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Jul 28, 2021, 9:50:16 AM7/28/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG

Cf: Logical Graphs • Discussion 1

https://inquiryintoinquiry.com/2021/07/28/logical-graphs-discussion-1/

Re: Laws of Form

https://groups.io/g/lawsofform/topic/software_for_lof/84501600

::: John Mingers ( https://groups.io/g/lawsofform/message/559

<QUOTE JM:>

I find it very frustrating not to be able to draw crosses and

expressions within emails or Word documents. Does anyone know

of any software or apps that can do this? If not, with so many

computer scientists on this group, could someone produce something?

</QUOTE>

Dear John, All …

People with backgrounds in computing, combinatorics, or graph theory

would immediately recognize Spencer Brown's expressions are isomorphic

to what graph theorists know and love as “trees”, more specifically

“rooted trees”, with a particular manner of attaching letters to the

nodes to be described later. In those fields there's a standard way

of mapping trees to strings of parentheses and letters. This operation

is called “traversing the tree” when one passes from trees to strings

and the reverse operation is called “parsing” when one passes from

strings to “parse trees”.

The transformation of Spencer Brown's simple closed figures in the plane,

or his formal expressions of “crosses”, into rooted trees, together with

the further transformation of those two forms to “pointer data structures”

in computer memory is discussed in the following post on my blog.

• Logical Graphs • Introduction

https://inquiryintoinquiry.com/2008/07/29/logical-graphs-1/

There's a more formal presentation of logical graphs, working from

the axioms or “initials” I borrowed with modifications from Peirce

and Spencer Brown, in the following blog post.

• Logical Graphs • Formal Development

https://inquiryintoinquiry.com/2008/09/19/logical-graphs-2/

Those two pieces are combined and extended in the following article.

• Logical Graphs ( https://oeis.org/wiki/Logical_Graphs

The program I developed all through the 80s using those data structures

in its logic module is documented so far as I've managed at this point

on the following page.

• Survey of Theme One Program

https://inquiryintoinquiry.com/2020/08/28/survey-of-theme-one-program-3/

Regards,

Jon

https://inquiryintoinquiry.com/2021/07/28/logical-graphs-discussion-1/

Re: Laws of Form

https://groups.io/g/lawsofform/topic/software_for_lof/84501600

::: John Mingers ( https://groups.io/g/lawsofform/message/559

<QUOTE JM:>

I find it very frustrating not to be able to draw crosses and

expressions within emails or Word documents. Does anyone know

of any software or apps that can do this? If not, with so many

computer scientists on this group, could someone produce something?

</QUOTE>

Dear John, All …

People with backgrounds in computing, combinatorics, or graph theory

would immediately recognize Spencer Brown's expressions are isomorphic

to what graph theorists know and love as “trees”, more specifically

“rooted trees”, with a particular manner of attaching letters to the

nodes to be described later. In those fields there's a standard way

of mapping trees to strings of parentheses and letters. This operation

is called “traversing the tree” when one passes from trees to strings

and the reverse operation is called “parsing” when one passes from

strings to “parse trees”.

The transformation of Spencer Brown's simple closed figures in the plane,

or his formal expressions of “crosses”, into rooted trees, together with

the further transformation of those two forms to “pointer data structures”

in computer memory is discussed in the following post on my blog.

• Logical Graphs • Introduction

https://inquiryintoinquiry.com/2008/07/29/logical-graphs-1/

There's a more formal presentation of logical graphs, working from

the axioms or “initials” I borrowed with modifications from Peirce

and Spencer Brown, in the following blog post.

• Logical Graphs • Formal Development

https://inquiryintoinquiry.com/2008/09/19/logical-graphs-2/

Those two pieces are combined and extended in the following article.

• Logical Graphs ( https://oeis.org/wiki/Logical_Graphs

The program I developed all through the 80s using those data structures

in its logic module is documented so far as I've managed at this point

on the following page.

• Survey of Theme One Program

https://inquiryintoinquiry.com/2020/08/28/survey-of-theme-one-program-3/

Regards,

Jon

Jul 29, 2021, 4:00:51 PM7/29/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG

Cf: Logical Graphs • Discussion 2

https://inquiryintoinquiry.com/2021/07/29/logical-graphs-discussion-2/

Re: Category Theory

https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/logical.20graphs

::: Chad Nester

https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/logical.20graphs/near/245453493

<QUOTE CN:>

Recently a few of us have been using the “cartesian bicategories of

relations” of Carboni and Walters, in particular their string diagrams,

as syntax for relations. The string diagrams in question are more or

less a directed version of Peirce's lines of identity. They're usually

described in terms of commutative special frobenius algebras. I suspect

the reason we keep finding commutative special frobenius algebras is that

they support lines of identity in this way.

</QUOTE>

Dear Chad, Henry, …

Chaos rules my niche of the world right now so I'll just

break a bit of the ice by sharing the following links to

my ongoing study of Peirce's 1870 Logic Of Relatives.

• Peirce's 1870 LOR • Overview

https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview

• Part 1

https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1

• Part 2

https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_2

• Part 3

https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_3

• References

https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_References

See especially the following paragraph.

* Peirce • CP 3.93

https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_3#Selection_B

To my way of thinking the above paragraph is one of the most radical

passages in the history of logic, relativizing traditional assumptions

of an absolute distinction between generals (universals) and individuals.

Among other things, it pulls the rug out from under any standing for

nominalism as opposed to realism about universals.

