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Dear all,

I have always wondered why I have never read anything about this topic. My question is, are there are any books or articles covering this subject?

With this topic I mean the philosophical question, whether the foundation of mathematics consists of a single logic, or that it consists of multiple coexisting logics. If we compare it with programming languages, we see that multiple languages co-exist. One language is better in a certain domain than another, while this may not be true for another domain. There is no programming language that takes away the need of all others.

One could ask if this is the same with logics. That multiple logics co-exists. However, if you look at ZFC, then it is more an attempt to capture all in one logic. So, pursuing the idea of single logic foundation. While, more in the style of Hilbert's program, one starts with a simple logic (assembly) and then tries to build up other logics from there, so pursuing a multi-logic foundation.

Has there any serious discussion about this subject?

Regards,

Lucas

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A search for "mathematical pluralism" will lead you to some good initial reads on the matter. (For what it's worth, I personally recommend Peter Koellner's "Truth in mathematics: the question of pluralism.") –  Ed Dean Jan 24 '11 at 21:19
    
Ah, I never searched on that term. I will try that! –  Lucas K. Jan 24 '11 at 21:45

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