David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophia Mathematica 4 (2):124--47 (1996)
One kind of structuralism holds that mathematics is about structures, conceived as a type of abstract entity. Another denies that it is about any distinctively mathematical entities at all—even abstract structures; rather it gives purely general information about what holds of any collection of entities conforming to the axioms of the theory. Of these, pure structuralism is most plausibly taken to enjoy significant advantages over platonism. But in what appears to be its most plausible—modalised—version, even restricted to elementary arithmetic, it requires defence of a very strong possibility claim: that there could be a completed w-sequence of concrete objects. There are very serious epistemological difficulties in the way of providing the requisite defence.
|Keywords||structuralism logicism mathematics WAYS|
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Charles Parsons (2004). Structuralism and Metaphysics. Philosophical Quarterly 54 (214):56--77.
Jessica Carter (2008). Structuralism as a Philosophy of Mathematical Practice. Synthese 163 (2):119 - 131.
Robin Jeshion (2014). Intuiting the Infinite. Philosophical Studies 171 (2):327-349.
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