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BEGIN:VEVENT
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 PoincarĂ© 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 \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
oincaré and Borel: mathematics has an extra
-logical content too.\n

\n \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

\n \n \n For more
information, see \n http://www.science.uva.nl/research/math
/calendar/colloq/\n

URL:/NewsandEvents/Archives/2004/newsitem/658/17-M
arch-2004-General-Mathematics-Colloquium-John-Kuip
er
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