Citations of:
Pythagorean powers or a challenge to platonism
Australasian Journal of Philosophy 74 (4):639 – 645 (1996)
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In this paper, I defend an indexical analysis of the abstractconcrete distinction within the framework of modal realism. This analysis holds the abstractconcrete distinction to be conceptually inseparable from the distinction between the actual and the merely possible, which is assumed to be indexical in nature. The resulting view contributes to the case for modal realism by demonstrating how its distinctive resources provide a reductive analysis of the abstractconcrete distinction. This indexical analysis also provides a solution to a sceptical problem (...) 

Some recent work by philosophers of mathematics has been aimed at showing that our knowledge of the existence of at least some mathematical objects and/or sets can be epistemically grounded by appealing to perceptual experience. The sensory capacity that they refer to in doing so is the ability to perceive numbers, mathematical properties and/or sets. The chief defense of this view as it applies to the perception of sets is found in Penelope Maddy’s Realism in Mathematics, but a number of (...) 

Mathematics has a great variety ofapplications in the physical sciences.This simple, undeniable fact, however,gives rise to an interestingphilosophical problem:why should physical scientistsfind that they are unable to evenstate their theories without theresources of abstract mathematicaltheories? Moreover, theformulation of physical theories inthe language of mathematicsoften leads to new physical predictionswhich were quite unexpected onpurely physical grounds. It is thought by somethat the puzzles the applications of mathematicspresent are artefacts of outdated philosophical theories about thenature of mathematics. In this paper I argue (...) 



According to standard mathematical platonism, mathematical entities (numbers, sets, etc.) are abstract entities. As such, they lack causal powers and spatiotemporal location. Platonists owe us an account of how we acquire knowledge of this inaccessible mathematical realm. Some recent versions of mathematical platonism postulate a plenitude of mathematical entities, and Mark Balaguer has argued that, given the existence of such a plenitude, the attainment of mathematical knowledge is rendered nonproblematic. I assess his epistemology for such a profligate platonism and find (...) 

In this paper I will take into examination the relevance of the main indispensability arguments for the comprehension of the applicability of mathematics. I will conclude not only that none of these indispensability arguments are of any help for understanding mathematical applicability, but also that these arguments rather require a preliminary analysis of the problems raised by the applicability of mathematics in order to avoid some tricky difficulties in their formulations. As a consequence, we cannot any longer consider the applicability (...) 



An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...) 



Recently Colin Cheyne and Charles Pigden have challenged supporters of mathematical indispensability arguments to give an account of how causally inert mathematical entities could be indispensable to science. Failing to meet this challenge, claim Cheyne and Pigden, would place Platonism in a no win situation: either there is no good reason to believe in mathematical entities or mathematical entities are not causally inert. The present paper argues that Platonism is well equipped to meet this challenge. 