{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T05:02:58Z","timestamp":1742965378236,"version":"3.40.3"},"publisher-location":"Cham","reference-count":12,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031712906"},{"type":"electronic","value":"9783031712913"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T00:00:00Z","timestamp":1725840000000},"content-version":"vor","delay-in-days":252,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The theoretical study of Aristotelian diagrams is at an all-time high since the conception of logical geometry. This framework studies Aristotelian diagrams in a systematic way, revealing many links with contemporary mathematics (esp. algebra). Most recently, this has led to the introduction of several notions of morphism between Aristotelian diagrams, which we are studying in the context of category theory. This is not merely a mathematical enterprise, but also carries major philosophical importance. As a proof of concept of this claim, we investigate the historically rich discussion on the status of singular propositions. It has been debated for centuries whether these should be viewed as a special kind of universal propositions or particular propositions, or as a third, completely separate kind. Interpreting each of these views as a morphism in one of our categories, we obtain a clean picture of the entire discussion in a single image. Additionally, we apply the machinery from category theory (in casu, the notion of equalizer) to make some interesting comparative observations regarding the three views on singular propositions.<\/jats:p>","DOI":"10.1007\/978-3-031-71291-3_13","type":"book-chapter","created":{"date-parts":[[2024,9,8]],"date-time":"2024-09-08T14:02:00Z","timestamp":1725804120000},"page":"153-161","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Category Theory for\u00a0Aristotelian Diagrams: The Debate on\u00a0Singular Propositions"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-4906-7130","authenticated-orcid":false,"given":"Alexander","family":"De Klerck","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8955-7945","authenticated-orcid":false,"given":"Leander","family":"Vignero","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0176-1958","authenticated-orcid":false,"given":"Lorenz","family":"Demey","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,9,9]]},"reference":[{"key":"13_CR1","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1007\/s10849-014-9207-y","volume":"23","author":"H Smessaert","year":"2014","unstructured":"Smessaert, H., Demey, L.: Logical geometries and information in the square of oppositions. J. Logic Lang. Inform. 23, 527\u2013565 (2014)","journal-title":"J. Logic Lang. Inform."},{"key":"13_CR2","volume-title":"Studies and Exercises in Formal Logic","author":"JN Keynes","year":"1906","unstructured":"Keynes, J.N.: Studies and Exercises in Formal Logic, 4th edn. MacMillan and Co, New York (1906)","edition":"4"},{"key":"13_CR3","first-page":"218","volume":"10","author":"J-Y B\u00e9ziau","year":"2003","unstructured":"B\u00e9ziau, J.-Y.: New light on the square of oppositions and its nameless corner. Logical Invest. 10, 218\u2013232 (2003)","journal-title":"Logical Invest."},{"key":"13_CR4","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1007\/s10992-017-9430-5","volume":"47","author":"L Demey","year":"2018","unstructured":"Demey, L., Smessaert, H.: Combinatorial bitstring semantics for arbitrary logical fragments. J. Philos. Log. 47, 325\u2013363 (2018)","journal-title":"J. Philos. Log."},{"key":"13_CR5","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/978-3-030-86062-2_20","volume-title":"Diagrammatic Representation and Inference","author":"L Vignero","year":"2021","unstructured":"Vignero, L.: Combining and relating Aristotelian diagrams. In: Basu, A., Stapleton, G., Linker, S., Legg, C., Manalo, E., Viana, P. (eds.) Diagrams 2021. LNCS (LNAI), vol. 12909, pp. 221\u2013228. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-86062-2_20"},{"key":"13_CR6","unstructured":"De Klerck, A., Vignero, L., Demey, L.: Morphisms Between Aristotelian Diagrams. Logica Universalis (forthcoming)"},{"key":"13_CR7","unstructured":"Khomskii, Y.: William of Sherwood, singular propositions and the hexagon of opposition. In: B\u00e9ziau, J.-Y. & Payette, G. (eds.) The Square of Opposition. A General Framework for Cognition, pp. 43\u201360. Peter Lang, Bern (2012)"},{"key":"13_CR8","unstructured":"Englebretsen, G.: Something to Reckon With. The Logic of Terms. University of Ottawa Press, Ottawa (1966)"},{"key":"13_CR9","unstructured":"Quine, W.V.O.: Methods of Logic. Holt, Rinehart and Winston, New York (1966)"},{"key":"13_CR10","unstructured":"Parkinson, G.H.R.: Leibniz. Logical Papers. Oxford Univ. Press, Oxford (1966)"},{"key":"13_CR11","unstructured":"Kretzmann, N. (ed.).: William of Sherwood\u2019s Introduction to Logic. University of Minnesota Press, Minneapolis (1966)"},{"key":"13_CR12","doi-asserted-by":"publisher","first-page":"392","DOI":"10.1093\/mind\/LXIV.255.392","volume":"64","author":"T Cze\u017cowski","year":"1955","unstructured":"Cze\u017cowski, T.: On certain peculiarities of singular propositions. 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