JY B
University of Brazil, Philosophy, Faculty Member
- University of California, San Diego, Philosophy, Department Memberadd
- Jean-Yves Béziau (JYB), PhD in Philosophy and PhD in Mathematics. Born January 15, 1965 in Orléans. He holds French ... moreJean-Yves Béziau (JYB), PhD in Philosophy and PhD in Mathematics. Born January 15, 1965 in Orléans. He holds French and Swiss nationalities and has been working in France, Brazil, Switzerland, Poland, Corsica and California.
http://www.jyb-logic.org/edit
website of the journal
http://www.springer.com/birkhauser/mathematics/journal/11787
latest issue
http://link.springer.com/journal/11787/9/3/page/1
http://www.springer.com/birkhauser/mathematics/journal/11787
latest issue
http://link.springer.com/journal/11787/9/3/page/1
Editor of the logic area of IEP
Recent released entries
Natural Deduction
http://www.iep.utm.edu/nat-ded/
F. H. Bradley: Logic
http://www.iep.utm.edu/brad-log/
Recent released entries
Natural Deduction
http://www.iep.utm.edu/nat-ded/
F. H. Bradley: Logic
http://www.iep.utm.edu/brad-log/
Research Interests:
South America is one of the 7 continents of the earth with many different countries and languages. The SAJL will promote interaction among logicians based in South America and also between logicians from South America and logicians from... more
South America is one of the 7 continents of the earth with many different countries and languages. The SAJL will promote interaction among logicians based in South America and also between logicians from South America and logicians from other continents.
The aim of the South American Journal of Logic is to promote logic in all its aspects: philosophical, mathematical, computational, historical by publishing high quality peer-reviewed papers.
http://www.sa-logic.org/
The aim of the South American Journal of Logic is to promote logic in all its aspects: philosophical, mathematical, computational, historical by publishing high quality peer-reviewed papers.
http://www.sa-logic.org/
Research Interests:
------------------------------------------------------------------------------------ The 6th UNILOG - WORLD CONGRESS AND SCHOOL ON UNIVERSAL LOGIC will take place in Vichy, France, June 16-26, 2018 after previous editions in Montreux... more
------------------------------------------------------------------------------------
The 6th UNILOG - WORLD CONGRESS AND SCHOOL ON UNIVERSAL LOGIC
will take place in Vichy, France, June 16-26, 2018
after previous editions in Montreux 2005, Xi'an 2007, Lisbon 2010, Rio
2013 and Istanbul 2015:
http://www.uni-log.org/vichy2018
Along these years UNILOG has been a leading international logical event
with the participation of many famous logicians such as Wilfrid Hodges,
Daniele Mundici, Saul Kripke, Jaakko Hintikka, Dov Gabbay, Arnon Avron,
Benedikt Löwe, David Makinson, Yde Venema, Newton da Costa, Mike Dunn,
Val Goranko, Yuri Gurevich, Janusz Czelakowski, Stephen Read, Sara Negri,
Arnold Koslow, Peter Schröder-Heister, Gila Sher, Hiroakira Ono, John Corcoran,
Hartry Field, Gerhard Jaeger, Ernest Lepore, Marcus Kracht, Melvin Fitting,
Luciano Floridi, Patrick Blackburn, Jan Wolenski, Krister Segerberg,
Dale Jacquette, Sun-Joo Shin, Jouko Väänänen, John Woods and many
more.
UNILOG is a logic event in a broad sense. It gathers people from many horizons
(philosophy, mathematics, linguistics, computer science, semiotics, cognitive science ...)
and the idea is to promote interaction between all these people.
The previous edition in Istanbul gathered more than 400 logicians from
about 50 different countries.
For the 6th edition we will follow the same format:
- A school of logic of 5 days with 30 tutorials
- A congress of 6 days with about 30 sessions/workshops
- A contest (the topic will be announced soon)
- A secret speaker (speaker whose identity is revealed only at the time
of her / its / his speech).
Vichy is a charming relaxing thermal city at the middle of France,
developed by Napoleon III in the second half of the 19th century, who in
particular created beautiful parks with species of trees from all over
the world. Vichy, in the Duchy of Bourbon, a region full of castles,
is a small city, where it is possible to go everywhere just by walking.
The event will take place at the university campus nearby the Celestins spring,
the banks of the Allier river (where it is possible to swim) and the city center.
June is a very nice time to be in Vichy with lots of animations,
including on June 21 a very lively musical day celebrating summertime.
