[PEIRCE-L] Logic and Semitotics

[jean-yves beziau]

A new book series:
http://www.collegepublications.co.uk/las/
submissions are welcome !
The first volume
The Arbitrariness of the Sign in Question
Proceedings of a CLG100 Workshop, Geneva, January 10-12, 2017
http://www.collegepublications.co.uk/las/?1
will be launched next week at the 14th International Congress of Semiotics
in Buenos Aires
https://www.worldcongressofsemiotics2019.org/en
JYB

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Re: [PEIRCE-L] Intuitionistic Existential Graphs (IEGs)

[Jon Alan Schmidt]

Jeff, List:

Indeed, I provided the same link to the English slide presentation in my
post that started this thread.  Again, the papers include plenty of IEG
examples, and once one figures out the Spanish terms and abbreviations,
they are relatively easy to follow.  Moreover, I am finding that
https://translate.google.com/ does a surprisingly decent job with the text.
:-)

I also previously quoted Zalamea and linked to his short article (
https://riviste.unimi.it/index.php/Lebenswelt/article/view/3/10508) that
summarizes both Oostra's IEGs and Francisco Vargas's proposal for a new
mathematical model of Peirce's continuum; he calls the latter "a single
stroke of genius" (p. 79).  Even so, he later states, "I have had the
chance of having fantastic students, which, then, with time, have become my
teachers. Arnold Oostra is possibly the greatest student I have
encountered, and, undoubtedly, he has now become the foremost international
scholar on Peirce's mathematics" (p. 82).  High praise, especially
considering the source!

Incidentally, as you probably know, Vargas's paper on the continuum is in
volume 7 of *Cuadernos de Sistemática Peirceana* along with your own
contribution, "On the Hypotheses that Lie at the Bases of Discrete Systems
of Mathematics:  Drawing on Peirce’s Phenomenology."  Zalamea's brief
synopsis in English is already well beyond my competence, so in this case I
do not hold out much hope of being able to make sense of the details in
Spanish.

Regards,

Jon S.

On Thu, Sep 5, 2019 at 4:47 PM Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Hi Jon S, John S, List,
>
> Arnold Oostra gave presentations in English on his work on intuitionistic
> logics and the EG at the Peirce Centennial Congress in 2014 and on related
> themes at the later meeting on Peirce's work on mathematics in Bogota
> (organized by Fernando Zalamea). At the latter, he was effectively the
> keynote speaker.
>
> Having searched Google Scholar, it is hard to fund much of his work that
> isn't in Spanish. Here is an example of a presentation in English to give
> you a flavor of what he is doing:
> https://matematicas.uniandes.edu.co/eventos/SLALM2012/slides/arnold_oostra.pdf
>
> Fernando has created a community of students and scholars in Bogota who
> are working on Peirce and the EGs. Arnold has reproduced that model in
> Tolima. The quality of the research products of his *undergraduate*
> students is quite strong. It is clear that both Fernando and Arnold are
> remarkable teachers as well as researchers.
>
> --Jeff
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354
> --
> *From:* Jon Alan Schmidt 
> *Sent:* Thursday, September 5, 2019 1:04:55 PM
> *To:* peirce-l@list.iupui.edu
> *Subject:* Re: [PEIRCE-L] Intuitionistic Existential Graphs (IEGs)
>
> John, List:
>
> Thanks for the additional background information.  For anyone interested
> in further details about Oostra's approach, attached is a combined PDF with
> his relevant papers in Spanish from the first five volumes of *Cuadernos
> de Sistemática Peirceana*.  The first and last relate Peirce's thought to
> intuitionistic mathematics and logic in general, while the middle three
> specifically explain his Alpha, Beta, and Gamma systems of IEGs.  He
> concludes by stating that (ironically) omitting what is now known as
> Peirce's Law from his 1885 article in *The American Journal of
> Mathematics*, "On the Algebra of Logic:  A Contribution to the Philosophy
> of Notation" (CP 3.359-403), would have provided the nucleus for an
> axiomatization of intuitionistic logic.
>
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Professional Engineer, Amateur Philosopher, Lutheran Layman
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
> On Thu, Sep 5, 2019 at 1:46 PM John F. Sowa  wrote:
>
>> Intuitionistic logic was founded by the Dutch mathematician L. E. J.
>> Brouwer.  He objected to "nonconstructive" proofs by contradiction.
>>
>> Many mathematicians have been sympathetic, but they were reluctant to use
>> Brower's logic because it made many legitimate theorems more difficult to
>> prove.
>>
>> For more info, see https://plato.stanford.edu/entries/intuitionism/
>>
>> Re EGs:  Peirce's diagrammatic reasoning, which begins with diagrams and
>> reasons about them is by its very nature constructive.  However, Peirce's
>> rules of inference also allow proofs by contradiction.
>>
>> The idea of making EGs intuitionistic would enforce constraints on the
>> rules of inference to prohibit the options that are nonconstructive.  That
>> could be considered as a kind of three-valued logic with True, False, and
>> Not provable.  But that's different from True, False, and Unknown -- or the
>> fuzzy versions with a continuous range of values.
>>
>> Susan Haack strongly objected to Zadeh's idea of a continuum of truth
>> values.  But it would be more appropria

Re: [PEIRCE-L] Intuitionistic Existential Graphs (IEGs)

[Jeffrey Brian Downard]

Hi Jon S, John S, List,


Arnold Oostra gave presentations in English on his work on intuitionistic 
logics and the EG at the Peirce Centennial Congress in 2014 and on related 
themes at the later meeting on Peirce's work on mathematics in Bogota 
(organized by Fernando Zalamea). At the latter, he was effectively the keynote 
speaker.


