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AntonioLao · **philosophical foundation of mathematics -** 08-02-2005, 09:06 PM

Reference: Morris Kline, ‘Mathematical Thought: From Ancient to Modern Times’, Volumes 1, 2, and 3, Oxford University Press, Oxford, 1972.

The mathematical foundation built upon three pillars of mathematical philosophy and as far as we know, reached an impasse and could possibly remain so for a very long time.

The problem started when mathematicians tried to axiomatize set theory in order to solve the paradoxes (contradictions) and the consistency problem.

The first foundational pillar is the school of logic founded by Russell and Whitehead.

The second foundational pillar is the school of intuitionist philosophy founded by Kronecker before the 20th century, modernized, and systematized by Brouwer beginning in 1907.

The third foundational pillar is the school of formalist philosophy founded by Hilbert.

So far, none of these philosophies achieved the objective of providing a universally accepted approach to mathematics.

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AntonioLao Raider of the lost time Status: Offline Posts: 5,613 Thanks Given: 790 Thanked 180x in 174 Posts Join Date: Nov 2003 Rep Power: 80	philosophical foundation of mathematics - 08-02-2005, 09:06 PM Reference: Morris Kline, ‘Mathematical Thought: From Ancient to Modern Times’, Volumes 1, 2, and 3, Oxford University Press, Oxford, 1972. The mathematical foundation built upon three pillars of mathematical philosophy and as far as we know, reached an impasse and could possibly remain so for a very long time. The problem started when mathematicians tried to axiomatize set theory in order to solve the paradoxes (contradictions) and the consistency problem. The first foundational pillar is the school of logic founded by Russell and Whitehead. The second foundational pillar is the school of intuitionist philosophy founded by Kronecker before the 20th century, modernized, and systematized by Brouwer beginning in 1907. The third foundational pillar is the school of formalist philosophy founded by Hilbert. So far, none of these philosophies achieved the objective of providing a universally accepted approach to mathematics.