Deadline to submit an abstract: September 15, 2017
Looking forward to seeing you in Vichy in June 2018
Jean-Yves Beziau (Federal University of Rio de Janeiro and CNPq)
Christophe Rey (University Clermont Auvergne, CNRS, LIMOS)
Organizers of UNILOG'2018
-------------------------------------------------------------------------------
U N I L O G - World Congress and School on Universal Logic - U N I LO G
Montreux 2005, Xi'an 2007, Lisbon 2010, Rio 2013, Istanbul 2015, Vichy 2018
http://www.uni-log.org/vichy2018
The 6th UNILOG - WORLD CONGRESS AND SCHOOL ON UNIVERSAL LOGIC
will take place in Vichy, France, June 16-26, 2018
after previous editions in Montreux 2005, Xi'an 2007, Lisbon 2010, Rio
2013 and Istanbul 2015:
http://www.uni-log.org/vichy2018
Along these years UNILOG has been a leading international logical event
with the participation of many famous logicians such as Wilfrid Hodges,
Daniele Mundici, Saul Kripke, Jaakko Hintikka, Dov Gabbay, Arnon Avron,
Benedikt Löwe, David Makinson, Yde Venema, Newton da Costa, Mike Dunn,
Val Goranko, Yuri Gurevich, Janusz Czelakowski, Stephen Read, Sara Negri,
Arnold Koslow, Peter Schröder-Heister, Gila Sher, Hiroakira Ono, John Corcoran,
Hartry Field, Gerhard Jaeger, Ernest Lepore, Marcus Kracht, Melvin Fitting,
Luciano Floridi, Patrick Blackburn, Jan Wolenski, Krister Segerberg,
Dale Jacquette, Sun-Joo Shin, Jouko Väänänen, John Woods and many
more.
UNILOG is a logic event in a broad sense. It gathers people from many horizons
(philosophy, mathematics, linguistics, computer science, semiotics, cognitive science ...)
and the idea is to promote interaction between all these people.
The previous edition in Istanbul gathered more than 400 logicians from
about 50 different countries.
For the 6th edition we will follow the same format:
- A school of logic of 5 days with 30 tutorials
- A congress of 6 days with about 30 sessions/workshops
- A contest (the topic will be announced soon)
- A secret speaker (speaker whose identity is revealed only at the time
of her / its / his speech).
Vichy is a charming relaxing thermal city at the middle of France,
developed by Napoleon III in the second half of the 19th century, who in
particular created beautiful parks with species of trees from all over
the world. Vichy, in the Duchy of Bourbon, a region full of castles,
is a small city, where it is possible to go everywhere just by walking.
The event will take place at the university campus nearby the Celestins spring,
the banks of the Allier river (where it is possible to swim) and the city center.
June is a very nice time to be in Vichy with lots of animations,
including on June 21 a very lively musical day celebrating summertime.
Deadline to submit an abstract: September 15, 2017
Looking forward to seeing you in Vichy in June 2018
Jean-Yves Beziau (Federal University of Rio de Janeiro and CNPq)
Christophe Rey (University Clermont Auvergne, CNRS, LIMOS)
Organizers of UNILOG'2018
-------------------------------------------------------------------------------
U N I L O G - World Congress and School on Universal Logic - U N I LO G
Montreux 2005, Xi'an 2007, Lisbon 2010, Rio 2013, Istanbul 2015, Vichy 2018
http://www.uni-log.org/vichy2018
Research Interests:
Research Interests: Jainism, Artificial Intelligence, Music Theory, Political Philosophy, Computational Logic, and 27 moreAristotle, Proof Theory, Fuzzy Logic, Category Theory, Hegel, Colour Theory, History of Logic in Poland, Philosophy of Logic, Emmanuel Kant, Mathematical Logic, Apuleius, Boethius, Boolean Algebra, Leibniz, Kurt Godel, Lewis Carroll, JAIN PHILOSOPHY, Universal Logic, George Boole, Aristotlean Logic, Leibniz Characteristics Logic, History of Medieval Logic, Boethius of Dacia, History and Philosophy of Logic, Immanuel Kant is Logic, Stoic Logic, and Lógica universal
This was the 4th world congress organized about the square of opposition after very succesful previous editions in Montreux, Switzerland 2007, Corté, Corsica 2010, Beirut, Lebanon, 2012. An interdisciplinary event gathering logicians,... more
This was the 4th world congress organized about the square of opposition after very succesful previous editions in Montreux, Switzerland 2007, Corté, Corsica 2010, Beirut, Lebanon, 2012. An interdisciplinary event gathering logicians, philosophers, mathematicians, semioticians, theologians, cognitivists, artists and computer scientists.
http://www.square-of-opposition.org/square2014.html
http://www.square-of-opposition.org/square2014.html
Research Interests:
The square of opposition is a diagram related to a theory of opposi-tions that goes back to Aristotle. Both the diagram and the theory have been discussed throughout the history of logic. Initially, the diagram was employed to present the... more
The square of opposition is a diagram related to a theory of opposi-tions that goes back to Aristotle. Both the diagram and the theory have been discussed throughout the history of logic. Initially, the diagram was employed to present the Aristotelian theory of quantifi-cation, but extensions and criticisms of this theory have resulted in various other diagrams. The strength of the theory is that it is at the same time fairly simple and quite rich. The theory of oppositions has recently become a topic of intense interest due to the development of a general geometry of opposition (polygons and polyhedra) with many applications. A congress on the square with an interdisciplinary character has been organized on a regular basis (Montreux 2007, Corsica 2010, Beirut 2012, Vatican 2014, Rapa Nui 2016). The volume at hand is a sequel to two successful books: The Square of Opposition - A General Framework of Cognition, ed. by J.-Y. Béziau & G. Payette, as well as Around and beyond the Square of Oppo-sition, ed. by J.-Y. Béziau & D. Jacquette, and, like those, a collection of selected peer-reviewed papers. The idea of this new volume is to maintain a good equilibrium between history, technical developments and applications. The volume is likely to attract a wide spectrum of readers, mathematicians, philosophers, linguists, psychologists and computer scientists, who may range from undergraduate students to advanced researchers.
