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UID:/NewsandEvents/Archives/2022/newsitem/13645/21
---22-May-2022-Meeting-in-Internal-Categoricity-He
lsinki-Finland-Virtual
DTSTAMP:20220515T214231
SUMMARY:Meeting in Internal Categoricity, Helsinki
(Finland) & Virtual
DTSTART;VALUE=DATE:20220521
DTEND;VALUE=DATE:20220522
LOCATION:Helsinki (Finland) & Virtual
DESCRIPTION:The categoricity of an axiom system me
ans that its non-logical symbols have, up to isomo
rphism, only one possible interpretation. The firs
t axiomatizations of mathematical theories such as
number theory and analysis by Dedekind, Hilbert,
Huntington, Peano and Veblen were indeed categoric
al. These were all second order axiomatisations, s
uffering from what many consider a weakness, namel
y dependence on a strong metatheory, casting a sha
dow over these celebrated categoricity results. In
finer analysis a new form of categoricity has eme
rged. It is called internal categoricity because i
t is perfectly meaningful without any reference to
a metatheory, and it is now known that the classi
cal theories, surprisingly even in their first ord
er formulation, can be shown to be internally cate
gorical. In this workshop various aspects of and
approaches to internal categoricity are presented
and the following questions, among others, are dis
cussed: What is the philosophical import/advantage
of internal categoricity over ordinary categorici
ty? Is internal categoricity the right concept of
categoricity? Does internal categoricity play a ro
le also in first order theories?
X-ALT-DESC;FMTTYPE=text/html:\n The categorici
ty of an axiom system means that its non-logical s
ymbols have, up to isomorphism, only one possible
interpretation. The first axiomatizations of mathe
matical theories such as number theory and analysi
s by Dedekind, Hilbert, Huntington, Peano and Vebl
en were indeed categorical. These were all second
order axiomatisations, suffering from what many co
nsider a weakness, namely dependence on a strong m
etatheory, casting a shadow over these celebrated
categoricity results. In finer analysis a new form
of categoricity has emerged. It is called interna
l categoricity because it is perfectly meaningful
without any reference to a metatheory, and it is n
ow known that the classical theories, surprisingly
even in their first order formulation, can be sho
wn to be internally categorical.

\n In this
workshop various aspects of and approaches to int
ernal categoricity are presented and the following
questions, among others, are discussed: What is t
he philosophical import/advantage of internal cate
goricity over ordinary categoricity? Is internal c
ategoricity the right concept of categoricity? Doe
s internal categoricity play a role also in first
order theories?

URL:https://www.helsinki.fi/en/beta/conferences/in
ternal-categoricity
CONTACT:Juliette Kennedy at juliette.kennedy at he
lsinki.fi
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