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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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SUMMARY:Generality explained: A truth-maker semantics - Øystein Linnebo (
Oslo)
DTSTART;VALUE=DATE-TIME:20170220T163000Z
DTEND;VALUE=DATE-TIME:20170220T173000Z
UID:https://talks.ox.ac.uk/talks/id/ca57e064-7bce-4907-acd3-cdd3a15c7539/
DESCRIPTION:\nSpeakers:\nØystein Linnebo (Oslo)
LOCATION:Radcliffe Humanities (Ryle Room\, First Floor)\, Woodstock Road O
X2 6GG
URL:https://talks.ox.ac.uk/talks/id/ca57e064-7bce-4907-acd3-cdd3a15c7539/
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DESCRIPTION:Talk:Generality explained: A truth-maker semantics - Øystein
Linnebo (Oslo)
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SUMMARY:Consistency\, a catchword making the second incompleteness theorem
more spectacular than the first: Comments on a comment by Georg Kreisel
- Doukas Kapantais (Athens)
DTSTART;VALUE=DATE-TIME:20170213T163000Z
DTEND;VALUE=DATE-TIME:20170213T183000Z
UID:https://talks.ox.ac.uk/talks/id/7af4865c-52bf-4a29-bb81-bb57ed6042b3/
DESCRIPTION:As Gödel himself stressed\, back in 1931\, his second theorem
is irrelevant to any sensible consistency problem. In any case\, if ConF
is in doubt\, why should it be proved in F (and not in an incomparable sys
tem)? […] He knew only too well the publicity value of this catch word [
i.e. “consistency”]\, which –contrary to his own view of the matter
– had made his second incompleteness theorem more spectacular than the f
irst.” \nGeorg Kreisel\, 1980\, “Kurt Gödel. 28 April 1906-14 January
1978”\, Biographical Memoirs of the Fellows of the Royal Society\, 26:
174.\n\nI will comment on this passage in relation to the several projects
of creating formal theories of arithmetic which\, unlike Peano Arithmetic
\, could possibly prove their own consistency. I distinguish between thos
e formulas of a formal theory F which\, under their canonical interpretati
on\, (i) carry the information that F is consistent and (ii) those that do
not carry the information that F is consistent. ConF trivially belongs to
(ii). Assume that we believe in F’s soundness\, and thereby its consis
tency. If a formula does not carry the information that F is consistent\,
it is a sensible project to try to prove/disprove this formula in F: one b
elieves that F always tells the truth\, and so\, one will believe F’s ve
rdict on this formula\, which says something different from the things one
already believes in. On the other hand\, if the formula carries the info
rmation that F is consistent\, and we already believe that F is sound\, an
d thereby consistent\, F’s possibly affirmative verdict is of purely alg
orithmic interest. We would believe the formula\, but only because we alre
ady believe in F’s soundness\, and thereby its consistency. Finally\, i
f we do not already believe in the soundness of F\, F’s potentially affi
rmative verdict on any formula belonging to (ii)\, would\, in itself\, hav
e no epistemological value whatsoever with regard to F’s consistency. I
will elaborate on this argument and apply it to arithmetics using Rosser
provability.\n\nSpeakers:\nDoukas Kapantais (Athens)
LOCATION:Radcliffe Humanities (Ryle Room\, First Floor)\, Woodstock Road O
X2 6GG
URL:https://talks.ox.ac.uk/talks/id/7af4865c-52bf-4a29-bb81-bb57ed6042b3/
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DESCRIPTION:Talk:Consistency\, a catchword making the second incompletenes
s theorem more spectacular than the first: Comments on a comment by Georg
Kreisel - Doukas Kapantais (Athens)
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SUMMARY:Limits in the Revision Theory - Catrin Campbell-Moore (Bristol)
DTSTART;VALUE=DATE-TIME:20170130T163000Z
DTEND;VALUE=DATE-TIME:20170130T183000Z
UID:https://talks.ox.ac.uk/talks/id/5a6d8e12-e914-42b9-9ea6-01da9f7eaee6/
DESCRIPTION:The revision theory of truth is an influential way to account
for the liar paradox and more generally to work with circular definitions.
We present a new proposal for what to do at the limit stages in the revis
ion theory. The usual limit criterion is that the limit stage should agree
with any definite verdicts that have been brought about. We suggest consi
dering more general properties that are brought about. This more general f
ramework is required if one is interested in considering revision theories
for concepts that are concerned with real numbers\; such as a revision th
eory that can account for cases of self-referential probabilities. These a
re useful for modelling situations where what one believes can affect what
happens\; for example a case where my confidence that I will be able to j
ump across a river will affect whether I’ll actually be able to or not.
The more general framework also has consequences for the more traditional
revision theory of truth.\nSpeakers:\nCatrin Campbell-Moore (Bristol)
LOCATION:Radcliffe Humanities (Ryle Room\, First Floor)\, Woodstock Road O
X2 6GG
URL:https://talks.ox.ac.uk/talks/id/5a6d8e12-e914-42b9-9ea6-01da9f7eaee6/
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DESCRIPTION:Talk:Limits in the Revision Theory - Catrin Campbell-Moore (B
ristol)
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SUMMARY:The substitutional theory of logical consequence - Volker Halbac
h (University of Oxford)
DTSTART;VALUE=DATE-TIME:20170123T163000Z
DTEND;VALUE=DATE-TIME:20170123T183000Z
UID:https://talks.ox.ac.uk/talks/id/49f4511c-7b65-44a4-8f59-511fcce5feda/
DESCRIPTION:\nSpeakers:\nVolker Halbach (University of Oxford)
LOCATION:Radcliffe Humanities (Ryle Room\, First Floor)\, Woodstock Road O
X2 6GG
URL:https://talks.ox.ac.uk/talks/id/49f4511c-7b65-44a4-8f59-511fcce5feda/
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DESCRIPTION:Talk:The substitutional theory of logical consequence - Volk
er Halbach (University of Oxford)
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