The Relativity and Universality of Logic : Synthese de la Mayonnaise

Jean-Yves Beziau


I wrote two years ago a paper entitled The relativity and universality of logic which was published on-line first in the journal Synthese on March 20, 2014. Few days ago i.e. 22 months later, this paper raised some hot disusssions. This paper could have been never read by anyone. As it is known , most of what is published in academic journals is never read, unless it is published in a journal with a very high Impact factor, like SuperNature .
On September 29, 2014, Greg Restall twitted: "This paper sets new standards for criticising my logical pluralism", without making any further comments. This twitting apparently had absolutely no effects even on the twitter himself who seemed not to have read the paper at this time. It is not clear that this quicky technology is very efficient for the academic world.
I have been accused of homophobia and sexism based on a few sentences extracted from the paper and pinned up on the web. Blogs have been commenting the topic: see e.g. In defense of journal editors who make mistakes. Some people say that this paper should not have been published, that its general contents is weak, that moreover other things I have written are dum - a kind of global warming started by a spark of irritation.
To reply to criticisms I will go from the general to the particular following the winning strategy of my uncle, the glorious General Bourbaki.


My mother tongue is the Swiss language - spoken by people like Piaget, Jung, Euler, Rousseau, Frutiger, Dunant, Gruyère, Heidi, Botta, Patek, Tinguely, Lindt, Chevrolet, Hofmann, Nestlé, Godard, Bernays, Ubs, Federer, Klee, and of course Saussure. I learned English by reading James Joyce, Lewis Carroll and Fredric Brown. So the way I am writing sometimes may look strange or punny. And my mother was teacher at the Montessori school of Casablanca, this possibly explains the freeway of my thought.


This paper is not a collection of random hazardous ideas that I wrote one day by chance. I have been working in mathematics, philosophy, logic since many years and this paper is a synthesis, in harmony with the title of the journal in which it was published following the standard norms of peer review.

The Journal SYNTHESE

January 7, 2016 I gave the talk "Is thought computable?" at the Israel Institute for Advanced Studies in Jerusalem. I started by saying that, like Plato, I consider that philosophy is at the top. I wrote a Master's thesis on Plato's cave under the direction of Sarah Kofman at the University Panthéon-Sorbonne, the number 1 in Paris, one step away from the Panthéon, and two from the Lycée Henri IV where I was before. Sarah, a PhD student of Deleuze and friend of the pseudo-American philosopher Jacques Derrida, was much concerned by women but never declared herself as a feminist. She wrote lots of books and papers, such as Aberrations: Le devenir-femme d'Auguste Comte and "The Imposture of Beauty: The Uncanniness of Oscar Wilde's Picture of Dorian Gray." I remember pretty well the first class I had with her, it was an analysis of the notion of Mimesis in Plato. Another funny woman I was attending classes of at this time was Suzanne Bachelard.

Sarah Kofman 1934-1994

Plato had the idea that the practice of mathematics was a good training for philosophy, cf. the motto at the entrance of the Academy. This motto was placed at the entrance of the Santa Fe Institute by David Krakauer, president of this institute, where I gave the talk Squaring Complexity the 1st of October 2015 and took the following picture:


A fundemental aspect of mathematics is proof. Bourbaki started his Elements of Mathematic saying: "Depuis les Grecs, qui dit mathématique, dit démonstration". Bourbaki decided to withdraw the "s" at the end "Mathematics" in search of unity.
Proving is a complex activity that can be understood only by practice, and that should not be confused with the sophistry of argumentation, where duels of thoughts replace the previous more bestial fights between pre-rational animals. Some people said that there are no arguments in my paper and I hope there are no. I am not interested in arguing.

Qui veut avoir raison a perdu la raison
Baron de Chambourcy

I don't believe that peace on earth will be reached by the fight of different groups defending their "own" rights but that it will emerge through intelligence.
Seeing the attacks I was facing one colleague wrote me:

1. Hire a libel/defamation lawyer, as soon as possible.
2. Provide documentation from the places where this has been published (including Wikipedia, Feminist Philosophers, Daily Nous, New APPS) showing where you've been accused of "homophobia" and "sexism".
3. Ask the lawyer if there is a way to challenge these publications immediately.

