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Computing with Numbers and Other Non-syntactic Things: De re Knowledge of Abstract Objects
Philosophia Mathematica 25 (2):268-281 (2017)
Abstract
ABSTRACT Michael Rescorla has argued that it makes sense to compute directly with numbers, and he faulted Turing for not giving an analysis of number-theoretic computability. However, in line with a later paper of his, it only makes sense to compute directly with syntactic entities, such as strings on a given alphabet. Computing with numbers goes via notation. This raises broader issues involving de re propositional attitudes towards numbers and other non-syntactic abstract entities.Author's Profile
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Citations of this work
On the Invariance of Gödel’s Second Theorem with Regard to Numberings.Balthasar Grabmayr - 2021 - Review of Symbolic Logic 14 (1):51-84.
On Two Different Kinds of Computational Indeterminacy.Philippos Papayannopoulos, Nir Fresco & Oron Shagrir - 2022 - The Monist 105 (2):229-246.
On Algorithms, Effective Procedures, and Their Definitions.Philippos Papayannopoulos - 2023 - Philosophia Mathematica 31 (3):291-329.
Wittgenstein and Gödel: An Attempt to Make ‘Wittgenstein’s Objection’ Reasonable†.Timm Lampert - 2018 - Philosophia Mathematica 26 (3):324-345.
Computational Complexity Theory and the Philosophy of Mathematics†.Walter Dean - 2019 - Philosophia Mathematica 27 (3):381-439.
References found in this work
On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
Context and Content: Essays on Intentionality in Speech and Thought.Robert Stalnaker - 1999 - Oxford, GB: Oxford University Press UK.
The ways of paradox, and other essays.Willard Van Orman Quine (ed.) - 1976 - Cambridge: Harvard University Press.
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