Leo's Links on the Logical Hexagon POSTED in HR 788 10/24/23
Links on the Logical Hexagon
POSTED in HR 788 10/24/23:
My father contributed to the recovery of the implicit HEXOGONAL structure of Aristotelian logic - another aspect of ancient Greece legacy.
See this article: ::https://poj.peeters-leuven.be/content.php?url=article&id=3149529&journal_code=LEA:: (The Square of Opposition in Catholic Hands: A Chapter in the History of 20th-Century Logic by JASPERS, Dany , SEUREN, Pieter A.M. in Logique et Analyse Vol. 233 2016 "restore traditional predicate logic to a position of respectability by expanding the classic Square of Opposition to a hexagon of logical relations, showing the logical and cognitive advantages of such an expansion.)
Google "logical hexagon Jacoby"for more, eg.: ::https://oppositionalgeometryblog.wordpress.com/2015/09/30/paul-jacoby/::
MORE LINKS NOT POSTED in HR:
> ::https://logicalgeometry.org/assets/pdf/Smessaert_Demey_Diagrams2014_Complementarities_preprint.pdf::
> ::https://logicalgeometry.org/:: (mission: "...to develop an interdisciplinary framework for the study of logical diagrams in the analysis of logical, linguistic and conceptual systems.
> ::https://logicalgeometry.org/diagrams/three_dimensional::
> ::https://www.researchgate.net/figure/Three-Aristotelian-hexagons-for-S5-a-strong-Jacoby-Sesmat-Blanche-JSB-b_fig3_314472210:: (citations on logcial geometry)
> ::https://typeset.io/topics/logical-hexagon-1nn9azjh:: (Logical hexagon as a research topic)
> ::https://dl.acm.org/doi/10.1007/s10849-014-9207-y:: (Logical Geometries and Information in the Square of Oppositions by Hans Smessaert, Lorenz Demey 2014 includes references and citations)
> ::https://arxiv.org/abs/2303.06498:: (Nelson's Logical Diagrams by Andrew Aberdein 11 Mar 2023 "similar diagrams by the German philosopher Leonard Nelson (1882-1927).... significance of Nelson's work for the history of the JSB hexagon and for logical geometry more widely.")
> ::https://anapavlovic.com/2014/06/13/logical-hexagon/::
> ::https://en.wikipedia.org/wiki/Logical_hexagon::
> ::https://reknew.org/2020/01/the-logical-hexagon-made-simple/::
> ::https://www.academia.edu/27598070/Why_the_Logical_Hexagon:: (Alessio Moretti 2012, Logica Universalis)
> ::https://www.youtube.com/watch?v=nNnfGa3kjQs:: (3:51 The Deontic Hexagon of Opposition)
> ::https://logica-universalis.org/HEXAG.html:: (This issue is connected with the second world congress on the square of opposition which was organized in Corsica, June 17-20, 2010)
> ::https://dj60.be/wp-content/uploads/2018/01/potssonnaert.pdf:: (The Kite of Dany-ness by Cora Pots & Jolijn Sonnaert 7 pp. -- cf. > ::https://en.wikipedia.org/wiki/Heptahedron::)
ADDED
> ::https://www.researchgate.net/figure/Basic-natural-quantificational-logic-with-NO-NOT-SOME-exc_fig4_43647909:: (The Natural Logic of Language and Cognition by Pieter A. M. Seuren 2006 "This paper aims at an explanation of the discrepancies between natural intuitions and standard logic in terms of a distinction between NATURAL and CONSTRUCTED levels of cognition, applied to the way human cognition deals with sets. NATURAL SET THEORY (NST) restricts standard set theory cutting it down to naturalness." Includes citations in other articles.)
> ::https://lirias.kuleuven.be/retrieve/542941:: (Between Square and Hexagon in Oresme’s Livre du Ciel et du Monde by Lorenz Demey 2022 17 pp.)
> ::https://logicalgeometry.org/assets/pdf/Demey_2017_metametaLG.pdf:: (Metalogic, Metalanguage and Logical Geometry by Lorenz Demey)
> ::https://www.semanticscholar.org/paper/The-Logical-Geometry-of-Russell-%E2%80%99-s-Theory-of-Demey/c466e85e1d4fb5d335ed274d9979404570d72bc6:: (The Logical Geometry of Russell ’ s Theory of Definite Descriptions by L. Demey 2018)
> ::https://www.lotpublications.nl/Documents/419_fulltext.pdf:: (Most or the Art of Compositionality: Dutch de/het meeste at the Syntax-Semantics Interface by Koen Roelandt 2016 448 pp.)
