Edward Zalta & Uri Nodelman - October 28th -Colloquium Logicae @CLE-Unicamp

[Walter Alexandre Carnielli]

Dear joyfull logicians and enthusiasts of logic:

The Colloquium Logicae, traditional conferences held the Centre for Logic,
Epistemology and the History of Science at Unicamp,now linked to the
“Logic Supergroup
https://logic.uconn.edu/supergroup/ is glad to announce its

NEXT TALK:
"Number Theory Without Mathematics"
Edward N. Zalta (Senior Research Scholar, Stanford University)
Uri Nodelman (Senior Research Engineer, Stanford University)

Wednesday, October 28h, 2020, 16:00 São Paulo/Brasília time
(4:00PM, GMT -3 hours)

Permanent link to participate:
https://conferenciaweb.rnp.br/spaces/unicamp-cle-colloquium-logicae

Abstract: No specifically mathematical primitives or axioms are
required to derive second order Peano Arithmetic (PA2) or to prove the
existence of an infinite cardinal. We establish this by improving and
extending the results of Zalta 1999 ("Natural Numbers and Natural
Cardinals as Abstract Objects", J. Philosophical Logic, 28(6):
619-660), in which the Dedekind-Peano axioms for number theory were
derived in an extension of object theory. We improve the results by
developing a Fregean approach to numbers that accommodates a modal
setting, yielding numbers that are stable across possible worlds, even
though the equivalence classes of equinumerous properties vary. To
extend the results, we (a) prove a Recursion theorem (which shows that
recursive functions are relations grounded in second-order
comprehension), (b) derive PA2, and (c) re-derive the existence of an
infinite cardinal and (d) derive the existence of an infinite set
(where sets are defined as non-mathematical extensions of properties).
Since the background framework of object theory has no mathematical
primitives and no mathematical axioms, we have a mathematics-free
foundation for number theory.
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For past and future talks, please visit https://seminarioscle.wordpress.com/



Walter Carnielli
https://waltercarnielli.com/
Centre for Logic, Epistemology and the History of Science and
Department of Philosophy
University of Campinas –UNICAMP
13083-859 Campinas -SP, Brazil

[Walter Alexandre Carnielli]

Dear spirited logicians and friends of logic:

The Colloquium Logicae, traditional conferences held at the Centre for Logic,
Epistemology and the History of Science at Unicamp now linked to the

“Logic Supergroup https://logic.uconn.edu/supergroup/ is glad to
announce its

NEXT TALK:

"Generalized topological semantics for weak negations and applications
to the analysis of Gödel's incompleteness theorem"
by David Fuenmayor, PhD candidate, Freie Universität Berlin, Germany
Visiting Researcher, Centre for Logic, Epistemology and the History
of Science, Unicamp, Brazil

Wednesday, December 2nd, 2020, 16:00 São Paulo/Brasília time


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Permanent link to participate:
https://conferenciaweb.rnp.br/spaces/unicamp-cle-colloquium-logicae

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"Generalized topological semantics for weak negations and applications
to the analysis of Gödel's incompleteness theorem"

Abstract: This talk is divided into two parts. First, I introduce a
sort of generalized topological semantics for paraconsistent and
paracomplete (e.g. intuitionistic) logics by drawing upon early works
on topological Boolean algebras (cf. Kuratowski, Zarycki, McKinsey &
Tarski). In the second part, I present some preliminary joint work
with Walter Carnielli [1] which formalizes the 'last mile' of the
proof of Gödel's incompleteness theorem using some weak paraconsistent
Logics of Formal Inconsistency (a special case of the logics discussed
in the first part). All presented results have been obtained with help
of the proof assistant Isabelle/HOL. The idea is to motivate a
(hopefully lively) discussion on the use of automated reasoning with
non-classical logics in the formalization and (re)interpretation of
influential meta-mathematical results.

[1] W. Carnielli, D. Fuenmayor (2020). Gödel blooming: the
incompleteness theorems from a paraconsistent perspective. Preprint.
Vol. 19 No. 4 (2020) CLE e-prints
(https://www.cle.unicamp.br/eprints/index.php/CLE_e-Prints/issue/view/243)
======================================================

For past and future talks, please visit https://seminarioscle.wordpress.com/

==========================
Walter Carnielli, Professor

Centre for Logic, Epistemology and the History of Science and
Department of Philosophy
University of Campinas –UNICAMP
13083-859 Campinas -SP, Brazil

Phone: (+55) (19) 3521-6517
Institutional e-mail: walter.c...@cle.unicamp.br
Website: http://www.cle.unicamp.br/prof/carnielli