TY - JOUR
T1 - Exploring the beta quadrant
AU - Pietarinen, Ahti Veikko
N1 - Funding Information:
Supported by DiaMind (The Diagrammatic Mind: Logical and Communicative Aspects of Iconicity, Estonian Research Council PUT267, 2013–2015 and the Academy of Finland 12786, 2013–2017, Principle Investigator A.-V. Pietarinen). Earlier versions were presented in the Peirce and Early Analytic Philosophy Symposium, University of Helsinki, May 2009, and in Logic Now & Then conference in Brussels in December 2011. Writing up of the final version was supported by the 2014 High-End Foreign Experts Program of State Administration of Foreign Experts Affairs, P. R. China. I thank the participants of these events and the reviewers of the present journal for helpful questions and comments.
Publisher Copyright:
© 2015, Springer Science Business Media Dordrecht
PY - 2015/4
Y1 - 2015/4
N2 - 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).
AB - 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).
KW - Beta
KW - Existential graphs
KW - Independence-friendly logic
KW - Linguistic analysis
KW - Philosophy of notation
KW - Quantifiers
UR - http://www.scopus.com/inward/record.url?scp=84940003591&partnerID=8YFLogxK
U2 - 10.1007/s11229-015-0677-5
DO - 10.1007/s11229-015-0677-5
M3 - Journal article
AN - SCOPUS:84940003591
SN - 0039-7857
VL - 192
SP - 941
EP - 970
JO - Synthese
JF - Synthese
IS - 4
ER -