I will not do that because I hope that intelligence will prevail. On the right column I am tyring to explain one of the suspected sentences of my paper.

What is important is to understand. How understanding unfold in mathemtatics is a mysterious phenomenon, which was described in different ways by André Weil and Alexander Gothendieck, two of the most famous members of Bourbaki and greatest mathematicians of the XXth century.

ANDRE WEIL with his sister SIMONE
Every mathematician worthy of the name has experienced, if only rarely, the state of exaltation in which one thought succeeds another as if miraculously, and in which the unconscious (however one interprets the word) seems to play a role … Unlike sexual pleasure, this feeling may last for hours at a time, even for days .
The Apprenticeship of a Mathematician

Discovery is the privilege of the child: the child who has no fear of being once again wrong, of looking like an idiot, of not being serious, of not doing things like everyone else.

Understanding is a creative activity of which, in mathematics, proofs are the resulting manifestation. Some people are not able to prove anything, so they are trying to disapprove. Disapproval is an easy destructive game, developed by people having no creativity, trying to find counter-examples or attacking on superficial details: this proof is wrong because it has been written using a blue pen.
People have tried to catch the mystery of mathematical understanding in various ways. Among them, David Hilbert, one of the greatest mathematicians of all time. He promoted the word "metamathematics" as synonymous to "proof theory" (In German: "Beweistheorie"), which for him was the highest thing.

DAVID HILBERT (1862-1943)
Die Axiome und beweisbaren Sätze, d.h. die Formeln, die in diesem Wechselspiel enstehen, sind die Abbilder der Gedanken, die das übliche Verfahren der Bisherigen Mathematik ausmachen, aber sie sind nicht selbst die Wahreiten im absoluten Sinne. Als die absoluten Wahreiten sind vielmehr die Einsichten anzusehen, die durch meine Beweistheorie hinsischtlich der Beweisbarkeit und der Widerspruchsfreiheit jener Formelsysteme geliefert werden. (Die logischen Grundlagen der Mathematik) .

But understanding understanding is the most difficult thing. Gödel's results show that we cannot reduce mathematical reasoning to an easy mechanism. It is not a linear logic, going from A to B, step by step.


The most incomprehensible thing about the world is that it is comprehensible.
Albert Einstein.

In I678 Leibniz made a claim of the universal characteristic. In essence it does not exist: any systematic procedure for solving problems of all kinds must be nonmechanical. My incompleteness theorem makes it likely that mind is not mechanical. Kurt Gödel

Mathematical logic is a fascinating topic which has led to some confusions. On the one hand it is difficult to have a right understanding of Gödel's theorem, on the other hand it has had an effect on philosophy which is ambiguous. As it is known Gödel himself didn't share the perespective of XXth century philosophy developed in connection with logic.

The Pernicious Influence of Mathematics upon Philosophy

The fake philosophical terminology of mathematical logic has misled philosophers into beleiving that mathematical logic deals with the truth in the philosophical sense. But this is a mistake. Mathematical logic deals not with the truth but only with the game of truth. The snobbish symbol-dropping found nowadays in philosophical papers raises eyebrows among mathematicians, like someone paying his grocery bill with Monopoly money... The prejudice that a concept must be precisely defined in order to be meaningful, or that an argument must be precisely stated in order to make sense, is one of the most insidious of the twentieth century.

Rota was lecturing at the department of mathematics of MIT and also at the philosophy department where people tried without success to kick him out.

Intoduction of Indiscrete Thoughts

The truth offends... We take offence at those truths that threathen any of the myths we believe in ... Only on rare occasions do we summon the courage to discard a wilting myth; more often we hand on to a wilting myth to a very end. If anyone dares question any of our wilting myths, we still lash out an label him "eltisit", "subversive", "reactionary", "irrational", "cynical", "nihilistic", "obscurantist", We will seize on some incorrect but irrelevant detail as an excuse to dismiss an entire argument.

I cannot debunk here all the myths, answer all criticisms. On the right column I will concentrate on one sentence, which has been criticized. People can do the job themsleves for other sentences, as a kind of home work. Later on maybe I will write more, for example about political correctness. But I don't think that writing and talking is necessarily the only methodology. I have also studied cinema, at the Universities Paris 1 and Paris 3, and produced some movies, paintings and photographs,

The house designed by Wittgenstein in Vienna
Part of the Photo Project
Do Not Enter in The World.

