A conversation about logic between Frege and Wittgenstein
Keywords:logic, thought, computation, logical alien
This paper begins with a conversation between Frege and Wittgenstein. Frege speaks first, advancing his point of view on the foundations of logic. Then, Wittgenstein replies in three moments: (a) first he plays with Frege’s ideas to examine their meaning, (b) then he begins to disclose his own ideas about logic, which challenge Frege’s point of view, (c) and finally, he manages to find an agreement with Frege, leaving a puzzle for us: the idea of a technique of thinking. Then it is our turn to enter the conversation, and our participation unfolds in two moments: (a) first we introduce Turing’s ideas to articulate the notion of a two levers mechanism, (b) and then we sketch an understanding of Wittgenstein’s technique of thinking in terms of this mechanism.
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Wittgenstein, L. 1967 [1937-44]. Bemerkungen Über die Grundlagen der Mathematik. Cambridge, Massachusetts and London: The MIT Press.
Wittgenstein, L. 2012 [1949-50]. Da Certeza. Tradução de Maria Elisa Costa. Lisboa: Edições 70.
Wang, H. 2016. From Mathematics to Philosophy. New York: Routledge.
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