Colloquium Logicae @CLE-Unicamp- Next talk by October 28th, 2020 (4: 00 PM, GMT -3 hours)

[Walter Carnielli]

Dear friends of Logic:
On Wednesday, October 28th, 2020 (4: 00 PM, GMT -3 hours) we will receive

Edward N. Zalta (Senior Research Scholar, Stanford University) and
Uri Nodelman (Senior Research Engineer, Stanford University)
talking about
"Number Theory Without Mathematics"

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 accomodates 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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This is a virtual session of the Colloquium Logicae,traditional
conferences held the Centre for Logic, Epistemology and the History of
Science at Unicamp,now linked to the “Logic Supergroup” organized by
the University of Connecticut Logic Group:
https://logic.uconn.edu/supergroup/

For past and future talks, please visit https://seminarioscle.wordpress.com/
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Permanent link to participate of the seminars:

https://conferenciaweb.rnp.br/spaces/unicamp-cle-colloquium-logicae
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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