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(2015) Synthese 192 (4).
The theory of existential graphs, which Peirce ultimately divided into four quadrants ((upalpha , upbeta , upgamma ) and (updelta )), is a rich method of analysis in the philosophy of logic. Its (upbeta )-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 (upbeta )-quadrant, he came close to inventing independence-friendly logic, the idea of which he found indispensable in fulfilling the tasks (i)–(iii).
Publication details
DOI: 10.1007/s11229-015-0677-5
Full citation:
Pietarinen, A. J. (2015). Exploring the beta quadrant. Synthese 192 (4), pp. 941-970.
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