Logical form and logical space in Wittgenstein’s Tractatus

Synthese 200 (1):1-23 (2022)
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Abstract

In this article I offer a novel explanation of Wittgenstein’s claim, in his Tractatus, that to represent the logical form of a proposition would require our being positioned outside of logic. The account here presented aims to exploit a connection, widely noticed, between the logical forms of objects and those of the propositions in which the names of those objects figure. I show that the logical forms of propositions may, on Wittgenstein’s view, be identified with places in logical space, and that places in logical space are reducible to the forms of both objects and their names. I argue, though, that according to Wittgenstein the representation of a proposition’s logical form would require the existence of a place in logical space not so reducible. I conclude that on Wittgenstein’s position, the attempt to represent logical forms cannot, therefore, succeed.

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Oliver Thomas Spinney
Royal Holloway University of London

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References found in this work

The Foundations of Mathematics and Other Logical Essays.Frank Plumpton Ramsey - 1925 - London, England: Routledge & Kegan Paul. Edited by R. B. Braithwaite.
Notebooks, 1914-1916.Ludwig Wittgenstein - 1979 - Chicago: University of Chicago Press. Edited by G. H. von Wright & G. E. M. Anscombe.
A Companion to Wittgenstein’s Tractatus.Max Black - 1964 - Cambridge University Press.

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