Research Interests:
The square of opposition is a simple geometrical figure expressing some fundamental ideas about cognition. It is based on Aristotle’s philosophy and has been fascinating people for two thousand years. The three notions of opposition... more
The square of opposition is a simple geometrical figure expressing some fundamental ideas about cognition. It is based on Aristotle’s philosophy and has been fascinating people for two thousand years. The three notions of opposition presented in the square can be applied to analyze and understand such diverse subjects as reasoning about mathematical objects, perceptions of reality, speech acts, moral reasoning and reasoning about possibility.
This book presents recent research papers dealing with the history and philosophy of the square, new diagrammatic and mathematical developments arising from it, and its applications to the fields of linguistics, psychology and argumentation.
It also includes a DVD composed of events from the first world congress on the square of opposition held in June 2007 in Montreux, featuring some of the speeches and presentations of the participants, like the professors Pascal Engel, Laurence Horn, Terence Parsons, Jan Wolenski. Further, the DVD contains extracts of a square jazz show which was composed and presented for this occasion and extracts of the movie «The Square of Salomé». The movie, which was produced for this event, is a remake of the famous biblical story using the square to display the relations between the main characters.
This book presents recent research papers dealing with the history and philosophy of the square, new diagrammatic and mathematical developments arising from it, and its applications to the fields of linguistics, psychology and argumentation.
It also includes a DVD composed of events from the first world congress on the square of opposition held in June 2007 in Montreux, featuring some of the speeches and presentations of the participants, like the professors Pascal Engel, Laurence Horn, Terence Parsons, Jan Wolenski. Further, the DVD contains extracts of a square jazz show which was composed and presented for this occasion and extracts of the movie «The Square of Salomé». The movie, which was produced for this event, is a remake of the famous biblical story using the square to display the relations between the main characters.
Research Interests:
Paraconsistent logics are logics which allow solid deductive reasoning under contradictions by offering a mathematical and philosophical support to contradictory yet non-trivial theories. Due to its role in models of scientific... more
Paraconsistent logics are logics which allow solid deductive reasoning under contradictions by offering a mathematical and philosophical support to contradictory yet non-trivial theories.
Due to its role in models of scientific reasoning and to its philosophical implications, as well as to its connections to topics such as abduction, automated reasoning, logic programming, and belief revision, paraconsistency has becoming a fast growing area.
The present volume, edited by Jean-Yves Beziau, Walter Carnielli and Dov Gabbay, expert logicians versed on heterodosx logics, originated around the III World Congress on Paraconsistency (WCP3) held in Toulouse, France, in July, 2003. It contains the most recent results on several aspects of paraconsistent logic, including philosophical debates on paraconsistency and its connections to philosophy of language, argumentation theory, computer science, information theory, and artificial intelligence.
The book is a basic tool for those who want to know ore about paraconsistent logic, its history and philosophy, the various systems of paraconsistent logic and their applications.
The present volume is edited by Jean-Yves Beziau, Walter Carnielli and Dov Gabbay, expert logicians versed in a wide variety of topics.
ISBN 978-1-904987-73-4
Due to its role in models of scientific reasoning and to its philosophical implications, as well as to its connections to topics such as abduction, automated reasoning, logic programming, and belief revision, paraconsistency has becoming a fast growing area.
The present volume, edited by Jean-Yves Beziau, Walter Carnielli and Dov Gabbay, expert logicians versed on heterodosx logics, originated around the III World Congress on Paraconsistency (WCP3) held in Toulouse, France, in July, 2003. It contains the most recent results on several aspects of paraconsistent logic, including philosophical debates on paraconsistency and its connections to philosophy of language, argumentation theory, computer science, information theory, and artificial intelligence.
The book is a basic tool for those who want to know ore about paraconsistent logic, its history and philosophy, the various systems of paraconsistent logic and their applications.
The present volume is edited by Jean-Yves Beziau, Walter Carnielli and Dov Gabbay, expert logicians versed in a wide variety of topics.
ISBN 978-1-904987-73-4
Research Interests:
This is a volume containing papers honoring Patrick Suppes (1922-2014). All contributors have worked directly with Suppes or/and with his ideas. The book contains also one of the last papers by Suppes (co-authored by two of his... more
This is a volume containing papers honoring Patrick Suppes (1922-2014). All contributors have worked directly with Suppes or/and with his ideas. The book contains also one of the last papers by Suppes (co-authored by two of his collaborators).
The so-called “semantic approach” to scientific theories is currently the main view in the philosophy of science. Suppes is considered as the founder of this approach. His ideas on semantics, models and axiomatization of scientific theories are very inspiring. The present volume provides original and relevant insights given by some leading philosophers in the field.
