Metamathematics | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-01-13

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Metamathematics


00:01:07 1 History
00:03:14 2 Milestones
00:03:23 2.1 The discovery of hyperbolic geometry
00:04:19 2.2 Begriffsschrift
00:05:27 2.3 Principia Mathematica
00:07:05 2.4 Gödel's incompleteness theorem
00:08:26 2.5 Tarski's definition of model-theoretic satisfaction
00:09:35 2.6 The impossibility of the Entscheidungsproblem
00:11:01 3 See also



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SUMMARY
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Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the term itself) owes itself to David Hilbert's attempt to secure the foundations of mathematics in the early part of the 20th century. Metamathematics provides "a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic" (Kleene 1952, p. 59). An important feature of metamathematics is its emphasis on differentiating between reasoning from inside a system and from outside a system. An informal illustration of this is categorizing the proposition "2+2=4" as belonging to mathematics while categorizing the proposition "'2+2=4' is valid" as belonging to metamathematics.