Mathematical Logic and Foundations
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|Dave Rusin; The Mathematical Atlas|
|A short article designed to provide an introduction to mathematical deduction. The subject has origins in philosophy, and indeed it is only by nonmathematical argument that one can show the usual rules for inference and deduction (law of excluded middle; cut rule; etc.) are valid. It is also a legacy from philosphy that we can distinguish semantic reasoning ("what is true?") from syntactic reasoning ("what can be shown?"). The first leads to Model Theory, the second, to Proof Theory. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.|
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