BEGIN:VCALENDAR
VERSION:2.0
PRODID:ILLC Website
BEGIN:VEVENT
UID:/NewsandEvents/Events/Upcoming-Events/newsitem
/9514/1-December-2017-Cool-Logic-Yvette-Oortwijn
DTSTAMP:20171204T133834
SUMMARY:Cool Logic, Yvette Oortwijn
ATTENDEE;ROLE=Speaker:Yvette Oortwijn
DTSTART:20171201T180000
DTEND:20171201T190000
LOCATION:F1.15, ILLC Seminar Room
DESCRIPTION:Michael Dummett has a variety of argum
ents for why we should favour intuitionistic over
classical logic. Most of his arguments attack the
complete realism one needs to believe in bivalence
, but there is one argument concerning mathematics
specifically, based on a phenomenon he calls inde
finite extensibility. We see what this phenomenon
is and why it matters for the foundation of mathem
atics. Now, most of us think that getting rid of
naive comprehension got us out of the biggest pro
blems of naive set theory. With this we abandon th
e possibility of forming a set of all sets and dod
ge all kinds of paradoxes. According to Dummett, t
hough, this is not enough. We got rid of a symptom
, but there still exists an underlying problem. He
argues that the only sensible thing to do is to a
dopt intuitionistic logic. But is this actually th
e case? And is it really sensible to claim that un
restricted quantification should be possible? We
will look into a different solution: the potentia
l hierarchy of sets, as formulated by Linnebo. Thi
s view of sets gives an explanation of why unrestr
icted quantification is not possible, instead of m
erely restricting it. This account of the hierarch
y of sets also sheds new light on the abandonment
of naive set theory.
X-ALT-DESC;FMTTYPE=text/html:\n Michael Dummet
t has a variety of arguments for why we should fav
our intuitionistic over classical logic. Most of h
is arguments attack the complete realism one needs
to believe in bivalence, but there is one argumen
t concerning mathematics specifically, based on a
phenomenon he calls indefinite extensibility. We s
ee what this phenomenon is and why it matters for
the foundation of mathematics.

\n

\n Now,
most of us think that getting rid of naive compre
hension got us out of the biggest problems of naiv
e set theory. With this we abandon the possibility
of forming a set of all sets and dodge all kinds
of paradoxes. According to Dummett, though, this i
s not enough. We got rid of a symptom, but there s
till exists an underlying problem. He argues that
the only sensible thing to do is to adopt intuitio
nistic logic. But is this actually the case? And i
s it really sensible to claim that unrestricted qu
antification should be possible?

\n

\n We
will look into a different solution: the potentia
l hierarchy of sets, as formulated by Linnebo. Thi
s view of sets gives an explanation of why unrestr
icted quantification is not possible, instead of m
erely restricting it. This account of the hierarch
y of sets also sheds new light on the abandonment
of naive set theory.

\n
URL:http://events.illc.uva.nl/coollogic/talks/81
CONTACT:Dean McHugh at coollogic.uva at gmail.com
END:VEVENT
END:VCALENDAR