Structuralism, indiscernibility, and physical computation

نویسندگان

چکیده

Abstract Structuralism about mathematical objects and structuralist accounts of physical computation both face indeterminacy objections. For the former, problem arises for cases such as complex roots i $$-i$$ - i , which a (non-trivial) automorphism can be defined, thus establishing structural identity these importantly distinct (see e.g. Keränen in Philos Math 3:308–330, 2001). In case latter, logical duals AND OR, have invertible profiles Shagrir Mind 110(438):369–400, This makes their implementations indeterminate, sense that alone cannot establish whether given component is an AND-gate or OR-gate. Doherty (PhilPapers, https://philpapers.org/rec/DOHCI-3 2021) has recently shown problems to analogous, argued computational structuralism threatened with absurd conclusion digits might indiscernible, that, if properties are all we go on, binary digit 0 must treated identical 1 (rendering pure absurd). However, think solution indiscernibility structuralists, drawing on work David Hilbert, adapted analogous case, thereby rescuing approach computation.

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ژورنال

عنوان ژورنال: Synthese

سال: 2022

ISSN: ['0039-7857', '1573-0964']

DOI: https://doi.org/10.1007/s11229-022-03691-1