JOHN MAYBERRY The Foundations of Mathematics in the Theory of Sets
نویسندگان
چکیده
In The Foundations of Mathematics in the Theory of Sets, John Mayberry attacks the 2000-year-old problem of accounting for the foundations of mathematics. His account comes in three interrelated parts: determining exactly what one should (and should not) expect from a foundation; arguing that set theory can in fact provide such a foundation, and presenting a novel version of set theory (or at least a novel exposition of traditional set theory) which can fulfil this foundational role. He addresses the first of these issues (in Chapters 1 and 6) by arguing that the most important aspect of mathematics is the axiomatic method, and thus a foundation for mathematics must provide a justification of this method (but need provide little more). Axiom systems, according to Mayberry, isolate particular mathematical structures (or are meant to), and all that is left for a foundation to supply is a guarantee that some appropriate structure exists that satisfies the axioms:
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