Paraconsistent Newsletter Winter-Summer 2022

Thu Mar 24 07:17:12 EDT 2022

In the Winter-Summer 2022 edition of the Paraconsistent Newsletter we have:
- latest papers and books about paraconsistent logic
- videos of interest for paraconistentists
- interview with Max Urchs
- forthcoming events  for paraconistentists
https://www.paraconsistency.org/2022winter-summer

In the part events of this edition of the paraconsistent newsletter is
announced the 6th edition of the Word Congress on Paraconsistency (WCP6)
that  will take place at the  University Nicolaus Copernicus in Torun,
Poland 5-8 September 2022. The deadline to submit an abstract is April 30.
I am very  glad that Marek Nasieniewski, main organizer of the event, took
the initiative to organize  WCP6, with the full support of the current head
of the Department of Logic of this University (yes there are universities
with a department of logic !), Tomasz Jarmuzek, also  a long time friend.
The University Nicolaus Copernicus is where the logician Stanisław
Jaśkowski was working (he was also at some point the rector of this
University). WCP6 is also the Second Stanisław Jaśkowski Memorial
Symposium, Toruń
The first took place in 1998 in Torun to celebrate Jaśkowski's first paper
on Discussive Logic, considered as a fundamental step in the history of
paraconsistent logic.
The interview of this edition of the newsletter is with Max Urchs, one of
the keynote speakers of WCP6, who worked in Torun in the 1970s. We were
both colleagues at the Department of Logic of the University of Wroclaw in
1990s. In 1993 we went together with his cas (together with Andrew
Wisniewskli, one of the best specialists of Erotetic Logic), to Prague to
take part in the "Logica" meeting, crossing Bohemia.

The latest edition of the WCP was in India in 2015. I organized it
jointly with my colleague Mihir Chakarborty from Kolkata. I also was the
co-organizer of WCP3 in Toulouse France in 2003, jointly with Walter
Carnielli and Andreas Herzig. WCP1 took place in Ghent in 1997. It was the
initiative of Graham Priest.
At this time he was still working in Australia but decided to organize the
event in Belgium with his friend Diderik Batens (three people took part in
all WCPs: Diderik Batens, Walter Carnielli and myself) because he thought
that not so many people would come to Australia.  Then I proposed to
organize WCP2 in Brazil in 1999, for the 70th birthday of Newton da Costa
(born in 1929).
The  event was organized by my colleagues from  Campinas: Itala
D'Ottaviano,  Walter Carnielli, Marcelo Coniglio, with the support of
their  students. It was delayed by one year. It took place May 8-12, 2000.
In 2000 and 2001. I was working at Stanford University in California but
came for the event. Before that, I succeeded in convincing my colleagues to
organize the event on the beach, rather than at the campus of UNICAMP. I
got the support of João Marcos, at the time a pos-graduated student at
UNICAMP. With his car we drove the littoral during a couple days to find a
good location. We chose Juquehy beach and the event was organized at
Juqehy Praia Hotel
https://juquehypraiahotel.com.br/
Everybody enjoyed it very much, according to Graham Priest,it was the best
event he ever took part in.

I think the success of an event depends 50% on its location. Since I am
organizing events I have always looked for a good location. I  have
organized events at the American University of Beirut in Lebanon,
Easter Island,  Istanbul University, Lateran Pontifical University,
Montreux, Switzerland,  Xi'an, the ancient capital of China, the Orthodox
Academy of Crete ... I have organized many events because I think research
is a collective enterprise and cooperation between people is fundamental.
This does not dismiss in any sense the merit of someone like Einstein. But
Einstein did not invent non-Euclidean geometry. In logic. The two most
famous logicians of the 20th century, Tarski and Göde,l on the basis on
which I created the World Logic day in 2919:
https://www.logica-universalis.org/wld4
were certainly both geniuses but Gödel grew up in the Hilbert-Bernays
School  and Tarski in the Lvov-Warsaw School:
The Lvov-Warsaw School. Past and Present
https://link.springer.com/book/10.1007/978-3-319-65430-0
(This book includes a  paper about Jaskowsi)

I started to work on paraconsistent logic in 1989, when I was a
pos-graduted student of philosophy at the Sorbone, University of Paris 1,
and of mathematics at Denis Diderot University (Paris 7). I discovered by
chance an interview with  Newton da Costa in the Lacanian magazine "L'âne"
(the donkey.) about paraconsistent logic as the logic of the unconscious. I
got interested in the topic because I wanted to understand the basis of
reasoning, of logic. That's why I decided to study logical systems
challenging the principle of non-contradiction. I did my master thesis
(1990) on mathematical logic about the logic C1 of Newton da Costa,
presenting a new version of its semantics, a sequent calculus for it and
the corresponding cut-elimination theorem (I studied proof-theory with
Jean-Yves Girard).  Then I did a PhD on mathematical logic on "universal
logic" (1995), a expression I put forward to develop a general theory of
logical structures with no axioms, inspired by what Garret Birkhood
did with "universal algebra"  for algebraic systems. I don't know if there
are some "laws of thoughts'". According to Boole the basic law of thought
is square x is identical to x, from which he derives the principle of
non-contradcition, see the paper:
"Is the Principle of Contradiction a Consequence of x 2=x ?""
http://www.jyb-logic.org/BOO
But I believe there is not one unique system of logic that describes human
reasoning and its understanding of reality.
That's why I think it is worth developing a general theory of all kinds of
logical systems, including those in which  the principle of
non-contradiction is not valid, or the law of identity or excluded middle,
transitivity, monotonicity, etc . I defend the idea of "axiomatic
emptiness":
"What is a logic? Towards axiomatic emptiness"
https://jyb-logic.org/papers/what%20is%20a%20logic%20-%20towards%20axiomatic%20emptiness%20-%20beziau.pdf

