C.S. Peirce and Category Theory

[Jon Awbrey]

Cf: C.S. Peirce and Category Theory • 1
https://inquiryintoinquiry.com/2021/06/23/c-s-peirce-and-category-theory-1/

Cf: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce
::: Jon Awbrey
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce/near/243321177

All,

I will use this space to post what comes to mind by way of Peirce.
Just to get the ball rolling (in good Sisyphean style) here's my
blog of mostly Peirce-related discussion and thought.

• Inquiry Into Inquiry ( https://inquiryintoinquiry.com/ )

Here's a historical perspective on the nature of signs
and the conduct of inquiry in Aristotle, Peirce, Dewey,
plus a few compatible thinkers.

• Interpretation as Action • The Risk of Inquiry
https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry

More later ...

Resources
=========

• Precursors Of Category Theory
https://oeis.org/wiki/Precursors_Of_Category_Theory

• Survey of Precursors Of Category Theory
https://inquiryintoinquiry.com/2020/09/20/survey-of-precursors-of-category-theory-2/

Regards,

Jon

[Jon Awbrey]

Cf: C.S. Peirce and Category Theory • 2
https://inquiryintoinquiry.com/2021/06/24/c-s-peirce-and-category-theory-2/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce
::: Henry Story
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce/near/243321300

<QUOTE HS:>
This book “Diagrammatic Immanence” has a whole chapter on Peirce and Category Theory.

• https://www.google.de/books/edition/Diagrammatic_Immanence/bjVYDwAAQBAJ
• https://www.google.de/books/edition/Diagrammatic_Immanence/bjVYDwAAQBAJ?gbpv=1
</QUOTE>

Dear Henry,

There's a two‑culture tension in the reception of Peirce these days.
Maybe it's always been that way but it strikes me as more bifurcated
today than any time since I began my Peirce studies 50+ years ago.
Peirce for the logic-math-science researcher and Peirce for the
humanities-literary-verbal stylist are almost immiscible types
of thinkers. I find this especially irksome in the case of Peirce
since I have felt from the beginning Peirce more than any other
thinker gave us the framework and the tools we need to integrate
the two‑culture divide in society at large.

The following paper touches on a number of related issues as
they affect the education and research missions of universities.

Awbrey, S.M., and Awbrey, J.L. (2001), “Conceptual Barriers to Creating
Integrative Universities”, Organization : The Interdisciplinary Journal
of Organization, Theory, and Society 8(2), Sage Publications, London, UK,
pp. 269–284.
https://journals.sagepub.com/doi/abs/10.1177/1350508401082013
https://www.academia.edu/1266492/Conceptual_Barriers_to_Creating_Integrative_Universities

Regards,

Jon

[Jon Awbrey]

Cf: C.S. Peirce and Category Theory • 3
https://inquiryintoinquiry.com/2021/06/27/c-s-peirce-and-category-theory-3/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce

::: Kyle Rivelli
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce/near/244015437

<QUOTE KR:>
I really enjoyed the “Diagrammatic Immanence” book.
Gangle has another book that goes into more depth with Peirce:
Gianluca Caterina and Rocco Gangle (2016), “Iconicty and Abduction”
https://www.amazon.com/Iconicity-Abduction-Philosophy-Epistemology-Rational/dp/3319442449
</QUOTE>

Thanks, Kyle,

I've been looking at this book for a while now, trying to decide
if there's anything in it I need to know badly enough to justify
the purchase.

The connection between the types of inference (Abduction, Induction, Deduction) and
the types of signs (Icons, Indices, Symbols) is a pivotal question in Peirce's logic,
occupying the interface between his theory of inquiry and his theory of signs. It's
an issue I've done a lot of thinking, dialoguing, and blogging about. I will dig up
some links later but here is one for starters.

