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Truth in mathematics

September 25, 2011

I encounter mathematicians in the Internet often. Lately I had a discussion with the type who says that the axioms of mathematics are something arbitrary and has no reference to truth. I must be old school as this sounded strange to me because I always thought that and have been taught that they are self evident truth. Mind you the gentleman came from a more applied branch of mathematics and not a mathematical logician himself so I suspect he is not well versed with foundational issues. It seemed to me that this rather post-modern approach is being picked up by today’s undergraduates too. I think it should be a worry. Such indifference to truth is not something I encountered 30 years ago when I was an undergraduate.

So it is quite a joy to stumble upon papers that promote the same idea as what I was taught, that one criteria for picking up an axiom is that it should be self-evidently true. Here is one paper from IJPAM wherein the author in picking up an axiom to extend ZFC set theory, relied on the idea of truth.

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