Peirce's Arrow and Satzsystem: A Logical View for the Language-Game
Keywords:C. S. Peirce, Ludwig Wittgenstein, Logic, Language-game
This article is an effort to understand how the Peirce's Arrow (Logical NOR), as a logical operation, can act within the concept of Ludwig Wittgenstein's language-game, considering that the language game is a satzsystem, i.e., a system of propositions. To accomplish this task, we will cover four steps: (1) understand the possible relationship of the thought of C. S. Peirce with the founding trio of analytic philosophy, namely Frege-Russell-Wittgenstein, looking for similarities between the logic of Peirce and his students (notably Christine Ladd and O.H. Mitchell) with a New Wittgensteinâ€™s approach, which sees Early Wittgenstein (Tractatus Logico-Philosophicus), Middle Wittgenstein and Last Wittgenstein (Philosophical Investigations) while a coherent way of thinking and not a theoretical break; (2) describe the operation of the Peirceâ€™s Arrow (Logical NOR) as a logical connective; (3) understand the notion of satzsystem (Middle Wittgenstein) and the possibility of applying the concept of language-game (Last Wittgenstein) on it; and (4) understand how the Logical NOR can operate within a satzsystem. The goal here is a search for the logic of the language-game and how the logical ideas of C. S. Peirce can help in this construction. And this construction might be interesting for a better understanding of the analytic philosophy of language.
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