Philosophy of Mathematics

Term Paper # 99879

Mathematics
Philosophy

An analysis of the universal nature of mathematics and developments in the philosophy of mathematics.

1,899 words () | 6 sources | APA | 2007 United States

Paper Summary:

This paper considers some of the major developments in the philosophy of mathematics regarding the capacity of mathematics to be universally valid and applicable. It presents some of the basic arguments and schools of thought of the philosophy of mathematics. The paper then analyzes whether, at its foundation, mathematics can have a legitimate claim to be universal.

Table of Contents:
The Problem Of The Ideal And The Real
Math As Logic
Math As Structure
Application And Universality

From the Paper:

"This problem, Russell's paradox, proved to be an intractable problem for Frege which, after it was pointed out to him, he could not overcome. The impact upon the philosophy of math was major. An important attempt to boil math down to logical principles had proven unsuccessfully, and eventual efforts to rescue the project by Russell and others were unable to develop a logicism that showed math as both consistent and complete. Therefore math cannot be said to be universal by appeal to logic alone."

Sample of Sources Used:

Franklin, J. (1995, Winter). "An interview." Philosopher 1(2): 31-38.
Greenberg, M.J. (1993). Euclidean and pseudo-Euclidean geometries: Development and history. New York: W. H. Freeman.
Klement, K.C. (2006). "Gottlob Frege (1848-1925)." The Internet Encyclopedia of Philosophy. Retrieved October 17, 2006, from http://www.iep.utm.edu/f/frege.htm.
Resnik, M. (1981). "Mathematics as a science of patterns: Ontology and reference." Nous Vol. 16.
Ross, K. (1999). Meaning and the problem of universals: A Kant-Friesian approach. www.friesian.com. Retrieved October 17, 2006, from http://www.friesian.com/universl.htm.