I am currently preparing the launching of a new journal of philosophy making crucial use of images:


With my wife, Catherine Chantilly, we have developed some years ago a project "La femme allongée", in English: "The lying woman".


The opening of the exhibition was performed on woman's day, March 8, 2009, at the Villa Aurélienne, Fréjus, with 400 women lying down.

And here is a video we produced some years ago together with Alessio Moretiti, a Nice smurf.

Sufffering from Intelligence I did a therapy
Using the latest technology of Bi-Psychoanalysis.
I am not sure it has beeen completely successful.
I hope that I am now at least half stupid.
You can judge yourself looking a the below picture I was able to produce :

author of How brains make up their minds
and Societies of Brains

To finish this column, below you will find;
1. Comments by Arnon Avron, Professor at Tel Aviv University, and also member of the Editorial Board of Logica Universalis.
2. Comments by Laurent Lafforgue, Fields Medal 2002
3. Remarks about political correctness by Helmut Newton.
4. The latest news about the geo-political situation in the world by the most realiable TV channel on earth with a spectacular twin team of speakers.
5. A video of Raul Seixas, famous singer from Brazil, followed by the flag of Brazil, a Land of the Future, with the original motto of Auguste Comte Love, Order and Progress and by the logos of the University of Brazil and the Brazilian Academy of Philosophy.
6. The flag "Je suis Paris", defending liberty after terrorist attacks in Paris, Nov 13 2015
7. The famous painting of Eugène Delacroix with Liberté, Egalité, Fraternité, the motto of the French Republic, the painting having been remastered to provide guidance also for American people.


I admit that I was strongly hesitating to write this message. I was afraid that if I write what I think, I'll also be immediately tagged as "Homophob" and "sexist", and I might even lose the friendship of some friends that I really love. But the very fact that I found myself fearing reminded me what such a fear means, and what kind of atmosphere is now created, sometimes by really good people. So I decided it is my *duty* to say what I think.
I do not know what Beziau's general opinions are. All I am speaking here about is the content of the paper in question (which I read as a logician, meaning that I read what is actually written - no more, no less). So I declare that I find the reaction on "Feminist Philosophers" 100 times more frightening than the paragraph in Beziau's paper it was about. It is a Stalinist reaction. No less. How can anyone who actually reads it in a rational way describe it as "Homophobic And Sexist"? Or claim that Beziau "compares homosexuality to dictatorship"?? It reminds me the incident in Milan Kundera's book "the Joke" that led the hero of the story into a camp.
To sum up: I do not want to live in a world where every word I write is checked by the party's censors who are looking for offending interpretations, and then punish severely when they happily find one!
(Personally, I have enough of similar behavior now in my own country, where people who disagree with our dear government's policy in the occupied areas are immediately described by many, many people as anti-Semitic (if they are not Jews) or traitors (if they are like me).


I recently noticed that some lines from a paper by JYB titled “The relativity and universality of logic” have become the object of a ridiculous and odious harangue that takes up more than half of his Wikipedia page.
The paper, which I have read in its entirety, is at once both extremely interesting in its own right, and also for setting in perspective the author’s whole corpus of work over many years and defining a precise discipline which JYB has dedicated his efforts to establishing, which he calls “universal logic”. Based on a distinction between logic as reasoning and logic as a theory of reasoning, the paper defines “universal logic” as the general science of reasoning, a little like the way general linguistics is the science of what all human languages have in common.
The paper spells out both the sense and the reference of “universal logic” by delineating its domain of study and at the same time justifying the choice of constituent words in its name, by evoking their semantic fields and those of neighbouring expressions.
In a third part, JYB makes a critical comparison with three other more or less scientific expressions which are currently in use and to which he prefers “universal logic”: “logical pluralism”, “non-classical logics”, and “cognitive science”. Following the logic of his paper, he draws these comparisons both from the point of view of their content and objects of study, and from the point of view of the meanings and associations of their constituent words. It is by examining the semantic field of the word “pluralism” that he arrives at his observations about the contemporary field of “political correctness”, which he criticizes for sound reasons, as it represents a danger for the freedom of expression and of thought.
I invite therefore the people who launched or contributed to the polemic against JYB, in particular those who despoiled his Wikipedia page with 30-plus lines of rant against 5 or 6 lines from one paper, to comment in the same proportion on the whole of this remarkable paper, and on the works and initiatives (such as the journal Logica Universalis which he founded, or the multiple congresses he has organized on this subject, etc.) whose meaning this article explicates.

