Notational Differences

Francesco Bellucci*, Ahti Veikko Pietarinen

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)289-314
Number of pages26
JournalActa Analytica
Issue number2
Publication statusPublished - Jun 2020
Externally publishedYes

Scopus Subject Areas

  • Philosophy

User-Defined Keywords

  • Begriffsschrift
  • Existential graphs
  • Frege
  • Linearity
  • Peirce
  • Philosophy of notation
  • Tabularity
  • Truth-tables
  • Vocabulary
  • Wittgenstein


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