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SUMMARY:An Aristotelian approach for contemporary mathematics - Donald Gil
lies (King’s College London)
DTSTART;VALUE=DATE-TIME:20170306T163000Z
DTEND;VALUE=DATE-TIME:20170306T183000Z
UID:https://talks.ox.ac.uk/talks/id/2c78280e-9f41-4d7a-a618-c9ffac6c0baf/
DESCRIPTION:I will begin the talk with a brief sketch of Aristotle’s ori
ginal philosophy of mathematics. This\, I will argue\, is based on two pos
tulates. The first is the embodiment postulate\, which states that mathema
tical objects do exist\, though not in a separate Platonic world\, but emb
odied in the material world. The second is that infinity is always potenti
al and never actual. I will then consider the extent to which this Aristot
elian approach holds for contemporary mathematics. I will assume that most
contemporary mathematicians accept ZFC. This rules out Aristotle’s seco
nd postulate since ZFC’s axiom of infinity implies the existence of an a
ctual infinity. However\, I will claim that the embodiment postulate can s
till be defended for contemporary mathematics. At first sight this seems a
curious claim since Cantor’s theory of transfinite alephs can be develo
ped within ZFC\, and surely transfinite alephs are not embodied in the mat
erial world. I will discuss this difficulty at length\, and try to overcom
e it using ideas from Fictionalist and If ..then-ist philosophies of mathe
matics.\nSpeakers:\nDonald Gillies (King’s College London)
LOCATION:Radcliffe Humanities (Ryle Room\, First Floor)\, Woodstock Road O
X2 6GG
URL:https://talks.ox.ac.uk/talks/id/2c78280e-9f41-4d7a-a618-c9ffac6c0baf/
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DESCRIPTION:Talk:An Aristotelian approach for contemporary mathematics - D
onald Gillies (King’s College London)
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