Having searched Google Scholar, it is hard to fund much of his work that isn't 
in Spanish. Here is an example of a presentation in English to give you a 
flavor of what he is doing:  
https://matematicas.uniandes.edu.co/eventos/SLALM2012/slides/arnold_oostra.pdf


Fernando has created a community of students and scholars in Bogota who are 
working on Peirce and the EGs. Arnold has reproduced that model in Tolima. The 
quality of the research products of his undergraduate students is quite strong. 
It is clear that both Fernando and Arnold are remarkable teachers as well as 
researchers.


--Jeff



Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354

From: Jon Alan Schmidt 
Sent: Thursday, September 5, 2019 1:04:55 PM
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Intuitionistic Existential Graphs (IEGs)

John, List:

Thanks for the additional background information.  For anyone interested in 
further details about Oostra's approach, attached is a combined PDF with his 
relevant papers in Spanish from the first five volumes of Cuadernos de 
Sistemática Peirceana.  The first and last relate Peirce's thought to 
intuitionistic mathematics and logic in general, while the middle three 
specifically explain his Alpha, Beta, and Gamma systems of IEGs.  He concludes 
by stating that (ironically) omitting what is now known as Peirce's Law from 
his 1885 article in The American Journal of Mathematics, "On the Algebra of 
Logic:  A Contribution to the Philosophy of Notation" (CP 3.359-403), would 
have provided the nucleus for an axiomatization of intuitionistic logic.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - 
twitter.com/JonAlanSchmidt

On Thu, Sep 5, 2019 at 1:46 PM John F. Sowa 
mailto:s...@bestweb.net>> wrote:

Intuitionistic logic was founded by the Dutch mathematician L. E. J. Brouwer.  
He objected to "nonconstructive" proofs by contradiction.

Many mathematicians have been sympathetic, but they were reluctant to use 
Brower's logic because it made many legitimate theorems more difficult to prove.

For more info, see https://plato.stanford.edu/entries/intuitionism/

Re EGs:  Peirce's diagrammatic reasoning, which begins with diagrams and 
reasons about them is by its very nature constructive.  However, Peirce's rules 
of inference also allow proofs by contradiction.

The idea of making EGs intuitionistic would enforce constraints on the rules of 
inference to prohibit the options that are nonconstructive.  That could be 
considered as a kind of three-valued logic with True, False, and Not provable.  
But that's different from True, False, and Unknown -- or the fuzzy versions 
with a continuous range of values.

Susan Haack strongly objected to Zadeh's idea of a continuum of truth values.  
But it would be more appropriate to consider the fuzzy values as degrees of 
confidence or belief.

Re EGs: It's possible to translate any algebraic notation to and from an EG 
form.  Therefore, any interpretation -- fuzzy, intuitionistic, modal, 
metalanguage -- that could be expressed in an algebraic form could be adapted 
to an EG version and vice-versa.

By the way, Brouwer was a member of Lady Welby's Significs group, but it's 
unlikely that Peirce and Brouwer ever communicated.

John

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Re: [PEIRCE-L] Intuitionistic Existential Graphs (IEGs)

[John F. Sowa]

Intuitionistic logic was founded by the Dutch mathematician L. E. J.
Brouwer.  He objected to "nonconstructive" proofs by
contradiction.
Many mathematicians have been sympathetic, but they
were reluctant to use Brower's logic because it made many legitimate
theorems more difficult to prove.
For more info, see
https://plato.stanford.edu/entries/intuitionism/
Re EGs:  Peirce's
diagrammatic reasoning, which begins with diagrams and reasons about them
is by its very nature constructive.  However, Peirce's rules of inference
also allow proofs by contradiction.
The idea of making EGs
intuitionistic would enforce constraints on the rules of inference to
prohibit the options that are nonconstructive.  That could be considered
as a kind of three-valued logic with True, False, and Not provable.  But
that's different from True, False, and Unknown -- or the fuzzy versions
with a continuous range of values.
Susan Haack strongly objected to
Zadeh's idea of a continuum of truth values.  But it would be more
appropriate to consider the fuzzy values as degrees of confidence or
belief.
Re EGs: It's possible to translate any algebraic notation to
and from an EG form.  Therefore, any interpretation -- fuzzy,
intuitionistic, modal, metalanguage -- that could be expressed in an
algebraic form could be adapted to an EG version and vice-versa.
By
the way, Brouwer was a member of Lady Welby's Significs group, but it's
unlikely that Peirce and Brouwer ever communicated.
John

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