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Mathematical logic

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Mathematical logic emerged in the mid-19th century as a subfield of mathematics independent of the traditional study of logic ([[#CITEREFFerreirós2001|Ferreirós 2001]], p.&nbsp;443). Before this emergence, logic was studied with [[rhetoric]], with ''calculationes'',<ref>[[Richard Swineshead]] (1498), ''Calculationes Suiseth Anglici'', Papie: Per Franciscum Gyrardengum.</ref> through the [[syllogism]], and with [[philosophy]]. The first half of the 20th century saw an explosion of fundamental results, accompanied by vigorous debate over the foundations of mathematics.
=== Early history ===