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Chris Scambler
New York University
  1.  28
    Classical Logic and the Strict Tolerant Hierarchy.Chris Scambler - 2020 - Journal of Philosophical Logic 49 (2):351-370.
    In their recent article “A Hierarchy of Classical and Paraconsistent Logics”, Eduardo Barrio, Federico Pailos and Damien Szmuc present novel and striking results about meta-inferential validity in various three valued logics. In the process, they have thrown open the door to a hitherto unrecognized domain of non-classical logics with surprising intrinsic properties, as well as subtle and interesting relations to various familiar logics, including classical logic. One such result is that, for each natural number n, there is a logic which (...)
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  2.  32
    Ineffability and Revenge.Chris Scambler - 2020 - Review of Symbolic Logic 13 (4):797-809.
    In recent work Philip Welch has proven the existence of ‘ineffable liars’ for Hartry Field’s theory of truth. These are offered as liar-like sentences that escape classification in Field’s transfinite hierarchy of determinateness operators. In this article I present a slightly more general characterization of the ineffability phenomenon, and discuss its philosophical significance. I show the ineffable sentences to be less ‘liar-like’ than they appear in Welch’s presentation. I also point to some open technical problems whose resolution would greatly clarify (...)
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  3.  21
    An Indeterminate Universe of Sets.Chris Scambler - 2020 - Synthese 197 (2):545-573.
    In this paper, I develop a view on set-theoretic ontology I call Universe-Indeterminism, according to which there is a unique but indeterminate universe of sets. I argue that Solomon Feferman’s work on semi-constructive set theories can be adapted to this project, and develop a philosophical motivation for a semi-constructive set theory closely based on Feferman’s but tailored to the Universe-Indeterminist’s viewpoint. I also compare the emergent Universe-Indeterminist view to some more familiar views on set-theoretic ontology.
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  4.  19
    A Justification for the Quantificational Hume Principle.Chris Scambler - forthcoming - Erkenntnis:1-16.
    In recent work Bruno Whittle has presented a new challenge to the Cantorian idea that there are different infinite cardinalities. Most challenges of this kind have tended to focus on the status of the axioms of standard set theory; Whittle’s is different in that he focuses on the connection between standard set theory and intuitive concepts related to cardinality. Specifically, Whittle argues we are not in a position to know a principle I call the Quantificational Hume Principle, which connects the (...)
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  5.  45
    Can All Things Be Counted?Chris Scambler - forthcoming - Journal of Philosophical Logic:1-28.
    In this paper, I present and motivate a modal set theory consistent with the idea that there is only one size of infinity.
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  6.  18
    Transfinite Meta-inferences.Chris Scambler - 2020 - Journal of Philosophical Logic 49 (6):1079-1089.
    In Barrio et al. Barrio Pailos and Szmuc prove that there are systems of logic that agree with classical logic up to any finite meta-inferential level, and disagree with it thereafter. This article presents a generalized sense of meta-inference that extends into the transfinite, and proves analogous results to all transfinite orders.
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