A polar concept argument for the existence of abstracta

Abstract

In this paper, I present a polar concept argument for the existence of abstract objects. After recalling the fundamentals concerning the debate about the existence of abstracta, I present in a detailed way the argument for the existence of abstracta. I offer two different variations of the argument: one, deductive and the other, inductive. The argument rests primarily on the fact that our universe is well-balanced. This well-balanced property results from the fact that all instantiable polar dualities are instantiated. Hence, the abstract pole of the abstract/concrete duality must also be exemplified. Lastly, I review several objections that can be raised against this latter argument.

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References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
[Letter from Gilbert Ryle].Gilbert Ryle - 1932 - Philosophy 7 (26):250 -.
Abstract Objects.Gideon Rosen - 2014 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. Stanford, CA: The Metaphysics Research Lab.
Science without numbers, A Defence of Nominalism.Hartry Field - 1980 - Revue Philosophique de la France Et de l'Etranger 171 (4):502-503.
Science without Numbers.Michael D. Resnik - 1983 - Noûs 17 (3):514-519.

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