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Philosophy of Mathematics
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Learning Objectives and Expected Outcomes: Graduates of the Department of Philosophy acquire considerable skills in abstract thinking, analysis, and critical writing (constructing and critiquing arguments). Because of these skills, philosophical training is invaluable in almost any area of life. Recent graduates have been successful in software development, financial planning, journalism, teaching, and aviation. A few go on to graduate school and become professional philosophers.
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This is intended to become the script for a course on the Philosophy of Mathematics. It may then serve as basis for books and other materials as well as discussions and research.
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Each of the following is a research and teaching interest of at least one person in the department: Plato and Aristotle, medieval philosophy, Descartes, Locke, Spinoza, Hume, Kant, Schopenhauer, Kierkegaard, Thoreau, Wittgenstein, Russell, and Frege. The Department offers graduate-level courses on these philosophers and the traditions they helped to develop.
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For a philosophy of mathematics that attempts to overcome some of the shortcomings of Quine and Gödel's approaches by taking aspects of each see Penelope Maddy's Realism in Mathematics. Another example of a realist theory is the embodied mind theory (see below).
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The purpose of this course is to introduce students to basic ideas in the philosophy of mathematics and to chart the history of mathematics from ancient to modern times. The accomplishments of many mathematicians from all cultures and historical eras will be covered.
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This is a big ongoing debate in the philosophy of mathematics. What is maths? Nominalists say that its like a game of checkers. There are pieces (numbers) and there are rules (methods of calculation) but there is no meaning. This view is not widely accepted. If maths was just a made up game, then why does it have such useful applications in the real world?
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Philosophy of Mathematics