Why a philosopher should know about set, model, computability and proof theory? I'm starting to study first order logic.
Proof Theory: An Intensive MA/PhD Course
I really like it. Propositional and predicate logic seems pretty useful for a philosopher. But what about set, model, computability and proof theory? I don't know what they are about and how it relates to the philosopher's work. Could you throw some light on these topics? Well, if you're interested in the philosophy of mathematics, then that's where they will be absolutely indispensable. They might also be good for you if you're into the philosophy of mind and artificial intelligence. Set theory: Is just the theory about sets and how they behave.
The way they behave is determined by our axioms of set theory. Important in the philosophy of mathematics because some people think that all of math can be reduced to set theory, and that numbers are just sets. Computability: Theory about what we can determine using some algorithm.
Philosophical aspects of proof theory | SpringerLink
When you study the foundations of mathematics, this is very important, since it will bear on how mathematics is justified look up the Church-Turing Thesis, and Godel's Incompleteness Theorem. It also bears on questions in the philosophy of mind: e. To answer that question, we need to understand what it means to compute, etc.
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- Proof Theory in Philosophy of Mathematics.
- Proof Theory (Stanford Encyclopedia of Philosophy).
- The Postman Always Rings Twice?
- Graduating with Confidence: A Guide to Making the Most of Your College Experience;
- Discrete and Computational Geometry: Japanese Conference, JCDCG 2000 Tokyo, Japan, November 22–25, 2000 Revised Papers.
Proof Theory and Model Theory 2. Logical Consequence 2.
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Table of contents 10 chapters Table of contents 10 chapters Introduction Pages Hendricks, et al.
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