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Joel David Hamkins: Philosophy of Mathematics and Truth
Paradigm
Formal Proofs vs. Informal Proofs
- Formal proofs are structured arrangements of statements within a formal language, using axioms and inference rules to arrive at a theorem.
- While Turing machines are a theoretical model of computation, formal proofs serve as a theoretical model of proof.
- Mathematicians use informal proofs for understanding and communication, while formal proofs are used to explore the nature of proof itself, including concepts like independence and consistency.
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