SOPhiA 2019

Salzburgiense Concilium Omnibus Philosophis Analyticis

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Programme - Talk

The indexing theory of numbers
(Metaphysics and Ontology, English)

In the last couple of decades some new light has been shed on the critique of the Quine-Putnam indispensability argument, coming from a new wave of nominalists (such as Joseph Melia, David Liggins, Simon Langford and Chris Daly). These authors argue against the indispensability argument by relying on a paraphrasing method to produce a scientific theory that does not quantify over numbers. I take issue with the paraphrasing method and the four aforementioned authors that support it. They believe that all sentences of our best scientific theory can be paraphrased into sentences of lower-ary paraphrases that do not refer to numbers and in doing so, they provide a theory that is not committed to the existence of such entities. I, on the other hand, believe that there are instances in which the paraphrases will have to be infinitely long so as to account for the meaning of sentences that they wish to replace them with. To evade this problem, I propose a nominalistic theory that does not utilize infinitely long statements. This theory however faces the objection from alien properties. I thus conclude that the nominalist theory cannot serve as an adequate paraphrase of our best scientific theory because it does not allow us knowledge of potential properties of concrete objects. Another objection to the nominalist theory is concerned with the modal status of the paraphrases that it utilizes. Some paraphrases that are granted by the paraphrasing method are metaphysically necessary at best. However, this is unsatisfactory because they are meant to replace sentences that are deduced from mathematical principles, which in turn grants them logical necessity. The notion of metaphysical necessity is weaker than the notion of logical necessity: that which is logically necessary is also metaphysically necessary but not vice versa. To conclude, the paraphrases that the nominalists offer do not serve as a good replacement for the sentences of our best scientific theory because they do not allow a specific type of knowledge that is provided by the latter, nor do they have the same modal status as the latter do. Thus, the paraphrasing method, and the theories that utilize it, are in need of some reconsideration before they can give ample reason for evading ontological commitment to numbers.

Chair:
Time: 12:00-12:30, 19 September 2019 (Thursday)
Location: SR 1.003

Aleksa Cupic 
(Belgrade University Faculty of Philosophy, Serbia)

I am a graduate student of the first year of doctoral studies at the Faculty of Philosophy, Belgrade University, Serbia.

Testability and Meaning deco