This is a follow up of a special issue of Synthese, New Directions in the Foundations of Science, (154 (3), 2007) edited by Béziau and Krause, after a meeting they organized with Suppes in Florianópolis, Brazil in 2002 fot his 80th birthday.
Jean-Yves Beziau worked with Suppes at Stanford University for two years (2000 and 2001) and has been continuously working in the Suppes tradition of logic, methodology and philosophy of science, which emphasizes structures and models.
Décio Krause has used Suppes’ approach to the axiomatization of scientific theories in many fields. With J.C.M. Magalhães, he presented a “Suppes predicate” for genetics and natural and with S. French he developed a Suppes predicate for quantum field theories via Fock spaces.
http://www.collegepublications.co.uk/tributes/?00028
The so-called “semantic approach” to scientific theories is currently the main view in the philosophy of science. Suppes is considered as the founder of this approach. His ideas on semantics, models and axiomatization of scientific theories are very inspiring. The present volume provides original and relevant insights given by some leading philosophers in the field.
This is a follow up of a special issue of Synthese, New Directions in the Foundations of Science, (154 (3), 2007) edited by Béziau and Krause, after a meeting they organized with Suppes in Florianópolis, Brazil in 2002 fot his 80th birthday.
Jean-Yves Beziau worked with Suppes at Stanford University for two years (2000 and 2001) and has been continuously working in the Suppes tradition of logic, methodology and philosophy of science, which emphasizes structures and models.
Décio Krause has used Suppes’ approach to the axiomatization of scientific theories in many fields. With J.C.M. Magalhães, he presented a “Suppes predicate” for genetics and natural and with S. French he developed a Suppes predicate for quantum field theories via Fock spaces.
http://www.collegepublications.co.uk/tributes/?00028
Research Interests:
The theory of oppositions based on Aristotelian foundations of logic has been pictured in a striking square diagram which can be understood and applied in many different ways having repercussions in various fields: epistemology,... more
The theory of oppositions based on Aristotelian foundations of logic has been pictured in a striking square diagram which can be understood and applied in many different ways having repercussions in various fields: epistemology, linguistics, mathematics, sociology, physics. The square can also be generalized in other two-dimensional or multi-dimensional objects extending in breadth and depth the original Aristotelian theory.
The square of opposition from its origin in antiquity to the present day continues to exert a profound impact on the development of deductive logic. Since 10 years there is a new growing interest for the square due to recent discoveries and challenging interpretations. This book presents a collection of previously unpublished papers by high level specialists on the square from all over the world.
The square of opposition from its origin in antiquity to the present day continues to exert a profound impact on the development of deductive logic. Since 10 years there is a new growing interest for the square due to recent discoveries and challenging interpretations. This book presents a collection of previously unpublished papers by high level specialists on the square from all over the world.
Research Interests: Logic, Decision Making, Fuzzy Logic, History of Logic, Philosophical Logic, and 13 morePhilosophy of Logic, Gottfried Wilhelm Leibniz, Beliefs, John Buridan, Gottlob Frege, Boethius, Avicenna, Averroes, Quantifiers, Negation, Generalized Quantifier Theory, Scientific Inquiry, and Square of Opposition
Dans un texte désormais célèbre, Ferdinand de Saussure insiste sur l’arbitraire du signe dont il vante les qualités. Toutefois il s’avère que le symbole, signe non arbitraire, dans la mesure où il existe un rapport entre ce qui représente... more
Dans un texte désormais célèbre, Ferdinand de Saussure insiste sur l’arbitraire du signe dont il vante les qualités. Toutefois il s’avère que le symbole, signe non arbitraire, dans la mesure où il existe un rapport entre ce qui représente et ce qui est représenté, joue un rôle fondamental dans la plupart des activités humaines, qu’elles soient scientifiques, artistiques ou religieuses. C’est cette dimension symbolique, sa portée, son fonctionnement et sa signification dans des domaines aussi variés que la chimie, la théologie, les mathématiques, le code de la route et bien d’autres qui est l’objet du livre La Pointure du symbole.
Jean-Yves Béziau, franco-suisse, est docteur en logique mathématique et docteur en philosophie. Il a poursuivi des recherches en France, au Brésil, en Suisse, aux États-Unis (UCLA et Stanford), en Pologne et développé la logique universelle. Éditeur-en-chef de la revue Logica Universalis et de la collection Studies in Universal Logic (Springer), il est actuellement professeur à l’Université Fédérale de Rio de Janeiro et membre de l’Académie brésilienne de Philosophie.
SOMMAIRE
PRÉFACE
L’arbitraire du signe face à la puissance du symbole
Jean-Yves BÉZIAU
La logique et la théorie de la notation (sémiotique) de Peirce (Traduit de l’anglais par Jean-Marie Chevalier)
Irving H. ANELLIS
Langage symbolique de Genèse 2-3
Lytta BASSET
Mécanique quantique : quelle réalité derrière les symboles ?
Hans BECK
Quels langages et images pour représenter le corps humain ?
