Bridging from Semiotics to Logical Deduction

Bridging from Semiotics to Logical Deduction

Alfred Olszok

Prior to the split up of European philosophy into continental and analytical, research on intersecting matters was much more common. One of these investigations will be the content of my talk: The logic of Charles Sanders Peirce. Shortly before the split up of philosophy, at the end of the 19th century, he developed the Existential Graphs. These are rooted solely in his semiotics, but nowadays, we would call them a system of logical deduction. Later on, many dierent kinds of such graphs were examined and developed, including classical, many valued, modal and intuitionistic. Although the origin of the graphs is of a philosophical nature, all of them satisfy many important formal logical standards: they are sound as well as complete, the modus ponens does hold, and much more. Therefrom follows a simple question, which shall be the linchpin of my talk: How can semiotics bridge to impeccable systems of logical deduction? To try my hand at answering this, I will present two topics in short:

1) the semiotics of C. S. Peirce and[3]

2) Existential Graphs for classical propositional logic.

On closer inspection, it becomes visible that 1) can verify how the signs of 2) are written. Furthermore, it is noticeable that one sign stands in the center of all Existential Graphs: the sheet of assertion (hereafter, SA). This is basically the sheet of paper on which a proof is written. By investigating how semiotics justies the SA, it can be shown that this semiotic justication leads directly to a sign, which is central to logical deduction. Therefor two perspectives are relevant:

A) the semiotic justication of the SA and

B) the logical interpretation of the SA.

By showing how A) leads to B) I hope to clarify, that semiotics can bridge to logic in a way, which is nowadays  due to the regrettable split up of philosophy in the early 20th century  heavily underestimated.