Gisele D Secco

The Four-Colour Theorem (4CT) proof, presented to the mathematical community in a pair of papers by Appel and Haken in the late 1970's, provoked a series of philosophical debates. Many conceptual points of these disputes still require some elucidation. After a brief presentation of the main ideas of Appel and Haken’s procedure for the proof and a reconstruction of Thomas Tymoczko’s argument for the novelty of 4CT’s proof, we shall formulate some questions regarding the connections between the points raised by Tymoczko and some Wittgensteinian topics in the philosophy of mathematics such as the importance of the surveyability as a criterion for distinguishing mathematical proofs from empirical experiments. Our aim is to show that the “characteristic Wittgensteinian invention” (Mühlhölzer 2006) – the strong distinction between proofs and experiments – can shed some light in the conceptual confusions surrounding the Four-Colour Theorem.

Departing from and closing with reflections on issues regarding teaching practices of philosophy of mathematics, I propose a comparison between the main features of the Leibnizian notion of symbolic knowledge and some passages from the Tractatus on arithmetic. I argue that this reading allows (i) to shed a new light on the specificities of the Tractarian definition of number, compared to those of Frege and Russell; (ii) to highlight the understanding of the nature of mathematical knowledge as symbolic or formal knowledge that Wittgenstein mobilizes in his book; (iii) to offer reasons for the claim that Wittgenstein can be considered the philosopher of mathematical practice avant la lettre. The paper ends with an overview, a return to the initial reflection on the connections between research and teaching, and a defense of the reading key used here in terms of its potential for the research in philosophy of mathematics.

O texto fornece distinções conceituais engendradas desde uma perspectiva para o ensino de filosofia que contempla, em seu horizonte, o projeto a construção de uma didática mínima da lógica para o ensino médio. Após a apresentação de alguns aspectos positivos da referida perspectiva são indicadas duas maneiras usuais de compreender e praticar o ensino de lógica. O objetivo central do texto é mostrar como, desde a perspectiva inicialmente esboçada, os esclarecimentos conceituais propostos podem sugerir caminhos interdisciplinares para a didática da lógica sem perda da especificidade da disciplina. The text provides some conceptual distinctions generated from a perspective on teaching philosophy according to which the project of a "didactica minima" for logic in high schools is contemplated. After a brief presentation of some positive aspects of the perspective from which the distinctions are proposed, two common ways of teaching logic are considered. The aim of the paper is to show how the perspective proposed can clarify some topics on the issue of teaching logic in an interdisciplinary way, without losing the specifics of the discipline.

This note presents an analysis of Symbolic Knowledge from Leibniz to Husserl, a collection of works from some members of The Southern Cone Group for the Philosophy of Formal Sciences. The volume delineates an outlook of the philosophical treatments presented by Leibniz, Kant, Frege, and the Booleans, as well as by Husserl, of some questions related to the conceptual singularities of symbolic knowledge –whose standard we find in the arts of algebra and arithmetic. The book’s unity of themes and (at least in part) style is examined with the aim of showing the articulation of its parts.

We offer a reading of some passages from Wittgenstein’s Tractatus Logico-Philosophicus in which, dealing with the symbolic constructions of arithmetic, Wittgenstein puts in motion the most outstanding features of Leibniz’s concept of Symbolic Knowledge: the computational and the “ecthetic” functions of the notion of Symbolic Blind Though. We begin with a brief presentation of some conceptual distinctions proposed by Oscar Miguel Esquisabel in his investigation about the Leibnizian origin of the tradition of Symbolic Knowledge. We then contrast these topics with the way Pasquale Frascolla interprets those same Tractarian passages, emphasizing the way in which he suspends any relevant sense in which we could speak about formal knowledge in Wittgenstein’s opera. To make our criticism better suited, our projection of Leibnizian lights into the Tractatus and into Frascolla’s interpretation of it is assisted with a concise exposition of one historical development in the Leibnizian tradition. Grounded in a study in which Javier Legris retraces the features of Symbolic Blind Though in Frege’s works, we then conclude proposing the advantages of our approach.

Este livro apresenta-se como o resultado da contribuição de professores e pesquisadores de diversos campos da filosofia e de diferentes universidades brasileiras durante a ocasião do I Encontro "Vozes femininas na Filosofia", ocorrido em junho de 2017, na UFRGS, em Porto Alegre, RS. Nossa motivação parte da constatação que a área de filosofia nas universidades brasileiras sofre uma evidente crise de representatividade: tanto nos cursos de graduação como nos programas de pós-graduação em filosofia, nos quais menos de 30% são mulheres, entre docentes e discentes. Procura-se, por meio dos textos organizados neste volume, entender a produção e a contribuição de filósofas cujas presenças se mostram diminuídas – senão totalmente esquecidas – na história de filosofia e na atualidade.

O verbete que ora apresentamos em tradução para a língua portuguesa foi originalmente publicado por Marianne Janack na Internet Encyclopedia of Philosophy. Seu principal objetivo é apresentar um mapeamento da subárea de pesquisa denominada “epistemologia feminista” detalhando algumas de suas principais abordagens. A autora mostra que existem diversas epistemologias feministas cujo traço em comum é o uso da noção de gênero como categoria fulcral de análise das modalidades de conhecimento, suas interações, hierarquizações e relações com a esfera propriamente normativa ou valorativa da vida humana.