Sarah CARVALLO
Des jeux symboliques aux rituels collectifs. Quelques apports de la psychologie du développement à l’étude du symbolisme
Fabrice CLÉMENT
Les panneaux de signalisation (Traduit de l’anglais par Fabien Shang)
Robert DEWAR
Remarques sur l’émergence des activités symboliques
Jean LASSÈGUE
Les illustrations du "Songe de Poliphile" (1499). Notule sur les hiéroglyphes de Francesca Colonna
Pierre-Alain MARIAUX
Signes de vie
Jeremy NARBY
Visualising relations in society and economics. Otto Neuraths Isotype-method against the background of his economic thought
Elisabeth NEMETH
Algèbre et logique symboliques : arbitraire du signe et langage formel
Marie-José DURAND – Amirouche MOKTEFI
Les symboles mathématiques, signes du Ciel
Jean-Claude PONT
La mathématique : un langage mathématique ?
Alain M. ROBERT
http://www.editionspetra.fr/ouvrage/206
Jean-Yves Béziau, franco-suisse, est docteur en logique mathématique et docteur en philosophie. Il a poursuivi des recherches en France, au Brésil, en Suisse, aux États-Unis (UCLA et Stanford), en Pologne et développé la logique universelle. Éditeur-en-chef de la revue Logica Universalis et de la collection Studies in Universal Logic (Springer), il est actuellement professeur à l’Université Fédérale de Rio de Janeiro et membre de l’Académie brésilienne de Philosophie.
SOMMAIRE
PRÉFACE
L’arbitraire du signe face à la puissance du symbole
Jean-Yves BÉZIAU
La logique et la théorie de la notation (sémiotique) de Peirce (Traduit de l’anglais par Jean-Marie Chevalier)
Irving H. ANELLIS
Langage symbolique de Genèse 2-3
Lytta BASSET
Mécanique quantique : quelle réalité derrière les symboles ?
Hans BECK
Quels langages et images pour représenter le corps humain ?
Sarah CARVALLO
Des jeux symboliques aux rituels collectifs. Quelques apports de la psychologie du développement à l’étude du symbolisme
Fabrice CLÉMENT
Les panneaux de signalisation (Traduit de l’anglais par Fabien Shang)
Robert DEWAR
Remarques sur l’émergence des activités symboliques
Jean LASSÈGUE
Les illustrations du "Songe de Poliphile" (1499). Notule sur les hiéroglyphes de Francesca Colonna
Pierre-Alain MARIAUX
Signes de vie
Jeremy NARBY
Visualising relations in society and economics. Otto Neuraths Isotype-method against the background of his economic thought
Elisabeth NEMETH
Algèbre et logique symboliques : arbitraire du signe et langage formel
Marie-José DURAND – Amirouche MOKTEFI
Les symboles mathématiques, signes du Ciel
Jean-Claude PONT
La mathématique : un langage mathématique ?
Alain M. ROBERT
http://www.editionspetra.fr/ouvrage/206
Research Interests:
A collection of papers from Paul Hertz to Dov Gabbay - through Tarski, Gödel, Kripke - giving a general perspective about logical systems. These papers discuss questions such as the relativity and nature of logic, present tools such as... more
A collection of papers from Paul Hertz to Dov Gabbay - through Tarski, Gödel, Kripke - giving a general perspective about logical systems. These papers discuss questions such as the relativity and nature of logic, present tools such as consequence operators and combinations of logics, prove theorems such as translations between logics, investigate the domain of validity and application of fundamental results such as compactness and completeness. Each of these papers is presented by a specialist explaining its context, import and influence.
Research Interests:
According to Boole it is possible to deduce the principle of contradiction from what he calls the fundamental law of thought and expresses as xx2 = xx. We examine in which framework this makes sense and up to which point it depends on... more
According to Boole it is possible to deduce the principle of contradiction from what he calls the fundamental law of thought and expresses as xx2 = xx. We examine in which framework this makes sense and up to which point it depends on notation. This leads us to make various comments on the history and philosophy of modern logic. Mathematics Subject Classification. Primary 03A05; Secondary 00A30; 01A55; 03B53; 03B22; 03B05; 03B10; 03G05
Autre être fidèle du tonneau sans loques malgré ses apparitions souvent loufoques le chien naît pas con platement idiot ne se laisse pas si facilement mener en rat d'eau il ne les comprend certes pas forcément toutes à la première coupe... more
Autre être fidèle du tonneau sans loques malgré ses apparitions souvent loufoques le chien naît pas con platement idiot ne se laisse pas si facilement mener en rat d'eau il ne les comprend certes pas forcément toutes à la première coupe ne sait pas sans l'ombre deux doutes la fière différance antre un loup et une loupe tout de foi à la croisade des parchemins il saura au non du hasard dès trousser la chienlit et non en vain reconnaître celle qui l'Amen à Rhum sans faim Baron Jean Bon de Chambourcy
Research Interests:
In this paper we explain that the paraconsistent logic LP (Logic of Paradox) promoted by Graham Priest can only be supported by trivial dialetheists, i.e., those who believe that all sentences are dialetheias.
