Scientific Philosophy from Helmholtz to Carnap and Quine

Friedman, Michaël

doi:10.1007/978-94-007-3929-1_1

Cited by 23 publications

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“…I am not sure that Quine would feel the force of this objection. As we will see in section 16.4, Quine thinks that all objects-sets, numbers, atoms, tables, chairs, etc.-are given only by their structural properties.6 On the tradition of scientific philosophy,Friedman (2012) andRichardson (1997).…”

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Explication as Elimination: W. V. Quine and Mathematical Structuralism

Morris¹

2020

The Prehistory of Mathematical Structuralism

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This chapter examines the development of and motives for Quine’s particular form of mathematical structuralism. It will argue that Quine, unlike many contemporary mathematical structuralists, does not appeal to structuralism as a way of accounting for what the numbers really are in any robust metaphysical sense. Instead, his structuralism is deeply rooted in an earlier structuralist tradition found in scientific philosophers such as Russell and Carnap, which emphasized structuralism as a critique of more metaphysical approaches to philosophy. On this view, a philosophy of mathematics answers, in a sense, only to mathematics itself. An account of mathematical objects requires only that the entities—whatever they are—serving as the mathematical objects satisfy the relevant postulates and theorems. Here we also see how Quine’s early work in the foundations of mathematics leads in a natural way to the more general naturalism of his later philosophy.

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confidence: 99%