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SUMMARY:Justification of axioms: a neglected topic in the history of mathe
matics? - Ralph Krömer (Bergische Universität Wuppertal)
DTSTART;VALUE=DATE-TIME:20180124T170000Z
DTEND;VALUE=DATE-TIME:20180124T183000Z
UID:https://talks.ox.ac.uk/talks/id/f04e1efb-25e2-4ab4-b37c-554ae1891e92/
DESCRIPTION:In joint work with Hans-Niels Jahnke (Universität Duisburg-Es
sen)\, we investigate the issue of justification of axioms in mathematics\
, from ancient Greek geometry to current debates on set theory\, category
theory and the foundations of mathematics. The aim of the talk is not to g
ive a complete history of the phenomenon but to highlight its relevance (n
ot sufficiently taken into account in the existing literature\, in our opi
nion) by focussing on some particular cases. We take a look at Proclus’s
discussion of Euclid’s axioms and postulates (especially\, but not excl
usively\, the parallel postulate)\, at how Archimedes and much later Klein
discuss the archimedean axiom\, and finally at Penelope Maddy’s account
of axioms of set theory\, inspired by Zermelo’s remarks on the axiom of
choice. The last case leads us to similar considerations concerning the r
ole of category theory in the foundations of mathematics.\nSpeakers:\nRalp
h Krömer (Bergische Universität Wuppertal)
LOCATION:All Souls College (Hovenden Room)\, High Street OX1 4AL
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/f04e1efb-25e2-4ab4-b37c-554ae1891e92/
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DESCRIPTION:Talk:Justification of axioms: a neglected topic in the history
of mathematics? - Ralph Krömer (Bergische Universität Wuppertal)
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