3 Pláticas impartidas por el Prof. Meir Buzaglo de la Univ. Hebrea en Jerusalén, Israel (actualmente visitando la Univ. de Rutgers en EU). Dos de las pláticas, sobre las matemáticas de paradojas, estan dirgidas principalmente a nuestros alumnos de licenciatura (pero todos invitados). La tercera plática, sobre el teorema de Goedel, sera en forma de coloquio en el depto de filosofia de la UG, al cual todos los interesados del CIMAT/FAMAT estan también cordialmente invitados. Las pláticas estan en inglés.

"The Mathematics of Paradoxes"

Martes 6; Primera plática

Lugar: Salón Diego Bricio Hernández
Hora: 16:30 Hrs.

Miércoles 7; Segunda plática

Lugar: Salón Diego Bricio Hernández
Hora: 17:30 Hrs.
Abstract: These are 2 lectures for general math audience (principaly undergraduate students) on the phenomenon of paradoxes in mathematics and their treatment by formalizing the notion of "concept expansion". Most mathematical fundamental notions were subject to the process of concept expansion (such as passing from natural to rational numbers, then real, complex, etc). There is a long tradition, starting from Kant and continuing with Russell, Hilbert and Goedel, that paradoxes are the result of expansion of concepts beyond their legitimate domains. In the first lecture I will give few characteristics of this process as well as presenting a logic that study the structure of "non-arbitrary expansions". In the second lecture I explore the application of this logic of expansions to the study of paradoxes as an alternative to getting rid of them (as we do in axiomatic set theories). These lectures present a dialogue with Frege, the founder of modern logic, as he thought that no logic can study expansions of concepts but was shocked by the paradoxes in set theory. Had he adopted the possibility of expansions he might have found an answer to the paradoxes.

"Goedel's Theorem"

Miércoles 7

Lugar: Auditorio de la facultad de filosofia de la UG (abajo del templo de la Valenciana)
Hora: 12:30 Hrs.
Abstract: In this lecture I wish to introduce Goedel's incompleteness theorem for the non-experts (both mathematicians and non-mathematicians). After introducing the theorem I will explain the main insight behind the proof as well as its significance.