The importance of nonexistent objects and of intensionality in mathematics

Philosophia Mathematica 11 (1):20-52 (2003)
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Abstract

In this article, extracted from his book Exploring Meinong's Jungle and Beyond, Sylvan argues that, contrary to widespread opinion, mathematics is not an extensional discipline and cannot be extensionalized without considerable damage. He argues that some of the insights of Meinong's theory of objects, and its modern development, item theory, should be applied to mathematics and that mathematical objects and structures should be treated as mind-independent, non-existent objects

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References found in this work

Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
Non-standard Analysis.Gert Heinz Müller - 2016 - Princeton University Press.
The foundations of arithmetic.Gottlob Frege - 1884/1950 - Evanston, Ill.,: Northwestern University Press.
Introduction to mathematical logic.Alonzo Church - 1944 - Princeton,: Princeton University Press. Edited by C. Truesdell.
Remarks on the Foundations of Mathematics.Ludwig Wittgenstein - 1956 - Oxford: Macmillan. Edited by G. E. M. Anscombe, Rush Rhees & G. H. von Wright.

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