The God-given Naturals: Induction and Recursion

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Capa edição 49
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Published: Jan 15, 2022
DOI: https://doi.org/10.32334/oqnfp.2021n49a804
Keywords:
Naturals, induction, recursion, parameters, universal properties, particular properties

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Paulo Veloso
Universidade Federal do Rio de Janeiro (UFRJ)
André da Silva Porto
Universidade Federal de Goiás (UFG)

Abstract

We discuss some basic issues underlying the natural numbers: induction and recursion. We examine recursive formulations and their use in establishing universal and particular properties.

Article Details

Issue
Vol. 29 No. 49 (2021): Logic, Philosophy and Computing: contemporary interactions
Section
Articles

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Author Biographies

Paulo Veloso, Universidade Federal do Rio de Janeiro (UFRJ)

IN MEMORIM

André da Silva Porto, Universidade Federal de Goiás (UFG)

Professor Associado da Universidade Federal de Goiás (UFG, Brasil), Pesquisador do CNPq nível 2. Prof. Porto é especialista em Wittgenstein e em Fundamentos da Matemática. Suas áreas principais de interesse incluem a Construtivismo, Intuicionismo, Teoria dos Tipos e e verficação automática de provas. Além dessa área prioritária de pesquisa, ele também tem se dedicado ao tratamento que Wittgenstein dá à Subjetividade.

References

ENDERTON, Herbert B. - A Mathematical Introduction to Logic. New York: Academic Press, 1972.
POLYA, G. - How to Solve it: a new aspect of the mathematical method. Princeton: Princeton Univ. Press, 1945 (2nd edition 1956, repr. 1971).
PORTO, Andr´e S. - Wittgenstein sobre as provas indutivas, 2009.
SHOENFIELD, Joseph R. - Mathematical Logic. Reading: Addison-Wesley, 1967.