• Survey of Abduction, Deduction, Induction, Analogy, Inquiry
https://inquiryintoinquiry.com/2020/12/16/survey-of-abduction-deduction-induction-analogy-inquiry-2/

Regards,

Jon

[Jon Awbrey]

Cf: C.S. Peirce and Category Theory • 4
https://inquiryintoinquiry.com/2021/06/28/c-s-peirce-and-category-theory-4/

Re: C.S. Peirce and Category Theory • 3

https://inquiryintoinquiry.com/2021/06/27/c-s-peirce-and-category-theory-3/
Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce
::: Kyle Rivelli
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce/near/244015437

Dear Kyle,

My Inquiry Into Inquiry ( https://inquiryintoinquiry.com/ ) blog
has a Survey ( https://inquiryintoinquiry.com/surveys/ ) page where
I collect blog and wiki resources on all the longer-running topics
I write and dialogue about. The following two collections bear on
the close relationship, almost a kind of noun-verb or product-process
duality, between signs and inquiry.

• Survey of Abduction, Deduction, Induction, Analogy Inquiry
https://inquiryintoinquiry.com/2020/12/16/survey-of-abduction-deduction-induction-analogy-inquiry-2/

• Survey of Pragmatic Semiotic Information
https://inquiryintoinquiry.com/2020/11/01/survey-of-pragmatic-semiotic-information-5/

Especially relevant to the complex of connections Peirce suggests
between the main types of signs (Icons, Indices, Symbols) and the
main types of inference (Abduction, Induction, Deduction) are my
study notes
( https://oeis.org/wiki/Information_%3D_Comprehension_%C3%97_Extension )
and blog series on Peirce's Laws of Information
( https://oeis.org/wiki/Information_%3D_Comprehension_%C3%97_Extension#Selection_17 ),
the spirit of which is captured by the following formula.

• Information = Comprehension × Extension

I appear destined to revisit this subject every other summer or so.
Here's an outline of the last time around.

Information = Comprehension × Extension } • Revisited
https://inquiryintoinquiry.com/2019/01/23/information-comprehension-x-extension-revisited/
Selections
https://inquiryintoinquiry.com/2019/01/26/information-comprehension-x-extension-revisited-selection-1/
https://inquiryintoinquiry.com/2019/01/28/information-comprehension-x-extension-revisited-selection-2/
https://inquiryintoinquiry.com/2019/01/30/information-comprehension-x-extension-revisited-selection-3/
https://inquiryintoinquiry.com/2019/02/03/information-comprehension-x-extension-revisited-selection-4/
https://inquiryintoinquiry.com/2019/02/06/information-comprehension-x-extension-revisited-selection-5/
https://inquiryintoinquiry.com/2019/02/08/information-comprehension-x-extension-revisited-selection-6/

Probably about due for another return ...

Jon

[Jon Awbrey]

Cf: C.S. Peirce and Category Theory • 5
https://inquiryintoinquiry.com/2021/06/29/c-s-peirce-and-category-theory-5/

Re: C.S. Peirce and Category Theory • 2
https://inquiryintoinquiry.com/2021/06/24/c-s-peirce-and-category-theory-2/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce

::: Henry Story
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce/near/243321300
::: Avi Craimer
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce/near/243429978
::: Henry Story
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce/near/243446476

Dear Avi, Henry,

Diagrams are a mixed bag, a complex and polymorphic species, in Peircean semiotics.
All diagrams in common use, especially in mathematics, involve all three types of signs —
Symbols, Icons, Indices — as interpreted by their user communities. There has been a
tendency in recent years to overemphasize the iconic aspects of Peirce's logical graphs
( https://oeis.org/wiki/Logical_Graphs ), reading them a bit too much on the analogy of
venn diagrams, but their real conceptual and computational power comes rather from their
generic symbolic character.

Here's an intro to Sign Relations from a Peircean point of view,
still a bit “working on it” from my POV.

• Sign Relations ( https://oeis.org/wiki/Sign_relation )

Here's the skinny on the three main types of signs —
Symbols, Icons, Indices — in Peirce's theory of signs.

• Semeiotic ( https://oeis.org/wiki/Semeiotic )
• Types of Signs ( https://oeis.org/wiki/Semeiotic#Types_of_signs )

Regards,

Jon

[Jon Awbrey]

Cf: C.S. Peirce and Category Theory • 6
https://inquiryintoinquiry.com/2021/06/30/c-s-peirce-and-category-theory-6/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce
::: Henry Story

https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce/near/243672428

<QUOTE HS:>
I'd love it of course if all of Peirce's graphs could be mapped to CT.
That would help me integrate that work a lot faster. Or alternatively,
if one could work out exactly where it could not be tied into CT, that
would also be very helpful.