Research Interests:
Paper presented at the congress Nikolai Vasiliev's Logical Legacy and Modern Logic October 24-25, 2012, Moscow, Russia to appear in D.Zaitsev (ed), Nikolai Vasiliev's Logical Legacy and Modern Logic, Springer, Dordrecht, 2015. In this... more
Paper presented at the congress Nikolai Vasiliev's Logical Legacy and Modern Logic
October 24-25, 2012, Moscow, Russia
to appear in D.Zaitsev (ed), Nikolai Vasiliev's Logical Legacy and Modern Logic, Springer, Dordrecht, 2015.
In this paper we examine up to which point Modern logic can be qualified as
non-Aristotelian. After clarifying the difference between logic as reasoning and
logic as a theory of reasoning, we compare syllogistic with propositional and
first-order logic. We touch the question of formal validity, variable and
mathematization and we point out that Gentzen’s cut-elimination theorem can
be seen as the rejection of the central mechanism of syllogistic – the cut-rule
has been first conceived as a modus Barbara by Hertz. We then examine the
non-Aristotelian aspect of some non-classical logics, in particular
paraconsistent logic. We argue that a paraconsistent negation can be seen as
neo-Aristotelian since it corresponds to the notion of subcontrary in Boethius’
square of opposition. We end by examining if the comparison promoted by
Vasiliev between non-Aristotelian logic and non-Euclidian geometry makes
sense.
October 24-25, 2012, Moscow, Russia
to appear in D.Zaitsev (ed), Nikolai Vasiliev's Logical Legacy and Modern Logic, Springer, Dordrecht, 2015.
In this paper we examine up to which point Modern logic can be qualified as
non-Aristotelian. After clarifying the difference between logic as reasoning and
logic as a theory of reasoning, we compare syllogistic with propositional and
first-order logic. We touch the question of formal validity, variable and
mathematization and we point out that Gentzen’s cut-elimination theorem can
be seen as the rejection of the central mechanism of syllogistic – the cut-rule
has been first conceived as a modus Barbara by Hertz. We then examine the
non-Aristotelian aspect of some non-classical logics, in particular
paraconsistent logic. We argue that a paraconsistent negation can be seen as
neo-Aristotelian since it corresponds to the notion of subcontrary in Boethius’
square of opposition. We end by examining if the comparison promoted by
Vasiliev between non-Aristotelian logic and non-Euclidian geometry makes
sense.
Research Interests:
Abstract. The hexagon of opposition is an improvement of the square of opposition due to Robert Blanch´e. After a short presentation of the square and its various interpretations, we discuss two important problems related with the square:... more
Abstract. The hexagon of opposition is an improvement of the square
of opposition due to Robert Blanch´e. After a short presentation of the
square and its various interpretations, we discuss two important problems
related with the square: the problem of the I-corner and the problem of
the O-corner. The meaning of the notion described by the I-corner does
not correspond to the name used for it. In the case of the O-corner, the
problem is not a wrong-name problem but a no-name problem and it
is not clear what is the intuitive notion corresponding to it. We explain
then that the triangle of contrariety proposed by different people such
as Vasiliev and Jespersen solves these problems, but that we don’t need
to reject the square. It can be reconstructed from this triangle of contrariety,
by considering a dual triangle of subcontrariety. This is the main
idea of Blanch´e’s hexagon. We then give different examples of hexagons
to show how this framework can be useful to conceptual analysis in many
different fields such as economy, music, semiotics, identity theory, philosophy,
metalogic and the metatheory of the hexagon itself. We finish by
discussing the abstract structure of the hexagon and by showing how we
can swing from sense to non-sense thinking with the hexagon.
of opposition due to Robert Blanch´e. After a short presentation of the
square and its various interpretations, we discuss two important problems
related with the square: the problem of the I-corner and the problem of
the O-corner. The meaning of the notion described by the I-corner does
not correspond to the name used for it. In the case of the O-corner, the
problem is not a wrong-name problem but a no-name problem and it
is not clear what is the intuitive notion corresponding to it. We explain
then that the triangle of contrariety proposed by different people such
as Vasiliev and Jespersen solves these problems, but that we don’t need
to reject the square. It can be reconstructed from this triangle of contrariety,
by considering a dual triangle of subcontrariety. This is the main
idea of Blanch´e’s hexagon. We then give different examples of hexagons
to show how this framework can be useful to conceptual analysis in many
different fields such as economy, music, semiotics, identity theory, philosophy,
metalogic and the metatheory of the hexagon itself. We finish by
discussing the abstract structure of the hexagon and by showing how we
can swing from sense to non-sense thinking with the hexagon.
