Logic List Mailing Archive

CfR: Workshop on Generality and Impredicativity, 26 February 2025, Vita-Salute San Raffaele University (Italy)

Workshop Generality and Impredicativity
February 26th 2025

Vita-Salute San Raffaele University
Campus Mi2 - Donatello building<https://www.unisr.it/en/ateneo/universita/s
edi> - Room DO 206
MTeams link<https://teams.microsoft.com/l/meetup-join/19%3ameeting_OGI0ZjY1
ZTAtNDc5OC00ZWFiLTk0MzYtMWM5MzRlMTVkOTYz%40thread.v2/0?context=%7b%22Tid%
22%3a%22332da351-3370-4472-aaf7-a03b2c9f58f8%22%2c%22Oid%22%3a%22b8e268e0-0
708-4a00-b8e1-cdeefb6c82d2%22%7d>


The workshop will investigate the interconnections between different notion
s of generality and the impredicativity/predicativity divide.

The opposition between predicative and impredicative reasoning is a standar
d and contemporary topic in the philosophy of mathematics. Some of its cent
ral questions are: In what way is impredicative reasoning (actually) proble
matic? And how do we demarcate predicative from impredicative reasoning?

One central aspect in this regard is the notion of generality involved. Rec
ently, questions of generality have been discussed in the debate on absolut
e generality, which does not seem to license the standard domain based acco
unt of quantification. In light of this, notions such as instance based, ge
neric, and schematic generality have been differentiated, and the respectiv
e logic and forms of comprehension that they license investigated.

The workshop aims at discussing possible applications of these notions of g
enerality to the problem of impredicativity. Can previously existing proble
ms with impredicativity be resolved when changing the notion of generality 
involved? And how do these notions of generality affect the way we draw the
 distinction between predicativity and impredicativity in the first place?


Programme

9.00-10.00 Crispin Wright (University of Stirling) - online: Is classical s
econd-order logic with full comprehension a fitting proof-theory for the ep
istemological ambitions of neo-logicism about arithmetic?
10.00-11.00 Francisca Silva (University of St Andrews): Impredicativity and
 grounding

11.00-11.30 Coffee break

11.30-12.30 Laura Crosilla (University of Florence): Hermann Weyl, predicat
ivity and generality

12.30-14.00 Lunch break

14.00-15.00 Ludovica Conti (University of Vienna): Impredicativity, general
ity, and abstraction
15.00-16.00 Simon Schmitt (University of Turin): Unfolding unfolding. A con
structivist approach to potentialism

16.00-16.30 Coffee break

16.30-17.30 Davide Sutto (University of Oslo) - online: Squeezing the predi
cative juice out of Gdel's constructible universe
17.30-18.30 ystein Linnebo (University of Oslo): Non-instantial generali
ty and Frege's theorem



Funded by PNRR - Next Generation EU, Mission 4 Component 2 Investment 1.1. 
Proj. 2022TYNY32 Proof and Understanding in Mathematics (PUMa). Purity of m
ethods, simplicity, and explanation in mathematical reasoning. CUP: D53D230
09890008
With the support of The Center for Experimental and Applied Epistemology CR
ESA, Vita-Salute San Raffaele PhD program in Philosophy, and the Division o
f Logic, Methodology and Philosophy of Science and Technology DLMPST
Under the auspices of the Italian Network for the Philosophy of Mathematics
 FilMat and of the Italian Society for Logic and Philosophy of Science SILFS

Organizers: Francesca Boccuni & Jann Paul Engler (Vita-Salute San Raffaele 
University)

Everyone is welcome (whether in person or online)!

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