In this paper we will show Peirce's distinction between deduction, induction and abduction. The aim of the paper is to show how Peirce changed his views on the subject, from an understanding of deduction, induction and hypotheses as types of reasoning to understanding them as stages of inquiry very tightly connected. In order to get a better understanding of Peirce's originality on this, we show Peirce's distinctions between qualitative and quantitative induction and between theorematical and corollarial deduction, passing then to the distinction between mathematics and logic. In the end, we propose a sketch of a comparison between Peirce and Whitehead concerning the two thinkers' view of mathematics, hoping that this could point to further inquiries.
Mathematics Subject Classification (2010). Primary 03A10; Secondary 00A30.In natural science this rigid method is the Baconian method of induction, a method which, if consistently pursued, would have left science where it found it. What Bacon omitted was the play of free imagination, controlled by the requirements of coherence and logic. The true method of discovery is like the flight of an aeroplane. It starts from the ground of particular observation; it makes a flight in the thin air of imaginative generalization; and it again lands for renewed observation rendered acute by rational interpretation. Alfred North Whitehead, Process and Reality.
Resenha de Bellucci, Francesco. Charles S. Peirce. Selected Writings on Semiotics, 1894–1912, Berlin, Boston: De Gruyter Mouton, 2020. https://doi.org/10.1515/9783110607390
O objetivo deste artigo é apresentar a leitura crítica feita por Charles S. Peirce (1839-1914) do conceito de indução de Aristóteles, tal como apresentado nos Primeiros analíticos, livro II, capítulo 23. Segundo Peirce, Aristóteles chegou um correto entendimento da indução, dando um exemplo perfeito de raciocínio indutivo em forma silogística. No entanto, o estagirita teria cometido dois equívocos: primeiro, a limitaçãoda indução a um único modo e uma única figura; segundo, a justificação da indução a uma enumeração exaustiva de itens específicos. Na sua crítica, Peirce alega que é possível explicar a indução fazendo uso de outros modos e figuras silogísticas, de modo a justificar outras formas de inferências não dedutivas como Aristóteles não pensara. Além disso, ele rejeita a ideia de uma enumeração completa de itens como a únicaforma de indução, lançando com isso as bases de uma crítica mais ampla a alguns pressupostos da filosofia moderna.
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