Synthese:1-22 (forthcoming)

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Abstract
This paper provides an analysis of the notational difference between Beta Existential Graphs, the graphical notation for quantificational logic invented by Charles S. Peirce at the end of the 19th century, and the ordinary notation of first-order logic. Peirce thought his graphs to be “more diagrammatic” than equivalently expressive languages for quantificational logic. The reason of this, he claimed, is that less room is afforded in Existential Graphs than in equivalently expressive languages for different ways of representing the same fact. The reason of this, in turn, is that Existential Graphs are a non-linear, occurrence-referential notation. As a non-linear notation, each graph corresponds to a class of logically equivalent but syntactically distinct sentences of the ordinary notation of first-order logic that are obtained by permuting those elements that in the graphs lie in the same area. As an occurrence-referential notation, each Beta graph corresponds to a class of logically equivalent but syntactically distinct sentences of the ordinary notation of first-order logic in which the identity of reference of two or more variables is asserted. In brief, Peirce’s graphs are more diagrammatic than the linear, type-referential notation of first-order logic because the function that translates the latter to the graphs does not define isomorphism between the two notations.
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DOI 10.1007/s11229-021-03134-3
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References found in this work BETA

The Nature and Structure of Content.Jeffrey C. King - 2007 - Oxford University Press.
Mathematical Logic.W. V. Quine - 1940 - Cambridge: Harvard University Press.
Frege: Philosophy of Language.Michael Dummett - 1973 - Philosophy 49 (190):438-442.
Facts and Propositions.F. P. Ramsey - 1927 - Aristotelian Society Supplementary Volume 7 (1):153-170.
Frege.Michael Dummett - 1975 - Teorema: International Journal of Philosophy 5 (2):149-188.

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