Philosophy of mathematics
Not offered in 1997
Dr John Arkinstall
3 points * Second semester * 2 hours per week * Gippsland/Distance (even numbered years only) * Prerequisites: At least four subjects of mathematics (subject GAS2614 and/or subject GAS2611 are useful) * Prohibition: MAP3092
Objectives The objectives for this subject are for students to develop an understanding of mathematics as a major cultural enterprise of humanity through a study of its historical and philosophical development; gain the modern perspective of mathematical truth as local to an axiomatic system, and vulnerable; develop critical skills and dialectic dexterity in respect of critique of mathematical methods and presumptions; differentiate between the schools of thought in mathematics; apply these skills in a major piece of work.
Synopsis A mainly informal consideration of philosophical problems centred on mathematics, with emphasis on the opinions of influential philosophers (eg Plato, Kant, Aristotle, Russell) on the nature of mathematics. Main topics are ancient Greek philosophy and mathematics, the history of infinitesimal concepts, the influence of the axiomatic method, formalism, some history of logic, logicism, intuitionism from Aristotle to Brouwer, Lakatos's fallibilist approach. The subject is assessed solely by written work. For distance students, there are four two-hour expository and discussion classes held over the semester to supplement class notes, textbook and readings.
Assessment Assignments: 60% * Long essay: 40%
Prescribed texts
Davis P J and Hersh R The mathematical experience Penguin, 1983
Recommended texts
Barker S Philosophy of mathematics Prentice-Hall, 1964
Baum R J Philosophy of mathematics Freeman, 1973
Lehman H Introduction to the philosophy of mathematics Rowman, 1979
Korner S Philosophy of mathematics Harper, 1960
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