Icons of Thought. On Peirce’s conception of proof

JAVIER LEGRIS

SALVADOR, BA

Congreso; XV Colóquio Conesul de Filosofías das Ciências Formais. Filosofia da Prática Matemática; 2011

UNIVERSIDAD FEDERAL DE BAHIA

@font-face { font-family: "Times New Roman"; }@font-face { font-family: "Tahoma"; }p.MsoNormal, li.MsoNormal, div.MsoNormal { margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: Tahoma; }table.MsoNormalTable { font-size: 10pt; font-family: "Times New Roman"; }div.Section1 { page: Section1; } Charles Sanders Peirce was undoubtedly one of the grounding fathers of mathematical logic. He developed in an algebraic framework a prototype of what is now called First Order Logic. Now, due to philosophical reasons (the same reasons that led him to his semiotic theory), he became dissatisfied with the algebraic notation for logic, so that he developed a diagrammatic or graphic system for logic: his existential graphs. This diagrammatic system has an iconic function with respect to deduction: It represents “the course of thinking”. According to Peirce, icons are characterized not only by being similar to their objects, but also as by being manipulated in order to obtain information concerning their denotation. Thus, deduction is the construction of an icon or diagram, whose relations correspond to the relations in the ‘object of thinking’. Peirce’s conception was in fact a consequence of his own idea of mathematical proof and mathematical practice. As a consequence, logic is not necessarily related to language.