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Download e-book for iPad: A Structural Account of Mathematics by Charles S. Chihara

By Charles S. Chihara

ISBN-10: 0199228078

ISBN-13: 9780199228072

ISBN-10: 0199267537

ISBN-13: 9780199267538

Charles Chihara's new booklet develops a structural view of the character of arithmetic, and makes use of it to give an explanation for a couple of remarkable good points of arithmetic that experience questioned philosophers for hundreds of years. particularly, this angle permits Chihara to teach that, so that it will know the way mathematical structures are utilized in technology, it's not essential to think that its theorems both presuppose mathematical gadgets or are even precise. He additionally advances numerous new methods of undermining the Platonic view of arithmetic. a person operating within the box will locate a lot to present and stimulate them right here.

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Extra resources for A Structural Account of Mathematics

Sample text

Thus, it is reasonable for Frege to ask: how can an axiom be both? Frege's objection that the axioms of Hilbert's geometry cannot be both does not rest upon any appeal to his theory of 6 Perhaps Hilbert could have responded that he was using the term 'axiom' in two different ways; according to the first way, the axioms are taken to be uninterpreted sentences, whereas according to the second, these same axioms are taken to be interpreted in such a way that they express facts basic to our intuition.

It is this third target that is most obviously relevant to the fourth of my five puzzles. ) How can axioms be definitions? Let us first consider Hilbert's claim that the axioms of his geometry are definitions. What is wrong with that claim? Here, we have to ponder more than one kind of characterization that Hilbert gave of his axioms. In the introduction to his Festschrift on geometry, Hilbert had written: "Geometry requires ... for its consequential construction only a few simple facts. "3 Notice that in this quotation, Hilbert is claiming that the axioms of his geometry express simple, basic facts.

It is this third target that is most obviously relevant to the fourth of my five puzzles. ) How can axioms be definitions? Let us first consider Hilbert's claim that the axioms of his geometry are definitions. What is wrong with that claim? Here, we have to ponder more than one kind of characterization that Hilbert gave of his axioms. In the introduction to his Festschrift on geometry, Hilbert had written: "Geometry requires ... for its consequential construction only a few simple facts. "3 Notice that in this quotation, Hilbert is claiming that the axioms of his geometry express simple, basic facts.

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A Structural Account of Mathematics by Charles S. Chihara


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