Defending the Axioms: On the Philosophical Foundations of Set Theory


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Return to Book Page. Preview — Defending the Axioms by Penelope Maddy. Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions.

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For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolat Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions.


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Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of the objectivity of mathematics emerges, one refreshingly free of metaphysical commitments.

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Oct 15, Peter Mcloughlin rated it it was amazing Shelves: complexity , mathematics , religion-or-not , good-things , intellectual-history , to , physics , world-history , to , to Penelope Maddy defends robust realism over fictionalism and the weak sauce of thin realism and argues for the realism of mathematics being as real as atoms or tables and chairs. I agree with Maddy there seems to be the kind of structure in mathematical concepts that leads the mathematician rather than the other way around.

Mathematics doesn't seem to be invented to someone working in it. They are like rocks if you kick around mathematical concepts the seem to kick back. In this way, Maddy argues Penelope Maddy defends robust realism over fictionalism and the weak sauce of thin realism and argues for the realism of mathematics being as real as atoms or tables and chairs.

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In this way, Maddy argues for the reality and naturalism of mathematical concepts. Short book but well done. Sep 30, Dylan rated it really liked it Shelves: , philosophy-of-math. Maddy looks into how we decide what axioms to add to set theory. In doing so she briefly recounts the history of math and its gradual tendency towards abstraction and rigor.

Then she gives an overview of two "natural" philosophies of math one slightly Platonistic she calls it "Thin Realism" , and one a bit nominalistic "Arealism" , before concluding that on some level it doesn't matter which of the two you choose, because you will more or less be saying the same thing.

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Defending the Axioms: On the Philosophical Foundations of Set Theory Defending the Axioms: On the Philosophical Foundations of Set Theory
Defending the Axioms: On the Philosophical Foundations of Set Theory Defending the Axioms: On the Philosophical Foundations of Set Theory
Defending the Axioms: On the Philosophical Foundations of Set Theory Defending the Axioms: On the Philosophical Foundations of Set Theory
Defending the Axioms: On the Philosophical Foundations of Set Theory Defending the Axioms: On the Philosophical Foundations of Set Theory
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