Notational Differences

Acta Analytica 35 (2):289-314 (2020)
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Abstract

Expressively equivalent logical languages can enunciate logical notions in notationally diversified ways. Frege’s Begriffsschrift, Peirce’s Existential Graphs, and the notations presented by Wittgenstein in the Tractatus all express the sentential fragment of classical logic, each in its own way. In what sense do expressively equivalent notations differ? According to recent interpretations, Begriffsschrift and Existential Graphs differ from other logical notations because they are capable of “multiple readings.” We refute this interpretation by showing that there are at least three different kinds of such multiple readings. While readings of the first kind do not capture any essential difference among notations but only among vocabularies, corresponding to readings of the second and the third kind two general parameters according to which notations may differ are defined: linearity vs. non-linearity, and tabularity vs. non-tabularity. This answers the question of how there can be substantially different but expressively equivalent logical notations.

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Author Profiles

Ahti-Veikko Pietarinen
Hong Kong Baptist University
Francesco Bellucci
University of Bologna

Citations of this work

Peirce’s Dragon-Head Logic.Minghui Ma & Ahti-Veikko Pietarinen - 2022 - Archive for History of Exact Sciences 76 (3):261-317.
Pragmaticism.Charles S. Peirce - 2024 - De Gruyter.

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References found in this work

Introduction to mathematical logic.Alonzo Church - 1944 - Princeton,: Princeton University Press. Edited by C. Truesdell.
Introduction to mathematical logic..Alonzo Church - 1944 - Princeton,: Princeton university press: London, H. Milford, Oxford university press. Edited by C. Truesdell.
Frege.Michael Dummett - 1975 - Teorema: International Journal of Philosophy 5 (2):149-188.

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