoke an informal argument for the truth of the Goedel sentence, an argument which is supposed to reconstruct our reasoning in seeing its truth. Against this, Field has argued in a series of papers that the principles involved in (...)
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  11. Luca Incurvati (2008). On Adopting Kripke Semantics in Set Theory. Review of Symbolic Logic 1 (1):81-96.
    Several philosophers have argued that the logic of set theory should be intuitionistic on the grounds that the open-endedness of the set concept demands the adoption of a nonclassical semantics. This paper examines to what extent adopting such a semantics has revisionary consequences for the logic of our set-theoretic reasoning. It is shown that in the context of the axioms of standard set theory, an intuitionistic semantics sanctions a classical logic. A Kripke semantics in the context of a weaker axiomatization (...)
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  12. Luca Incurvati (2008). Too Naturalist and Not Naturalist Enough: Reply to Horsten. Erkenntnis 69 (2):261 - 274.
    Leon Horsten has recently claimed that the class of mathematical truths coincides with the class of theorems of ZFC. I argue that the naturalistic character of Horsten’s proposal undermines his contention that this claim constitutes an analogue of a thesis that Daniel Isaacson has advanced for PA. I argue, moreover, that Horsten’s defence of his claim against an obvious objection makes use of a distinction which is not available to him given his naturalistic approach. I suggest a way out of (...)
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  13. Luca Incurvati & Julien Murzi (2008). How Basic is the Basic Revisionary Argument? Analysis 68 (4):303-309.
    Anti-realists typically contend that truth is epistemically constrained. Truth, they say, cannot outstrip our capacity to know. Some anti-realists are also willing to make a further claim: if truth is epistemically constrained, classical logic is to be given up in favour of intuitionistic logic. Here we shall be concerned with one argument in support of this thesis - Crispin Wright's Basic Revisionary Argument, first presented in his Truth and Objectivity. We argue that the reasoning involved in the argument, if correct, (...)
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  14. Luca Incurvati (2007). On Some Consequences of the Definitional Unprovability of Hume's Principle. In Pierre Joray (ed.), Contemporary Perspectives on Logicism and the Foundations of Mathematics. CDRS.