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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  <p>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.<br>\n  <br>\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?<br>\n  <br>\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.</p>\n
URL:http://events.illc.uva.nl/coollogic/talks/81
CONTACT:Dean McHugh at coollogic.uva at gmail.com
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