26/04/2016 — Henrique Antunes

Title: On Existence, Inconsistency, and Indispensability

Author: Henrique Antunes

Affiliation: State University of Campinas

Abstract: An indispensability argument is an argument to the effect that we ought be committed to the existence of mathematical/theoretical objects because they are indispensable to our best scientific theories. In [4], Mark Colyvan advances versions of the indispensability argument that are specifically concerned with inconsistent or contradictory theories and whose purported effect is to show that we ought be committed to the existence of inconsistent objects. In this paper I shall sketch a line of response to Colyvan’s arguments, being mainly concerned with the indispensability of inconsistent mathematical objects. My response will draw on a relatively recent nominalistic interpretation of mathematics put forward by Jody Azzouni [1]. I will argue that once that version of nominalism is adopted, semantic dialetheism and the metaphysical version of the principle of non-contradiction are not incompatible. Finally, I will tentatively propose a logical framework for regimenting inconsistent applied mathematical theories, when these theories are viewed along the lines being advanced.

Keywords: indispensability argument, deflationary nominalism, inconsistent theories, inconsistent objects, dialetheism, principle of non-contradiction

References

[1] Azzouni, J. Deflating Existential Consequence: A Case for Nominalism. Oxford University Press, 2004.

[2] Beall, J. C., and Armour-Garb, B. Should Deflationists Be Dialetheists? Nous 37 (2003), 303–324.

[3] Carnielli, W. A., João Marcos, and de Amo, S. Formal Inconsistency and Evolutionary Databases. Logic and Logical Philosophy 8 (2000), 115–152.

[4] Colyvan, M. The Ontological Commitments of Inconsistent Theories. Philosophical Studies 141 (2008), 115–123.

[5] Priest, G. Truth and Contradiction. The Philosophical Quartely 50 (2000), 305–319.

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