Helmut Newton: The term "political correctness" has always appalled me, reminding me of Orwell's "Thought Police" and fascist regimes.

Obey - Consume - Believe - Fear - Conform

Enquanto você se esforça prá ser
um sujeito normal e fazer tudo igual,
eu do outro lado aprendendo a ser louco,
um maluco total, mas na loucura real.
Controlando a minha maluquez,
misturada com a minha lucidez ...


Logical pluralism is fashionable and fashion is ephemeral and superficial, like a sexy young woman that 1 day will be a not so attractive old lady

This above sentence extracted from the paper has been criticized in particular by Feminists. The context: few lines before I was explaining that Greg Restall said, during a meeting we had in Hobart, Tasmania, that the expression "Logical Pluralism" - he was using to qualify a line of thought he was promoting with Jc Beall - was nice because it was "sexy".


Rather than going straight to the sexy point, let us start with some preliminaries. Nobody like to see a woman naked right at the start. Truth is not given in advance, this is the beauty of the Queen Aletheia. Let us start with the start, the number 1. And after climbing all the steps we will hopefully jump into infinity.

One may say that 1 is not the 1st. The question of the beginning is a difficult question.

Squirming around and up and down
Pushing together
Scattering mountains all around you
That is the sound of a new born world
And a light from a curious sky
It has begun
You're in the hands of destiny


When was all this? When that all began? When will it end?

Fundamantal questions are not easy to answer and maybe music or/and poetry is the best way.

RUDOLF CARNAP (1891 -1970)
The Elimination of Metaphysics
Through Logical Analysis of language

Perhaps music is the purest means of expression of the basic attitude because it is entirely free from any reference to objects ... Metaphysicians are musicians without musical ability... Our conjecture that metaphysics is a substitute, albeit an inadequate one, for art, seems to be further confirmed by the fact that the metaphysician who perhaps had artistic talent to the highest degree, viz. Nietzsche, almost entirely avoided the error of that confusion ... in Thus Spoke Zarathustra, he does not choose the misleading theoretical form, but openly the form of art, of poetry.

This was the prehistory of analytical philosophy. Post-modern analytic philosophy has embraced metaphysics as its daily bread in the machinery of academic philosophy which is a subfield in the system.

New York Times, January, 11, 2016

Philosophy adopted the scientific modus operandi of knowledge production, but failed to match the sciences in terms of making progress in describing the world. Much has been made of this inability of philosophy to match the cognitive success of the sciences. But what has passed unnoticed is philosophy’s all-too-successful aping of the institutional form of the sciences. We, too, produce research articles. We, too, are judged by the same coin of the realm: peer-reviewed products. We, too, develop sub-specializations far from the comprehension of the person on the street. In all of these ways we are so very “scientific.”
Our claim, then, can be put simply: Philosophy should never have been purified.


The sad fact is that in our field the referee system has collapsed. (There are undoubtedly some exceptions and your journal hopefully is one of them.) It is bad enough that competent referees are impossible to find in sufficient numbers. The catastrophe is that the referees that major journals rely on do not act responsibly any longer. They do not try to understand the paper they are reading. Instead they are looking for excuse to form a recommendation without having to do any thinking.
Furthermore, those few referees who are using substantial standards normally belong to one of the numerous cliques into which philosophy and philosophical logic has split. The members of one clique do not know and do not care what adherents of the other cult are doing. The standards that a referee is using are those of her or his private club and hence idiosyncratic and ill-educated. The outcome is well calculated to guarantee that no new ideas are published.
I was not surprised to hear that Donald Davidson never submitted any papers of his to the refereeing process.

E-mail of Hintikka to JYB, July 1st 2011.

