Exploring the beta quadrant

Ahti Veikko Pietarinen*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

25 Citations (Scopus)


The theory of existential graphs, which Peirce ultimately divided into four quadrants (α,β,γ and δ), is a rich method of analysis in the philosophy of logic. Its β-part boasts a diagrammatic theory of quantification, which by 1902 Peirce had used in the logical analysis of (i) natural-language expressions such as complex donkey-type anaphora, (ii) quantificational patterns describing new mathematical concepts, and (iii) cognitive information processing. In the β-quadrant, he came close to inventing independence-friendly logic, the idea of which he found indispensable in fulfilling the tasks (i)–(iii).
Original languageEnglish
Pages (from-to)941-970
Number of pages30
Issue number4
Publication statusPublished - Apr 2015
Externally publishedYes

Scopus Subject Areas

  • Philosophy
  • Social Sciences(all)

User-Defined Keywords

  • Beta
  • Existential graphs
  • Independence-friendly logic
  • Linguistic analysis
  • Philosophy of notation
  • Quantifiers


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