The logic in logicism

Dialogue 36 (2):341--60 (1997)
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Abstract

Frege's logicism consists of two theses: the truths of arithmetic are truths of logic; the natural numbers are objects. In this paper I pose the question: what conception of logic is required to defend these theses? I hold that there exists an appropriate and natural conception of logic in virtue of which Hume's principle is a logical truth. Hume's principle, which states that the number of Fs is the number of Gs iff the concepts F and G are equinumerous is the central plank in the neo-logicist argument for and. I defend this position against two objections Hume's principle canot be both a logical truth as required by and also have the ontological import required by ; and the use of Hume's principle by the logicist is in effect an ontological proof of a kind which is not valid

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Alexander James Bird
Cambridge University

Citations of this work

Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.
Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.

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References found in this work

Frege’s Conception of Numbers as Objects.Crispin Wright - 1983 - Critical Philosophy 1 (1):97.
Grundlagen der Mathematik I.G. T. Kneebone - 1970 - Journal of Symbolic Logic 35 (2):321-323.

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