Dear Henry,

The way I see it, Peirce's work as a whole requires us to stand back from
our current picture of category theory and adopt a more general perspective
on the subject as we know it. That has not been a popular opinion in math
circles and scarcely grasped in phil circles. It's on my big bucket list
of Failures To Communicate (
https://inquiryintoinquiry.com/?s=What+we%E2%80%99ve+got+here+is+%28a%29+failure+to+communicate ) but I haven't really
tried
all that hard lately so maybe I'll give another go.

Regards,

Jon

[Jon Awbrey]

Cf: C.S. Peirce and Category Theory • 7
https://inquiryintoinquiry.com/2021/07/01/c-s-peirce-and-category-theory-7/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce
::: Henry Story

https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce/near/243650168

<QUOTE HS:>
I'd be very interested in the comments of people who know about Peirce on the two chapters in the Book Diagrammatic
Immanence ( https://www.google.com/books/edition/Diagrammatic_Immanence/bjVYDwAAQBAJ ) I linked to above on “3. Peirce”
and “4. Diagrams of Variation : Functor Categories and Presheaves”. The chapter on Presheaves has some good intuitions
on how to explain them that I recognise from studying them a year ago. At the end of that chapter the author Rocco
Gangle argues that Peirce's diagrams can be modelled in terms of Category Theory. I would have expected a long list of
articles to follow to underwrite that claim. Perhaps this is all well known in Peirce or CT circles …
</QUOTE>

Dear Henry,

Things are a little calmer in my neck of the woods at the moment so
I'm paddling back up Peirce Bayou to clear up some of the points I missed
during last week's tempest and root canal. An hour's expedition through
Amazon's creeks and tributaries finally turned up a pearl of not too great
a price so far as Diagrammatic Immanence goes so I tumbled for a paperback
edition to arrive in a couple of weeks but the purchase lets me read it on
Kindle right away. So I'll be perusing that …

Regards,

Jon

[Jon Awbrey]

Cf: C.S. Peirce and Category Theory • 8
https://inquiryintoinquiry.com/2021/07/02/c-s-peirce-and-category-theory-8/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce
::: Henry Story
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce/near/243650168

Re: Laws of Form
https://groups.io/g/lawsofform/topic/c_s_peirce_and_category/83739798
::: Lyle Anderson
https://groups.io/g/lawsofform/message/374

<QUOTE LA:>
As I am trying to get “frame sync” on this discussion, as the satellite communications people say, I am taking clues
from the introduction to the listing for Gangle's Diagrammatic Immanence (
https://www.google.com/books/edition/Diagrammatic_Immanence/bjVYDwAAQBAJ ) .

<QUOTE Edinburgh University Press>
A renewal of immanent metaphysics through diagrammatic methods and the tools of category theory Spinoza, Peirce and
Deleuze are, in different ways, philosophers of immanence. Rocco Gangle addresses the methodological questions raised
by a commitment to immanence in terms of how diagrams may be used both as tools and as objects of philosophical
investigation. He integrates insights from Spinozist metaphysics, Peircean semiotics and Deleuze's philosophy of
difference in conjunction with the formal operations of category theory. Category theory reveals deep structural
connections among logic, topology and a variety of different areas of mathematics, and it provides constructive and
rigorous concepts for investigating how diagrams work.
</QUOTE></QUOTE>

Henry, Lyle, All,

This discussion keeps flashing me back to an unfinished syzygy from
the mid '80s when I took a course on “applications of λ-calculus” with
John Gray at Illinois pursuing the trio of combinators, computation, and
cartesian closed categories, all hot topics of the day, and followed it up
with a guided study on the connections to Peirce I had glimpsed at the time.
I'll dig up some notes and get back to that. For the moment I'll focus on
category theory in the light of Peirce. The lights of Spinoza and Deleuze
I'll leave to observers who see better by them.

Regards,

Jon