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BEGIN:VEVENT
UID:/NewsandEvents/Archives/current/newsitem/13539
/22-April-2022-Cool-Logic-Valentin-Müller
DTSTAMP:20220418T145345
SUMMARY:Cool Logic, Valentin Müller
ATTENDEE;ROLE=Speaker:Valentin Müller
DTSTART;TZID=Europe/Amsterdam:20220422T170000
DTEND;TZID=Europe/Amsterdam:20220422T190000
LOCATION:Room D1.111, Science Park 904, Amsterdam
DESCRIPTION:Among the variety of possible solution
s to the paradoxes of naive set theory, suggestion
s made by the mathematician Heinrich Behmann (1891
--1970) appear to be particularly remarkable (even
though they are commonly unknown today). From Beh
mann’s point of view, the paradoxes do not represe
nt proper contradictions, but rather “meaningless”
expressions that can be avoided by a simple and p
urely syntactical criterion. The main goal of my t
alk is to provide a partial confirmation of Behman
n’s view. To this end, I will present a new system
of natural deduction strongly inspired by Behmann
’s analysis of the set-theoretical paradoxes. It w
ill be demonstrated that a certain subclass of the
proofs in our system has the normalization proper
ty: every deduction in this class may be transform
ed into a “cut-free” proof. As a corollary, it the
n follows that the propositional fragment of our s
ystem is in fact consistent. In the last part of t
he talk, I will discuss some open problems and clo
sely related approaches such as the system of “Fit
ch-Prawitz Set Theory”.
X-ALT-DESC;FMTTYPE=text/html:\n Among the vari
ety of possible solutions to the paradoxes of naiv
e set theory, suggestions made by the mathematicia
n Heinrich Behmann (1891--1970) appear to be parti
cularly remarkable (even though they are commonly
unknown today). From Behmann’s point of view, the
paradoxes do not represent proper contradictions,
but rather “meaningless” expressions that can be a
voided by a simple and purely syntactical criterio
n. The main goal of my talk is to provide a partia
l confirmation of Behmann’s view. To this end, I w
ill present a new system of natural deduction stro
ngly inspired by Behmann’s analysis of the set-the
oretical paradoxes. It will be demonstrated that a
certain subclass of the proofs in our system has
the normalization property: every deduction in thi
s class may be transformed into a “cut-free” proof
. As a corollary, it then follows that the proposi
tional fragment of our system is in fact consisten
t. In the last part of the talk, I will discuss so
me open problems and closely related approaches su
ch as the system of “Fitch-Prawitz Set Theory”.

\n
URL:https://coollogic.wixsite.com/website/event-de
tails/proof-theoretical-solutions-to-the-paradoxes
-of-naive-set-theory
CONTACT:Vasiliy Romanovskiy, Tibo Rushbrooke at co
ollogic.uva at gmail.com
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