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I'm looking for something that dives into the philosophical idea of a "proof," and explains how the subjects of mathematics and logic deal with it. Does anyone have any book or article recommendations that might lead me to the discussion I am looking for?

Any information you can offer would be greatly appreciated!

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    For a peculiar but very interesting point of view, see by Imre Lakatos : Proofs and Refutations (1976). – Mauro ALLEGRANZA Oct 16 '15 at 19:04
  • Do you want something on the philosophy behind proofs (which can get into topics like the meaning of truth and verification), the philosophical value of proof, or proof as applied to philosophy? – R. Barzell Oct 16 '15 at 19:29
  • @R.Barzell I'm looking for something that goes into the philosophy behind proof methods used today, such as what we see in mathematics and logic. – IgnorantCuriosity Oct 16 '15 at 20:02
  • @IgnorantCuriosity What about this as a start? britannica.com/topic/truth-philosophy-and-logic – R. Barzell Oct 16 '15 at 23:01
  • "The Fabric of Reality" by David Deutsch Chapter 10 "The Nature of Mathematics" – alanf Apr 16 at 8:16
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Thurston, W. P. (1995). On proof and progress in mathematics. For the learning of mathematics, 15(1), 29-37.

Gold, B., & Simons, R. A. (Eds.). (2008). Proof and other dilemmas: Mathematics and philosophy (Vol. 59). MAA.

Krantz, S. G. (2011). The proof is in the pudding: The changing nature of mathematical proof. Springer Science & Business Media.

Detlefsen, M. (Ed.). (2005). Proof and knowledge in mathematics. Routledge.

Detlefsen, M. (Ed.). (2005). Proof, logic and formalization. Routledge.

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Davis and Hersh's The Mathematical Experience is an excellent read and gives an excellent introduction to the philosophy of mathematics.

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