With my wife Catherine Chantilly we are developing the project World Living Philosophers which is a series of movies. We have already shot a couple of them including Hintikka (available soon). Below extracts of a movie about some trendy French Philosophers.


La phénoménologie a l'ambition de parler des choses mêmes. Elle ne raconte pas d'histoires. Elle n'argumente pas. Elle décrit. Un vrai philosophe c'est quelqu'un qui parle des choses. Je ne parle pas des théories de la mort. Ce qui m'intéresse c'est de décrire le phénomène de la mort. Jean-Luc Marion

Let's come back to the the starting-block. In my paper it is written "1" and not "one" and some people have taken this as an excuse to claim that Synthese has a very poor editorial / proof-checking policy. On the contrary, I think they have a very good 1 because this is exactly what I wanted to write. "1" has not been transformed by a human robot into "one".


There are books on “style” (which frequently means typographical conventions), but their mechanical application by editorial assistants can be harmful. If you want to be an author, you must be prepared to defend your style; go forearmed into the battle.

Why writting "1" rather than "one"? When we say that "a sexy young woman will one day be a not so attractive old lady", it does not mean that suddenly on November 11, 2054, Sandy will switch from a sexy young woman into a not so attractive old lady. The idea to use "1" instead of "one" is to stress this ambiguity. Even if someone would like to biologically define sexiness in relation with menstruation, one is not valid, because menstruation does not stop in a specific given day.

FRANCOISE HARDY: On est bien peu de chose et mon amie la rose me l'a dit ce matin

There are some stages whose limits are a bit fuzzy: Sandy when she is a child, cannot give birth to children, and it is considered improper to qualify her as sexy. At some point it makes sense, this is another stage. This does not last forever and there is no problem at all with that. All stages of life are interesting. The sexy stage is surely important because at this point life can emerge. Is it outrageous to say that one day Sandy will not be anymore sexy? It is a kind of death. But not the final death. And anyway is natural death outrageous? This is part of life. What is outrageous is artificial death.


Some women would like to be sexy all their life, as if this was their only way to attract people. But can we fall in love with a woman just because she is sexy? Only if it is Love in C Minor ...


Or if her initials are BB:


But be aware that behind these initials there is perhaps something you were not even able to dream of:

Initials BB by THERION

This is a kind of artificial hell, but there are also artificial paradises, see one below. You can compare them having in mind this quote by Simone Weil: "Imaginary evil is romantic and varied; real evil is gloomy, monotonous, barren, boring. Imaginary good is boring; real good is always new, marvelous, intoxicating."

But before flying to artifical paradises with Tricky Jet, let us have a look at the source of the song "Initials BB". This is related in a mysterious encounter between Serge Gainsbourg and Louis Pauwels the author of The Morning of the Magicians and the conceptor of "sida mental".

Initials BB et l'Amour Monstre de Pauwels

The song "Initials BB" was directly inspired to Gainsbourg by his lover Brigitte Bardot. Gainsbourg wrote also "Je t'aime moins non plus" (in English: I love you my to to) for BB and they made an interpretation of it, which wasn't successful at all.

BB and Serge Gainsbourg - I love you my to to

A music score can have different interpretations. It is like a theory, that can have different models. Abandoned by BB, Serge produced another interpretation with another model, Jane B, he was not yet in love with. But this song, with a slightly modified title, turned into a world hit and was the beginning of a long love story between Serge and Jane.

Jane B. and Serge Gainsbourg - Je t'aime moi non plus

Including frequent visits in artificial paradises:


There are of course also men wanting to be sexy as long as possible. But men fade away too. Women and Men are not biologically similar, as you can see if you have a telescope. Men don't have menstruation and can reproduce until their death (unless they sterilized as "Nascimento" did). But anyway 1 man 1 terrible day is less sexy.

The Picture of Dorian Gray by Wilhelm Black

The modern world has a tendency to sexiness. What does all this mean? If you ask someone why he likes to talk about "sexy lecture", "sexy paper", "sexy computer", "sexy whatever", he will probably not be able to really explain what it means.
He can reply: why does it matter? But should not a philosopher (of language or anything) be curious about what he is saying? Some guys will say: I am doing philosophy when I am at my office, Monday to Friday, from 9 am to 5 pm, outside of that I am just an ordinary man, speaking in an informal way like everybody, using 4 letter words, including "sexy".

