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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DOI 10.1007/s12136-020-00425-1
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References found in this work BETA

Basic Laws of Arithmetic.Philip A. Ebert & Marcus Rossberg (eds.) - 2013 - Oxford University Press UK.
Introduction to Mathematical Logic.ALONZO CHURCH - 1944 - London: Oxford University PRess.
Frege.Michael Dummett - 1973 - Teorema: International Journal of Philosophy 5 (2):149-188.
Frege’s Logic.Danielle Macbeth - 2005 - Harvard University Press.

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