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EXISTENTIAL GRAPHS AS AN INSTRUMENT OF LOGICAL ANALYSIS: PART I. ALPHA

Published online by Cambridge University Press:  26 February 2016

FRANCESCO BELLUCCI  and
AHTI-VEIKKO PIETARINEN
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Abstract

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Peirce considered the principal business of logic to be the analysis of reasoning. He argued that the diagrammatic system of Existential Graphs, which he had invented in 1896, carries the logical analysis of reasoning to the furthest point possible. The present paper investigates the analytic virtues of the Alpha part of the system, which corresponds to the sentential calculus. We examine Peirce’s proposal that the relation of illation is the primitive relation of logic and defend the view that this idea constitutes the fundamental motive of philosophy of notation both in algebraic and graphical logic. We explain how in his algebras and graphs Peirce arrived at a unifying notation for logical constants that represent both truth-function and scope. Finally, we show that Shin’s argument for multiple readings of Alpha graphs is circular.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 2 , June 2016 , pp. 209 - 237
Copyright
Copyright © Association for Symbolic Logic 2016 

References

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