Sexy Way of Thinking

If you google "sexy" on the web of images, look at what you see. Can we promote a line of thought inspired by such "things"? It is not forbidden and there is no need to activate any police of thought to block that. But consciousness is a marvelous quality of human mind (We have already shot the Prince of Consciousness for our World Living Philosophers movie).
Sexy is sexist, in a syntactic way, as a grammatical tautology, and also semantically, in the newtork of meanings. Besides psychoanalysis, there are some more brainy analyses of associations. I have worked with Patrick Suppes to develop a theory of associations to explain how our brain is working.

Semantic Computation of Truth Based on Associations already Learned

The power of sexual attraction is very strong, almost like gravitation, and is leading to "gravideza".

ENIGMA Gravity of Love

But someone, something, can be interesting for some other reasons or for no reasons. Instead of saying that the reason I like the expression "The Rose is without a wherefore, she blooms because she blooms" is that it is sexy - is it really? - I can say that it is because it is beautiful.

Die Rose ist ohne Warum. Sie blühet, weil sie blühet. Sie achtet nicht ihrer selbst, fragt nicht, ob man sie siehet.
Angelus Silesius

Jimmy Wales started to work on some sexy project. Then he was able to go beyond that launching Wikipedia, which is a major project for humanity, beyond sexiness. A phenomenon which was prophesies by nobody - except perahps Isaac Asimov. With Wikipedia humanity is facing its own reality, has to take its destinity in its own hands. It is the birth of a kind of universal human mind.


At the present moment I am being crucified on Wikipedia. But that is not so dramatic, there were previous cases and there will be future ones. The project will go on and improve. What is fascinating on Wikipedia is that nearly everything can be tracked, this a good auto-control feature.
But it is not clear that the Wikipedia project will succeed. Will mankind find her way between the Scylla of specialization and the Charybdis of massification? This is a remake of an old Greek tragedy.
I am presently acting as Logic Area editor of the Internet Encyclopedia of Philosophy and jointly developing an Encyclopaedia of Logic. I don't think at this stage Wikipedia can seriously challenge these "Academic" projects. The ACADEMY is still alive. Wikipedia is good for information but not yet mature for knowledge.


Sexuality is only one aspects of human beings, connected with physical appearances. Up to which point are we depending on that and what can we do with it?

A beautiful woman looking at her image in the mirror may very well believe the image is herself. An ugly woman knows it is not. Simone Weil


He said: "I locked you in this body,
I meant it as a kind of trial.
You can use it for a weapon,
or to make some women smile."

A symbol of feminity is the Moon. Here is a nice song dedicated to her:

Minha lua navega serena
Vai de ipanema ao céu do irã.
Para ela a moda não é tudo a guerra
Não duvida o dia de amanhã.
Minha lua corre apaixonada
E a passarada segue o seu corcel.
Oh lua, oh lua rainha
Oh a lua é minha, é de quem quiser
Oh a lua, a lua é das princesas
E com mais certeza será dos garis,
Dos cantores, dos trabalhadores
Será dos atores quando a noite cair.
E será também dos prisioneiros,
Será dos canteiros e do chafariz
Oh lua, a lua da cidade,
Da humanidade e de quem quiser.

I am a logic

My wife is an artist, and I learned a lot from her; the fact that I can talk about things. I remember I was going out with her, before we were married, and we were walking from one part of the university to another part. My objective was to get from A to B, she wanted to stop and look at the moon, because it looked very nice. And I thought: 'What the hell would I want to look at the moon for, when I want to go to B?' Now, of course, I will look at the moon at all times with her.

Feminism is contrasting with feminity, the essence of woman, if any. Feminism is the reverse opposite of masculinism, a word that does not in fact really exist. There is only a purely negative word: "machismo".
What would be the female version of machismo? xachismo? See which value fits best here for the variable x. The range of the variable is of course from a to z and don't forget: "To be is to be the value of a variable!".

But beyond opposites there is perhaps something else.

Despite their physical and emotional differences, maybe men and women have the same capacity of reasoning, maybe logic is universal, and understanding can prevail.