> ::https://www.researchgate.net/publication/296835350_Logico-cognitive_structure_in_the_lexicon:: (Logico-cognitive structure in the lexicon by Pieter A. M. Seuren, Max Planck Institute for Psycholinguistics and Dany Jaspers, Hogeschool - Universiteit Brussel. September 2014Language 90(3):607-643 DOI:10.1353/lan.2014.0058)
Abstract
This study is a prolegomenon to a formal theory of the natural growth of conceptual and lexical fields. Negation, in the various forms in which it occurs in language, is found to be a powerful indicator. Other than in standard logic, natural language negation selects its complement within universes of discourse that are, for practical and functional reasons, restricted in various ways and to different degrees. It is hypothesized that a system of cognitive principles drives recursive processes of universe restriction, which in turn affects logical relations within the restricted universes.
This approach provides a new perspective in which to view the well-known clashes between standard logic and natural logical intuitions. Lexicalization in language, especially the morphological incorporation of negation, is limited to highly restricted universes, which explains, for example, why a dog can be said not to be a Catholic, but also not to be a non-Catholic. Cognition is taken to restrict the universe of discourse to contrary pairs, splitting up one or both of the contraries into further subuniverses as a result of further cognitive activity. It is shown how a logically sound SQUARE OF OPPOSITION, expanded to a hexagon (Jacoby 1950, 1960, Sesmat 1951, Blanche 1952, 1953, 1966), is generated by a hierarchy of universe restrictions, defining the notion 'natural' for logical systems.
The LOGICAL HEXAGON contains two additional vertices, one for 'some but not all' (the Y-type) and one for 'either all or none' (the U-type), and incorporates both the classic square and the Hamiltonian TRIANGLE OF CONTRARIES.
Some is thus considered semantically ambiguous, representing two distinct quantifiers. The pragmaticist claim that the language system contains only the standard logical 'some perhaps all' and that the 'some but not all' meaning is pragmatically derived from the use of the system is rejected.
Four principles are proposed according to which negation selects a complement from the subuniverses at hand. On the basis of these principles and of the logico-cognitive system proposed, the well-known nonlexicalization not only of *nall and *nand but also of many other nonlogical cases found throughout the lexicons of languages is analyzed and explained.*
> ::https://pure.mpg.de/rest/items/item_2031131_4/component/file_2072740/content:: (The Cognitive Ontogenesis of Predicate Logic by Pieter A. M. Seuren. Notre Dame Journal of Formal Logic Volume 55, Number 4, 2014)
> ::https://www.springerprofessional.de/the-road-to-universal-logic/2375522:: (The Road to Universal Logic: Festschrift for the 50th Birthday of Jean-Yves Béziau Volume II. This second volume of a collection of papers offers new perspectives and challenges in the study of logic. It is presented in honor of the fiftieth birthday of Jean-Yves Béziau. The papers touch upon a wide range of topics including paraconsistent logic, quantum logic, geometry of oppositions, categorical logic, computational logic, fundamental logic notions (identity, rule, quantification) and history of logic (Leibniz, Peirce, Hilbert).
The volume gathers personal recollections about Jean-Yves Béziau and an autobiography, followed by 25 papers written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Irving Anellis, Dov Gabbay, Ivor Grattan-Guinness, Istvan Németi, Henri Prade.)
These essays will be of interest to all students and researchers interested in the nature and future of logic.)
> ::https://philpapers.org/rec/JACCAT-7:: (Contrariety and the Triangle of Opposites in Valid Inferences by Paul Jacoby. New Scholasticism 34 (2):141-169 1960)
Similar books and articles
- A Triangle of Opposites for Types of Propositions in Aristotelian Logic.Paul Jacoby - 1950 - New Scholasticism 24 (1):32-56.
- Mixed inferences: A problem for pluralism about truth predicates.Christine Tappolet - 1997 - Analysis 57 (3):209–210.
- Aristotle's Theory of Opposites John Peter Anton: Aristotle's Theory of Contrariety. (International Library of Psychology, Philosophy and Scientific Method.) Pp. xiv + 253. London: Routledge & Kegan Paul, 1957. Cloth, 25s. net. [REVIEW]G. B. Kerferd - 1959 - The Classical Review 9 (01):30-31.
- Forcing with \triangle perfect trees and minimal \triangle-degrees.Alexander S. Kechris - 1981 - Journal of Symbolic Logic 46 (4):803-816.
- Comparative dialectics: Nishida kitarō's logic of place and western dialectical thought.G. S. Axtell - 1991 - Philosophy East and West 41 (2):163-184.
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- Getting from P to Q: Valid Inferences and Heuristics.Norman Swartz - 1993 - Dialogue 32 (4):689-.
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- Nietzsche’s Denial of Opposites.Steven D. Weiss - 1996 - Journal of Philosophical Research 21:261-305.
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by Paul Jacoby 1960
IN LOGIC, as in life, there are incompatibles which cannot be present together (with consistency) and compatible things which may or even must bc said or done if one is to be consistent. A study of the valid moods of inference in both the categorical and hypothetical forms reveals the importance of the relations of opposition—contrariety as well as contradiction—which must be distinguished and treated in and for an adcquatc theory of valid inference.
