Conhecimento simbólico em John Venn

Abstract

This dissertation presents a reconstruction of John Venn s (1834-1923) logical theory in Symbolic Logic (1881; 1894). In his work, Venn presents an algebra of logic, and faces a number of philosophical problems underlying this symbolic logic. Firstly, Venn needs to consider the relation between symbolic logic and traditional logic, i.e., Syllogistic. Secondly, Venn needs to consider the relation between symbolic logic and Mathematics. In treating these issues, Venn will have to reflect upon a number of philosophical notions concerning the nature of symbolic knowledge. The objective of this dissertation is to present Venn s treatment to the concept of symbolic knowledge. Throughout the research, it is shown that according to Venn s point of view the algebra of logic is a formal generalization of Syllogistic. Such formal generalization is possible due to the ecthetic function algebraic symbols perform in logical representation. Furthermore, according to Venn, the logic represented by his algebraic symbolism can be precisely differentiated from Mathematics. Such differencing is possible due to the reflection upon the different modes in which algebraic symbolism performs the subrogative function of symbolic knowledge. This dissertation achieves twofold results. On the one hand, it achieves a historiographically important result, for it permits the determination of the locus of Venn s work among the efforts of logical symbolization in the Nineteenth century. On the other, it achieves a philosophical result insofar it permits, through the analysis of a historical case, to clarify key-notions of symbolic knowledge. Venn is more recognized for the creation of Venn diagrams than for his work in the algebra of logic, however, Venn doesn t elaborate much any systematic reflection upon the nature of graphic knowledge. Nevertheless, the research of Venn s work in the algebra of logic provides results concerning the nature of Venn diagrams, which are here presented as a secondary issue.