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Philosophy of Mathematics: Plato
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Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. In the more eloquent words of Edward Everett, a distinguished nineteenth-century American scholar, "in pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to exist there when the last of their radiant host shall have fallen from heaven." In What is Mathematics, Really?, renowned mathematician Rueben Hersh takes these eloquent words and this pervasive philosophy to task, in a subversive attack on traditional philosophies of mathematics, most notably, Platonism and formalism. Virtually all philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman.
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Additionally, several faculty members regard history of philosophy as a primary interest. Jasper Hopkins focuses on medieval and Renaissance philosophy and ... pursues work in nineteenth-century German philosophy. Douglas Lewis is interested in early modern European philosophy, particularly Descartes, Spinoza, Locke, and Hume, and seeks to promote appreciation of the writings of women philosophers of the early modern period. Sandra Peterson and Norman Dahl investigate Aristotle's ethics and metaphysics and Plato's epistemology and philosophy of language. Each quarter Dahl, Peterson, and Elizabeth Belfiore of Classical and Near Eastern Studies participate in an Aristotle reading group. Students from classics and philosophy have organized informal translation/discussion groups on Parmenides and Heraclitus.
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Plato is not engaged in the philosophy of mathematics, since mathematics is not his main object either here or elsewhere, and he is not proposing the type of mathematical philosophy that aims to reduce philosophy in general to mathematics. Plato's point is a wider one, having to do with the teaching that is now called Platonic realism. But the form of analogy that maps reality into representation is a familiar theme in mathematics, and so it serves as the analogical image of a further analogy that Plato uses to illustrate his broader philosophy. Plato's reasoning in this part of the Republic is Plato at his subtlest, but it lays bare many of the founding metaphors of the Western tradition and will repay further consideration below.
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Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm.
Source:
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