Exploring the beta quadrant

Ahti Veikko Pietarinen*

*Corresponding author for this work

    Research output: Contribution to journalJournal articlepeer-review

    28 Citations (Scopus)

    Abstract

    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
    JournalSynthese
    Volume192
    Issue number4
    DOIs
    Publication statusPublished - Apr 2015

    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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