Banca de DEFESA: José Henrique Fonseca Franco

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : José Henrique Fonseca Franco
DATE: 24/02/2022
TIME: 14:00
LOCAL: UFSJ
TITLE:

The implications of Gödel's incompleteness theorems in the philosophy of mathematics

KEY WORDS:

Philosophy of Mathematics. Notion of Consistency. Formal Systems. Arithmetic Theories. Epistemology.

PAGES: 110
BIG AREA: Ciências Humanas
AREA: Filosofia
SUBÁREA: Lógica
SUMMARY:

The foundation of mathematics is a question that concerned logicians, mathematicians and philosophers in the late 19th and early 20th centuries. In this debate, the formalist strand emerges as an especially promising alternative. Hilbert's formalism conferred autonomy on mathematics, since his program conceived mathematics as a set of rules. Hilbert's axiomatization increasingly conferred independence of mathematical activity in relation to intuition, evidencing its logical-deductive aspect. Gödel's incompleteness theorems reveal, however, the difficulties of implementing the formalist project, since the incompleteness of arithmetical theories opens a kind of gap between arithmetic rules and truths. In general, Gödel's theorems show that in formal systems such as Russell's and Whitehead's Principia Mathematica, if the arithmetic is consistent it cannot be complete, that is, there are arithmetic statements that cannot be proved or disproved. This leads us to reflect on the philosophical assumptions of foundationalist currents, especially logicism and formalism. In this sense, our objective here was to present the main foundationalist currents of the philosophy of mathematics, that is, logicism, intuitionism and formalism, emphasizing the formalist program. From the consequences for the Hilbertian formalism through the presentation of Gödel's incompleteness theorems, we draw a parallel with the objectives of the functionalist program in the philosophy of mind, thus highlighting relevant aspects of the epistemology of mathematics.

BANKING MEMBERS:
Interno - 2124075 - RODRIGO AZEVEDO DOS SANTOS GOUVEA
Interno - 1550948 - MARCO AURELIO SOUSA ALVES
Externo à Instituição - GUILHERME ARAÚJO CARDOSO - UFOP
Externo à Instituição - HENRIQUE ANTUNES ALMEIDA - UFMG