Research Interests:
This article sets forth a detailed theoretical proposal of how the truth of ordinary empirical statements, often atomic in form, is computed. The method of computation draws on psychological concepts such as those of associative networks... more
This article sets forth a detailed theoretical proposal of how the truth of ordinary empirical statements,
often atomic in form, is computed. The method of computation draws on psychological
concepts such as those of associative networks and spreading activation, rather that the concepts
of philosophical or logical theories of truth. Axioms for a restricted class of cases are given, as well
as some detailed examples.
http://www.sciencedirect.com/science/article/pii/S1570868304000461
often atomic in form, is computed. The method of computation draws on psychological
concepts such as those of associative networks and spreading activation, rather that the concepts
of philosophical or logical theories of truth. Axioms for a restricted class of cases are given, as well
as some detailed examples.
http://www.sciencedirect.com/science/article/pii/S1570868304000461
Research Interests:
Many-valued logics are standardly de ned by logical matrices. They are truth- functional. In this paper non truth-functional many-valued semantics are presented, in a philosophical and mathematical perspective.... more
Many-valued logics are standardly de ned by logical matrices. They are truth-
functional. In this paper non truth-functional many-valued semantics are presented,
in a philosophical and mathematical perspective.
http://www.sciencedirect.com/science/article/pii/S1571066104805449
functional. In this paper non truth-functional many-valued semantics are presented,
in a philosophical and mathematical perspective.
http://www.sciencedirect.com/science/article/pii/S1571066104805449
Research Interests:
In this paper we study paraconsistent negation as a modal operator, considering the fact that the classical negation of necessity has a paraconsistent behavior. We examine this operator on the one hand in the modal logic S5 and on the... more
In this paper we study paraconsistent negation as a modal operator, considering the fact that the
classical negation of necessity has a paraconsistent behavior. We examine this operator on the one
hand in the modal logic S5 and on the other hand in some new four-valued modal logics.
http://www.sciencedirect.com/science/article/pii/S1570868304000497
classical negation of necessity has a paraconsistent behavior. We examine this operator on the one
hand in the modal logic S5 and on the other hand in some new four-valued modal logics.
http://www.sciencedirect.com/science/article/pii/S1570868304000497
Research Interests:
In this paper we discuss the difference between logic as reasoning and logic as a theory about reasoning. In the light of this distinction we examine central questions about history, philosophy and the very nature of logic. We study in... more
In this paper we discuss the difference between logic as reasoning and logic as a theory about reasoning. In the light of this distinction we examine central questions about history, philosophy and the very nature of logic. We study in which sense we can consider Aristotle as the first logician, Descartes‘s rejection of syllogistic as logical, Boole rather than Frege as the initiator of modern logic. We examine also in this perspective the unfolding of logic into logic and metalogic, the proliferations of logic systems, the questions of relativity and universality of logic and the position and interaction of logic with regards to other sciences such as physics, biology, mathematics and computer science.
Research Interests:
13 questions to Jean-Yves Beziau, by Linda Eastwood The expression “universal logic” prompts a number of misunderstandings pressing up against to the confusion prevailing nowadays around the very notion of logic. In order to clear up... more
13 questions to Jean-Yves Beziau, by Linda Eastwood
The expression “universal logic” prompts a number of misunderstandings pressing up against to the confusion prevailing nowadays around the very notion
of logic. In order to clear up such equivocations, I prepared a series of questions to Jean-Yves Beziau, who has been working for many years on his project of universal logic, recently in the University of Neuchˆatel, Switzerland.
The expression “universal logic” prompts a number of misunderstandings pressing up against to the confusion prevailing nowadays around the very notion
of logic. In order to clear up such equivocations, I prepared a series of questions to Jean-Yves Beziau, who has been working for many years on his project of universal logic, recently in the University of Neuchˆatel, Switzerland.
Research Interests:
The difference between truth and logical truth is a fundamental distinction of modern logic promoted by Wittgenstein. We show here how this distinction leads to a metalogical triangle of contrariety which can be naturally extended into a... more
The difference between truth and logical truth is a fundamental distinction of
modern logic promoted by Wittgenstein. We show here how this distinction
leads to a metalogical triangle of contrariety which can be naturally extended
into a metalogical hexagon of oppositions, representing in a direct and simple
way the articulation of the six positions of a proposition vis-à-vis a theory. A
particular case of this hexagon is a metalogical hexagon of propositions which
can be interpreted in a modal way. We end by a semiotic hexagon emphasizing
the value of true symbols, in particular the logic hexagon itself.
modern logic promoted by Wittgenstein. We show here how this distinction
leads to a metalogical triangle of contrariety which can be naturally extended
into a metalogical hexagon of oppositions, representing in a direct and simple
way the articulation of the six positions of a proposition vis-à-vis a theory. A
particular case of this hexagon is a metalogical hexagon of propositions which
can be interpreted in a modal way. We end by a semiotic hexagon emphasizing
the value of true symbols, in particular the logic hexagon itself.
Research Interests:
We discuss Sengupta's argumentation according to which Frege was wrong identifying reference with truth-value. After stating various possible interpretations of Frege's principle of substitution, we show that there is no coherent... more
We discuss Sengupta's argumentation according to which Frege was wrong identifying reference with truth-value.
After stating various possible interpretations of Frege's principle of substitution, we show that there is no coherent interpretation under which Sengupta's argumentation is valid.
Finally we try to show how Frege's distinction can work in the context of modern mathematics and how modern logic grasps it.
After stating various possible interpretations of Frege's principle of substitution, we show that there is no coherent interpretation under which Sengupta's argumentation is valid.
Finally we try to show how Frege's distinction can work in the context of modern mathematics and how modern logic grasps it.
