Peirce between Frege and Boole: on the search for possible dialogues with Wittgenstein

Abstract

This article seeks to discuss the position of Charles Sanders Peirce and his first students of Logic (Christine Ladd and O. H. Mitchell in “Studies in Logic”, 1883) in the debate which inspired the vision of language in Analytic Philosophy known as “Lingua Universalis vs. Calculus Ratiocinator”, whose origins can be traced back to the philosophy of Gottfried Leibniz. To do so, we will compare this field of the Peircean thought with the crucial debate between Gottlob Frege’s concept-script (Begriffsschrift, 1879) and George Boole’s algebraic logic (An investigation of the Laws of Thought on which are founded the mathematical theories of Logic and Probabilities, 1854). Our main goal is to see that this moment of Peircean philosophy can be compared with the Wittgensteinian thought, especially in its new interpretation, called “New Wittgenstein”, which tries to overcome the traditional division between “Tractatus Logico-Philosophicus” and “Philosophical Investigations”. Through this comparison between thinkers influenced by C. S. Peirce and the philosophy of Ludwig Wittgenstein, we will be able to open our search for ways to understand the concept of language-game, especially in its grammar and its symbolic operators, through the observation of the truth functions and truth tables as algebraic logic.