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UID:/NewsandEvents/Archives/2004/newsitem/658/17-M
 arch-2004-General-Mathematics-Colloquium-John-Kuip
 er
DTSTAMP:20040311T000000
SUMMARY:General Mathematics Colloquium, John Kuipe
 r
ATTENDEE;ROLE=Speaker:John Kuiper (Utrecht)
DTSTART;TZID=Europe/Amsterdam:20040317T111500
DTEND;TZID=Europe/Amsterdam:20040317T121500
LOCATION:Room P.014, Euclides building, Plantage M
 uidergracht 24, Amsterdam
DESCRIPTION:In the beginning of the twentieth cent
 ury a new movement was added to the existing two t
 hat attempted to lay a solid foundation for the ma
 thematical building. After Frege, Russell and Cout
 urat, who viewed logic as the ultimate basis for m
 athematics, and Hilbert's formalist approach in wh
 ich mathematics is just a manipulation with meanin
 gless signs and symbols, Brouwer worked out earlie
 r ideas by Poincaré and Borel: mathematics has an 
 extra-logical content too.    For Brouwer, the ult
 imate basis for all mathematics is the ur-intuitio
 n of `the move of time', that is, the experience o
 f the fact that two not-coinciding mental events a
 re connected by a time continuum. Departing from t
 his ur-intuition, the whole of mathematics, hence 
 including set theory and geometry, can be construc
 ted. In is early years as an active mathematician 
 (in his own terms: his `first intuitionistic perio
 d', between 1907 and, say, 1914; note that most of
  his time during those years was spent on topology
 ) his constructivistic requirements were very stri
 ct: only that what is constructed by the individua
 l mind (mathematics is essentially languageless) c
 ounts as a mathematical object. In this lecture we
  will work this out for the logical figure of the 
 hypothetical judgement in a mathematical context, 
 and we will see that, in hindsight, Brouwer went t
 oo far in his constructivism.    For more informat
 ion, see http://www.science.uva.nl/research/math/c
 alendar/colloq/
X-ALT-DESC;FMTTYPE=text/html:\n      <p>\n        
 In the beginning of the twentieth century a new mo
 vement was added to the existing two that attempte
 d to lay a solid foundation for the mathematical b
 uilding. After Frege, Russell and Couturat, who vi
 ewed logic as the ultimate basis for mathematics, 
 and Hilbert's formalist approach in which mathemat
 ics is just a manipulation with meaningless signs 
 and symbols, Brouwer worked out earlier ideas by P
 oincar&eacute; and Borel: mathematics has an extra
 -logical content too.\n      </p>\n      <p>\n    
     For Brouwer, the ultimate basis for all mathem
 atics is the ur-intuition of `the move of time', t
 hat is, the experience of the fact that two not-co
 inciding mental events are connected by a time con
 tinuum. Departing from this ur-intuition, the whol
 e of mathematics, hence including set theory and g
 eometry, can be constructed. In is early years as 
 an active mathematician (in his own terms: his `fi
 rst intuitionistic period', between 1907 and, say,
  1914; note that most of his time during those yea
 rs was spent on topology) his constructivistic req
 uirements were very strict: only that what is cons
 tructed by the individual mind (mathematics is ess
 entially languageless) counts as a mathematical ob
 ject. In this lecture we will work this out for th
 e logical figure of the hypothetical judgement in 
 a mathematical context, and we will see that, in h
 indsight, Brouwer went too far in his constructivi
 sm.\n      </p>\n    \n      <p>\n        For more
  information, see \n        <a target="_blank" hre
 f="http://www.science.uva.nl/research/math/calenda
 r/colloq/">http://www.science.uva.nl/research/math
 /calendar/colloq/</a>\n      </p>\n    
URL:/NewsandEvents/Archives/2004/newsitem/658/17-M
 arch-2004-General-Mathematics-Colloquium-John-Kuip
 er
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