Research Interests:
In this paper we point out the connection between sorites pardoxes and transitivity
Research Interests:
In this paper several systems of modal logic based on four-valued matrices are presented. We start with pure modal logics, i.e. modal logics with modal operators as the only operators, using the Polish framework of structural consequence... more
In this paper several systems of modal logic based on four-valued
matrices are presented. We start with pure modal logics, i.e. modal
logics with modal operators as the only operators, using the Polish
framework of structural consequence relation. We show that with a
four-valued matrix we can define modal operators which have the
same behavior as in pure S5 (S5 with only modal operators). We
then present modal logics with conjunction and disjunction based on
four-valued matrices. We show that if we use partial order instead
of linear order, we are avoiding Łukasiewicz’s paradox. We then
introduce classical negation and we show than defining implication
in the usual way using negation and disjunction Kripke law is valid
using either linear or partial order. On the other hand we show that
the difference between linear and partial order appears at the level
of the excluded middle and the replacement theorem.
matrices are presented. We start with pure modal logics, i.e. modal
logics with modal operators as the only operators, using the Polish
framework of structural consequence relation. We show that with a
four-valued matrix we can define modal operators which have the
same behavior as in pure S5 (S5 with only modal operators). We
then present modal logics with conjunction and disjunction based on
four-valued matrices. We show that if we use partial order instead
of linear order, we are avoiding Łukasiewicz’s paradox. We then
introduce classical negation and we show than defining implication
in the usual way using negation and disjunction Kripke law is valid
using either linear or partial order. On the other hand we show that
the difference between linear and partial order appears at the level
of the excluded middle and the replacement theorem.
Research Interests:
“Formal logic”, an expression created by Kant to characterize Aristotelian logic, has also been used as a name for modern logic, originated by Boole and Frege, which in many aspects differs radically from traditional logic. We shed light... more
“Formal logic”, an expression created by Kant to characterize Aristotelian logic, has also been used as a name for modern logic, originated by Boole and Frege, which in many aspects differs radically from traditional logic. We shed light on this paradox by distinguishing in this paper five different meanings of the expression “formal logic”: (1) Formal reasoning according to the Aristotelian dichotomy of form and content, (2) Formal logic as a formal science by opposition to an empirical science, (3) Formal systems in the sense of Hilbert, Curry and the formalist school, (4) Symbolic logic, a science using symbols, such as Venn diagrams, (5) Mathematical logic, a mathematical approach to reasoning. We argue that these five meanings are independent and that the meaning (5) is the one which better characterized modern logic, which should therefore not be called “formal logic”.
Research Interests:
The compound word “truth-value”, sometimes written “truth value”, is a bit monstrous and ambiguous. It is the name of a central concept of modern logic, but has not yet invaded everyday language. An ordinary man will say: it is true that... more
The compound word “truth-value”, sometimes written “truth value”, is a bit monstrous and ambiguous. It is the name of a central concept of modern logic, but has not yet invaded everyday language. An ordinary man will say: it is true that Paris is the capital of France, rather than: the truth-value of “Paris is the capital of France” is true. And a mathematician also will say: it is true that 2 + 3 = 5, rather than the truth-value of “2 + 3 = 5” is true. We don't even find “truth-values” in postmodern or new age discussions side by side with “quantum leap”, “imaginary number”, “betacognition”. It seems that “truth-value” is exclusively used by logicians, philosophers of logic and analytic philosophers. In this paper we will examine the origin of this strange way of speaking and the concept related to it.
Research Interests:
After recalling the distinction between logic as reasoning and logic as theory of reasoning, we first examine the question of relativity of logic arguing that the theory of reasoning as any other science is relative. In a second part we... more
After recalling the distinction between logic as reasoning and logic as theory
of reasoning, we first examine the question of relativity of logic arguing that the theory
of reasoning as any other science is relative. In a second part we discuss the emergence
of universal logic as a general theory of logical systems, making comparison with
universal algebra and the project of mathesis universalis. In a third part we critically
present three lines of research connected to universal logic: logical pluralism, nonclassical
logics and cognitive science.
of reasoning, we first examine the question of relativity of logic arguing that the theory
of reasoning as any other science is relative. In a second part we discuss the emergence
of universal logic as a general theory of logical systems, making comparison with
universal algebra and the project of mathesis universalis. In a third part we critically
present three lines of research connected to universal logic: logical pluralism, nonclassical
logics and cognitive science.
Research Interests:
We discuss the many aspects and qualities of the number one: the different ways it can be represented, the different things it may represent. We discuss the ordinal and cardinal natures of the one, its algebraic behavior as a neutral... more
We discuss the many aspects and qualities of the number one: the different ways it can be represented, the different things it may represent. We discuss the ordinal and cardinal natures of the one, its algebraic behavior as a neutral element and finally its role as a truth-value in logic.
Click here for the full version of MANY 1 or go to http://www.jyb-logic.org/MANY1
This paper has been written in such a way that it can be understood and/or tasted by any gentleman or gentlewoman with an average IQ but is not recommended for people with an emotional intelligence less than
Click here for the full version of MANY 1 or go to http://www.jyb-logic.org/MANY1
This paper has been written in such a way that it can be understood and/or tasted by any gentleman or gentlewoman with an average IQ but is not recommended for people with an emotional intelligence less than