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

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.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
DOI 10.1007/s12136-020-00425-1
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 54,431
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

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.

View all 19 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

On the Concept of a Notational Variant.Alexander W. Kocurek - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan). pp. 284-298.
Ontological Pluralism and Notational Variance.Bruno Whittle - forthcoming - Oxford Studies in Metaphysics.
Digital Pictures, Sampling, and Vagueness: The Ontology of Digital Pictures.John Zeimbekis - 2012 - Journal of Aesthetics and Art Criticism 70 (1):43-53.
Notationality and the Information Processing Mind.Vinod Goel - 1991 - Minds and Machines 1 (2):129-166.
Peirce’s Logic.Francesco Bellucci & Ahti-Veikko Pietarinen - 2015 - Internet Encyclopedia of Philosophy.


Added to PP index

Total views
11 ( #780,962 of 2,374,844 )

Recent downloads (6 months)
6 ( #129,977 of 2,374,844 )

How can I increase my downloads?


My notes