scholarly journals Observações sobre a meta final do modo de fazer filosofia de Ludwig Wittgenstein

2019 ◽  
Vol 22 (3) ◽  
pp. 411-438
Author(s):  
Gustavo Augusto Fonseca

In The Principles of Mechanics, physicist Heinrich Hertz argues that instead of replying to the question “what is force?” like physicists and philosophers had been doing unsuccessfully, Newtonian physics should be reformulated without considering “force” a basic concept. Decades after Hertz’s book, Ludwig Wittgenstein considered the physicist’s proposal a perfect model for how philosophical problems should be solved, to the point that he made it the foundation of his way of doing philosophy. This article addresses Wittgenstein’s way of doing philosophy, while it also proposes the reason why he failed in solving the philosophical problems — as did Hertz in his project on reformulating Newtonian physics without considering the concept “force”. And to illustrate Wittgenstein’s failure, it examines his disputes with mathematicians Kurt Gödel and Alan Turing on the foundations of mathematics.

Author(s):  
Jan von Plato

It may sound paradoxical, but if around 1930 Kurt Gödel had not thought very deeply about the foundations of mathematics, there would be no information society in the form in which we have it today. Gödel’s solitary work was the single most important factor in the development of precise theories of formal languages, ones that through the coding he invented could be handled by a machine. Likewise, his work led to precise notions of algorithmic computability from which a direct path led to the first theoretical ideas of a computer, in the work of Alan Turing in 1936 and John von Neumann some years later....


2018 ◽  
Vol 17 (1) ◽  
pp. 97-113
Author(s):  
Gustavo Augusto Fonseca Silva

No ensaio “Wittgenstein on mathematics”, publicado no Oxford Handbook of Wittgenstein, Michael Potter procura não apenas analisar por que a filosofia da matemática de Wittgenstein é tão controvertida entre filósofos e matemáticos como justificar essa situação. Com esse intuito, Potter enfatiza o caráter inacabado das reflexões de Wittgenstein sobre a matemática. Neste artigo, tem-se por objetivo explicitar algumas inconsistências e contradições no pensamento matemático de Wittgenstein que ratificam as críticas que esse autor vem recebendo há décadas, mas que não tiveram a mesma atenção dos especialistas que os comentários de Wittgenstein sobre os teoremas da incompletude de Kurt Gödel e suas discussões com Alan Turing sobre os fundamentos da matemática.


2014 ◽  
Vol 45 (5) ◽  
pp. 423-439 ◽  
Author(s):  
Louise Amoore

In this article, I explore a specific relation between mathematics and security calculations. Recalling the confrontations between the mathematician Alan Turing and the philosopher Ludwig Wittgenstein in the 1930s, I am interested in the relationship between intuition and ingenuity. During Wittgenstein’s 1930 lectures on the foundations of mathematics, Turing interjects in order to insist upon the capacity of number: ‘one can make predictions’. Wittgenstein replies that mathematics ‘makes no predictions’, but instead is a form of grammar: ‘taken by itself we shouldn’t know what to do with it; it’s useless. But there is all kind of use for it as part of a calculus’. It is just such a formulation of a calculus or grammar – ‘decision trees’, ‘event trees’, ‘attribute-based algorithms’ – that characterizes contemporary security. As for Turing, the logic comprises ‘two faculties, which we may call intuition and ingenuity’. The intuitive realm of imagination and speculation reaches toward a possible solution, while the ingenuity seeks arrangements of propositions. The advent of ‘rules-based’ and ‘risk-based’ security decisions, then, are always already political because they precisely involve combinatorial possibilities whose arrangement has effects in the world.


2019 ◽  
Vol 4 (3) ◽  
Author(s):  
Liesbeth De Mol

It was not Alan Turing or Kurt Gödel, but Emil Post, who reflected most deeply on issues of absolutely unsolvable problems. He proposed an open-ended research program that was abandoned upon his death.


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