Now it has been the practice in many introductory courses of so-called traditional logic to minimize the Aristotelian theory of opposition and to present the content of the De Interpretatione as though it were itself disparate, if not contrarily incompatible with thc theory of the categorienl syllogism as found in the Analytica Priora and with the valid moods of the hypothetical (or compound) syllogism that are neglected, if not misunderstood by so many who profess to write manuals in the Aristotelian tradition. Modern treatises in the tradition of symbolic logie following the Principia Mathematica of Whitehead and Russell suffer considerable loss of coherency, as well as needless diffteulty for the scholastic logician, and so they lose contact with much of conventional logic, by their failure to recognize the role of contrary opposition in inference as a basis for the various moods of the syllogism. It would appear that sometimes the unqualified acceptance of the square of opposition by the Aristotelian logician simply because it is in every scholastic manual of logic, is somewhat interesting, and is somehow useful—and its rejection by the contemporary...
> ::https://semantics.uchicago.edu/kennedy/classes/f09/semprag1/horn90.pdf:: (Hamburgers and Truth: Why Gricean explanation is Gricean by Laurence R. Horn 1990)
- https://community.ubiquityuniversity.org/posts/triangle-of-opposition:: (by Leo Jacoby March 28, 2021 Includes picture of Dr. Jacoby teaching
"ATTENTION Peter Merry:
I noticed you are offering reflections on "The Universal Trinity" and some underlying dynamic that informs religious traditions that use a triadic form. Will your April 6 Merry Musings be recorded for future access?
My ears perked up because in 2012 two professors in Europe informed me that my father was the first to publish an alternative diagram to the "Square of Opposition" used for centruries to teach Aristotelian logic. My father devised a "Triangle of Opposites," actually a "double triangle" now found in Google searches as the "logical hexagon."
Dany Jaspers, CRISSP (www.crissp.be and www.danyjaspers.com) HUBrussel, affiliated with KULeuven, Brussels, Belgium and Pieter A. M. Seuren, Max Planck Institute for Psycholinguistics wrote a paper describing my father's contribution to the history of logic. You can access the abstract below and the paper here: ::https://pure.mpg.de/rest/items/item_2227064_4/component/file_2305859/content::
They found my name on the net to inquire about the author of 1950 and 1960 articles, the few my father had published. They wondered how three devoted Catholics, my father and two in France, came up with similar notions in the same decade. My immediate response was, "Is it mere coincidence a thinker soaked in Trinitarian faith would turn to the triangle for intellectual expression?" Given our understanding that humans are created in the image of God, known as Trinity, is it any wonder that the meta-logic description of human faculty would be trinitarian?
I scanned my father's handwritten papers for the two researchers. One of the notes includes a tantalizing marginalia: "Eureka!" He would be amazed that the 7th World Congress on the Square of Opposition convenes in Leuven, Belgium, September 7-11, 2021 ::http://www.square-of-opposition.org/leuven2021.html::
Jaspers and Seuren employ empirical linguistic studies to substantiate a trinitarian perspective. My father's Ph.D. in philosophy is in the Aristotelian-Thomistic tradition that includes medieval logicians and theologians.
Peter, I hope you find this, at least tangentially, relevant to your own studies.
Cordially,
Leo Jacoby, "HR fan"
Stevens Point WI
leopjacoby@gmail.com
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Abstract
The present study describes how three now almost forgotten mid-20th-century logicians, the American Paul Jacoby and the Frenchmen Augustin Sesmat and Robert Blanché, all three ardent Catholics, tried to restore traditional predicate logic to a position of respectability by expanding the classic Square of Opposition to a hexagon of logical relations, showing the logical and cognitive advantages of such an expansion. The nature of these advantages is discussed in the context of modern research regarding the relations between logic, language, and cognition. It is desirable to call attention to these attempts, as they are, though almost totally forgotten, highly relevant against the backdrop of the clash between modern and traditional logic. It is argued that this clash was and is unnecessary, as both forms of predicate logic are legitimate, each in its own right. The attempts by Jacoby, Sesmat, and Blanché are, moreover, of interest to the history of logic in a cultural context in that, in their own idiosyncratic ways, they fit into the general pattern of the Catholic cultural revival that took place roughly between the years 1840 and 1960. The Catholic Church had put up stiff resistance to modern mathematical logic, considering it dehumanizing and a threat to Catholic doctrine. Both the wider cultural context and the specific implications for logic are described and analyzed, in conjunction with the more general philosophical and doctrinal issues involved.
Jaspers, D., & Seuren, P. A. M. (2016). The Square of opposition in catholic hands: A chapter in the history of 20th-century logic. Logique et Analyse, 59(233), 1-35. Cite as: ::http://hdl.handle.net/11858/00-001M-0000-0029-024A-7::