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. =================================== 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 -- Você está recebendo esta mensagem porque se inscreveu no grupo "LOGICA-L" dos Grupos do Google. Para cancelar inscrição nesse grupo e parar de receber e-mails dele, envie um e-mail para logica-l+unsubscr...@dimap.ufrn.br. Para ver esta discussão na web, acesse https://groups.google.com/a/dimap.ufrn.br/d/msgid/logica-l/CAOrCsLcCq9oGCq3O7iOSfeANravFRoqjf%2B-gM4C_cre%3DRD41sg%40mail.gmail.com.
