In Objects, Structures and Logics (forthcoming)

Laura Crosilla
University of Oslo
In this article I present a disagreement between classical and constructive approaches to predicativity regarding the predicative status of so-called generalised inductive definitions. I begin by offering some motivation for an enquiry in the predicative foundations of constructive mathematics, by looking at contemporary work at the intersection between mathematics and computer science. I then review the background notions and spell out the above-mentioned disagreement between classical and constructive approaches to predicativity. Finally, I look at possible ways of defending the constructive predicativity of inductive definitions.
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References found in this work BETA

Elementary Induction on Abstract Structures.Yiannis Nicholas Moschovakis - 1974 - Amsterdam, Netherlands: Dover Publications.
Constructive Set Theory.John Myhill - 1975 - Journal of Symbolic Logic 40 (3):347-382.
The Entanglement of Logic and Set Theory, Constructively.Laura Crosilla - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (6).
The Impredicativity of Induction.Charles Parsons - 1992 - In Michael Detlefsen (ed.), Proof, Logic, and Formalization. Routledge. pp. 139--161.

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Citations of this work BETA

Bishop's Mathematics: A Philosophical Perspective.Laura Crosilla - forthcoming - In Handbook of Bishop's Mathematics. CUP.

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