Mathematics is a flourishing field of human endeavor, a field that is accorded great respect and high standing. For 2500 years or more, many of the best minds available have worked in this field; and the results produced have indirectly been of enormous value to other fields, such as physics, engineering, architecture, economics, and so on. But with is mathematics about? Physics studies moving bodies; engineering studies bridges; architecture studies buildings; economics studies commercial behavior: here there are phenomena we can point to that constitute the subject matter. But what does mathematics study? If you answer “Numbers”, or “Abstract types of order”, these answers are puzzling, for they represent nothing concrete that one can point to. Unlike other flourishing fields, mathematics does not seem to have a subject matter to which we can point. How are we to understand what mathematics is about, and why it is of value? How can a subject be of value unless is has a definite observable subject matter? This paper discusses these two questions of philosophy as it relates to the field of mathematics.
Barker, Stephen, "Two Philosophical Problems About Mathematics" (1979). ACMS Conference Proceedings 1979. 6.
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