Is Set Theory Indispensable?
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چکیده
Although Zermelo-Fraenkel set theory (ZFC) is generally accepted as the appropriate foundation for modern mathematics, proof theorists have known for decades that virtually all mainstream mathematics can actually be formalized in much weaker systems which are essentially number-theoretic in nature. Feferman has observed that this severely undercuts a famous argument of Quine and Putnam according to which set theoretic platonism is validated by the fact that mathematics is “indispensable” for some successful scientific theories (since in fact ZFC is not needed for the mathematics that is currently
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