Although universal logic has been my main focus since then, I always
continued to work on paraconsistent logic (and also on other non classical
logics, different philosophical topics, semiotics, etc).
In paraconsistent logic one of my main contributions was the discovery that
there is a paraconsistent negation in the modal logic S5 and that therefore
S5 is a paraconsistent logic (as well as first-order classical logic,
considering Wajsberg theorem). I first built a logic I called "Z"
inspired by Jaskowski's discussive logic.
The negation of a proposition is false according to a group of people
iff everybody of the group agrees that the proposition is true. For example
if in a group of people everybody agrees that "The earth is flat" is true,
then "The earth is not flat" is false according to this group of people.
But if there is at least one who does not agree, then "The earth is not
flat" is also true according to this same group of people, which therefore
accepts to have  a given proposition and its negation both true:
 “The paraconsistent logic Z - A possible solution to Jaskowski's problem”,
Logic and Logical Philosophy, 15 (2006), pp.99-111
https://www.jyb-logic.org/Beziau_LLP_cor.pdf
The content of this paper was first presented on a talk   at the frist
Stanisław Jaśkowski Memorial Symposium in  Toruń in 1998.Poland
This logic used only classical conjunctions, disjunction and implication
and a paraconsistent negation semantically defined by a possible world
semantics (this is why I decided to call it "Z", by reference to LeibniZ)
.  Then a friend of mine, Claudio Pizzi showed me that in Z it is possible
to define necessity and classical negation, so at the end  Z = S5.
If we consider S5 as it is generally presented, the paraconsistent negation
is the classical negation of necessity not box.
“The Contingency of Possibility”, Principia, vol.20 n.1 (2016), pp.99-115.
https://periodicos.ufsc.br/index.php/principia/article/view/1808-1711.2016v20n1p99/32670
So what I did with Z is a new formulation of S5  (both semantically and
proof-theoretically) starting with this sole unary operator, not using
necessity, possibility or classical negation.
Routley (with Montgomery in the 1960s) started with the conjunction of
diamond and not box, they called "contingency". This is very interesting
from a philosophical point of view because this contingency operator  is
the usual sense of the word "possible" in natural language: something which
is possible ... but not necessary!  I met Richard Routley (then Sylvan)
the first and last time in  1994 when he was visiting Newton da Costa in
São Paulo with Graham Priest. I gave to  him the draft of my first paper on
universal logic, "Universal Logic":
https://www.jyb-logic.org/papers/LogicaYB94%20-%20Beziau.pdf
The following day he gave it back to me with some annotations and told me
that he will speak about it in the forthcoming second volume of  "Relevant
Logics and Their Rivals", but not long after, back to Australia he died. I
started the Paraconsistent Newsletter in 2006, inspired by a paper by
Sylvan where he was speaking about the importance of a newsletter for
relevant logic.
I met Bob Meyer at the meeting of the Society for Exact Philosophy in
Montreal in 1997 and explained to him the results about Z/S5, asking if
someone had already done a similar work, he told me he never heard about
such a thing.
This paraconsistent negation has good properties, in particular it is
self-extensional, i.e. it obeys the replacement theorem, by contrast to
most of paraconsistent negations (C1, Asenjo-Priest  three-valued logic,
etc.) as shown here:
“Idempotent full paraconsistent negations are not algebraizable”, Notre
Dame Journal of Formal Logic, 39 (1998), pp.135-139.
https://www.jyb-logic.org/idempotent.pdf
When I was working with Tel-Aviv in 1995-96 with Arnon Avron within the
Marie-Curie GeTFun project led by João Marcos and Carlos Caleiro
http://sqig.math.ist.utl.pt/GeTFun
I asked Arnon if it would be possible to have a self-extensional logic
three-valued paraconsistent logic with a standard implication and the
result is no! :
A.Avron and J.-Y.Beziau, “Self-extensional three-valued paraconsistent
logics have no implication”, Logic Journal of the IGPL, Volume 25, Issue 2
(April 2017), pp.183-194.
https://academic.oup.com/jigpal/article-abstract/25/2/183/2739325/Self-extensional-three-valued-paraconsistent?redirectedFrom=fulltext&login=false
I then asked him about such a situation for four-valued matrix semantics,
and later on he published the paper, giving a positive answer to the
question:
"The Normal and Self-extensional Extension of Dunn–Belnap Logic"
https://link.springer.com/article/10.1007/s11787-020-00254-1
Arnon Avroin will also be a keynote speaker of WCP6
Coming back to S5, it has not only good formal properties but the
paraconsistent negation of Z has a good intuitive motivation /
interpretation, as shown by the reconstruction of S5 through Z.
So at the end I think S5 is one of the best paraconsistent logic ! (it has
a paracomplete negation too, not possible).

I also worked on the fundamental  philosophical aspects of paraconsistent
logic, may main contributions are the two following papers
"Cats that are not cats - Towards a natural philosophy of paraconsistency"
http://www.jyb-logic.org/CATS
"Round Squares are no Contradictions"
http://www.jyb-logic.org/ROS

Jean-Yves Beziau
Creator and Editor of the Paraconsistent Newsletter
Paraconsistent Logician and Artist
https://sites.google.com/view/miaou-rio/jyb

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