BEGIN:VCALENDAR VERSION:2.0 PRODID:ILLC Website X-WR-TIMEZONE:Europe/Amsterdam BEGIN:VTIMEZONE TZID:Europe/Amsterdam X-LIC-LOCATION:Europe/Amsterdam BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19700329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19701025T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:/NewsandEvents/Archives/2017/newsitem/9514/1-D ecember-2017-Cool-Logic-Yvette-Oortwijn DTSTAMP:20171204T133834 SUMMARY:Cool Logic, Yvette Oortwijn ATTENDEE;ROLE=Speaker:Yvette Oortwijn DTSTART;TZID=Europe/Amsterdam:20171201T180000 DTEND;TZID=Europe/Amsterdam: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.