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SUMMARY:Leibniz as inventor of conceptual mathematics? - David Rabouin (CN
 RS (Centre national de la recherche scientifique))
DTSTART:20250120T143000Z
DTEND:20250120T153000Z
UID:TALK220513@talks.cam.ac.uk
DESCRIPTION:On numerous occasions\, Leibniz argued that mathematical demon
 strations could be resolved into two indemonstrable elements: definitions 
 and axioms\, themselves ultimately reducible to &ldquo\;identicals&rdquo\;
 . Based on the famous demonstration of &ldquo\;2 + 2 = 4&rdquo\; in the No
 uveaux Essais sur l'entendement humain\, Frege saw in this statement the f
 irst evidence of a form of "logicism". This reading has played a major rol
 e in the interpretation of Leibniz right up to the present day\, even amon
 g those who dispute the &ldquo\;logicist&rdquo\; interpretation and often 
 simply dismiss the role of &ldquo\;reduction to the identicals&rdquo\;. It
  is then argued that this motto is an ideal that Leibniz never put into pr
 actice. In this presentation\, based on a recent exploration of the archiv
 es\, I will show that this classic fracture in commentary is based on two 
 errors of appreciation: on the one hand\, &ldquo\;logicist&rdquo\; interpr
 etations have failed to take into account the fact that &ldquo\;identical&
 rdquo\; axioms are stated in the plural\; on the other\, interpretations m
 ore focused on mathematical practice have failed to see that the strategy 
 of reduction to the identical is indeed at the heart of a certain practice
  that I propose to call &ldquo\;conceptual&rdquo\;. Following the thread o
 f Leibniz's drafts\, I'll try to explain how and why this strategy came ab
 out\, showing in the process how it led to a new way of thinking about mat
 hematics.
LOCATION:Seminar Room 1\, Newton Institute
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