Regards,

Jon

https://inquiryintoinquiry.com/2021/07/29/logical-graphs-discussion-2/

Re: Category Theory

https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/logical.20graphs

::: Chad Nester

https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/logical.20graphs/near/245453493

<QUOTE CN:>

Recently a few of us have been using the “cartesian bicategories of

relations” of Carboni and Walters, in particular their string diagrams,

as syntax for relations. The string diagrams in question are more or

less a directed version of Peirce's lines of identity. They're usually

described in terms of commutative special frobenius algebras. I suspect

the reason we keep finding commutative special frobenius algebras is that

they support lines of identity in this way.

</QUOTE>

Dear Chad, Henry, …

Chaos rules my niche of the world right now so I'll just

break a bit of the ice by sharing the following links to

my ongoing study of Peirce's 1870 Logic Of Relatives.

• Peirce's 1870 LOR • Overview

https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview

• Part 1

https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1

• Part 2

https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_2

• Part 3

https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_3

• References

https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_References

See especially the following paragraph.

* Peirce • CP 3.93

https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_3#Selection_B

To my way of thinking the above paragraph is one of the most radical

passages in the history of logic, relativizing traditional assumptions

of an absolute distinction between generals (universals) and individuals.

Among other things, it pulls the rug out from under any standing for

nominalism as opposed to realism about universals.

Regards,

Jon

Jul 31, 2021, 12:12:14 PM7/31/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG

Cf: Logical Graphs • Discussion 3

https://inquiryintoinquiry.com/2021/07/31/logical-graphs-discussion-3/

Re: Peirce List

https://list.iupui.edu/sympa/arc/peirce-l/2021-07/thrd4.html#00111

::: John Sowa

https://list.iupui.edu/sympa/arc/peirce-l/2021-07/msg00111.html

•••

::: Robert Marty

https://list.iupui.edu/sympa/arc/peirce-l/2021-07/msg00144.html

Dear John, Robert, Edwina,

This discussion reminds me of the time I spent the big bucks buying a copy of

Stjernfelt's Diagrammatology ( https://www.springer.com/gp/book/9781402056512 )

which ran to over 500 pages with many sections in very small print and had just

over 50 diagrams in the whole book.

So I think the real “versus” being dealt with here is not so much the

difference between “thinking in diagrams” and “thinking in words” as

the difference between “thinking in words about thinking in diagrams”

and “thinking in words about thinking in words”.

Those of us, the very few, who have actually been working on “moving pictures”

from the very get-go, have learned to see things somewhat differently.

Peirce Syllabus • Metaphysics, Normative Science, Phenomenology, Mathematics

http://inquiryintoinquiry.files.wordpress.com/2014/08/peirce-syllabus.jpg

“Normative science rests largely on phenomenology and on mathematics;

metaphysics on phenomenology and on normative science.”

❧ Charles Sanders Peirce • Collected Papers, CP 1.186 (1903)

Syllabus • Classification of Sciences (CP 1.180–202, G-1903-2b)

http://web.archive.org/web/20111105121054/http://www.princeton.edu/~batke/peirce/cl_o_sci_03.htm

Regardez,

Jon

https://inquiryintoinquiry.com/2021/07/31/logical-graphs-discussion-3/

Re: Peirce List

https://list.iupui.edu/sympa/arc/peirce-l/2021-07/thrd4.html#00111

::: John Sowa

https://list.iupui.edu/sympa/arc/peirce-l/2021-07/msg00111.html

•••

::: Robert Marty

https://list.iupui.edu/sympa/arc/peirce-l/2021-07/msg00144.html

Dear John, Robert, Edwina,

This discussion reminds me of the time I spent the big bucks buying a copy of

Stjernfelt's Diagrammatology ( https://www.springer.com/gp/book/9781402056512 )

which ran to over 500 pages with many sections in very small print and had just

over 50 diagrams in the whole book.

So I think the real “versus” being dealt with here is not so much the

difference between “thinking in diagrams” and “thinking in words” as

the difference between “thinking in words about thinking in diagrams”

and “thinking in words about thinking in words”.

Those of us, the very few, who have actually been working on “moving pictures”

from the very get-go, have learned to see things somewhat differently.

Peirce Syllabus • Metaphysics, Normative Science, Phenomenology, Mathematics

http://inquiryintoinquiry.files.wordpress.com/2014/08/peirce-syllabus.jpg

“Normative science rests largely on phenomenology and on mathematics;

metaphysics on phenomenology and on normative science.”

❧ Charles Sanders Peirce • Collected Papers, CP 1.186 (1903)

Syllabus • Classification of Sciences (CP 1.180–202, G-1903-2b)

http://web.archive.org/web/20111105121054/http://www.princeton.edu/~batke/peirce/cl_o_sci_03.htm

Regardez,

Jon

Aug 1, 2021, 5:00:13 PM8/1/21

Cf: Logical Graphs • Discussion 4

https://inquiryintoinquiry.com/2021/08/01/logical-graphs-discussion-4/

Re: Category Theory

https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/logical.20graphs

::: Henry Story

https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/logical.20graphs/near/245454945

<QUOTE HS:>

Evan Patterson's “Knowledge Representation in Bicategories of Relations”

( https://arxiv.org/abs/1706.00526 ) is also drawn up in terms of string

diagrams, as a way of explaining the W3C RDF and OWL standards. So it

looks like we have a nice route from Peirce to RDF via string diagrams.

Or the other way around: whichever route one prefers to travel.

</QUOTE>

Dear Henry,

I opened a topic on Zulip | Relation Theory

https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/relation.20theory

to discuss the logic of relative terms and the mathematics of relations

as they develop from Peirce’s first breakthroughs (1865–1870). As I keep

telling people, there are radical innovations in this work, probing deeper

strata of logic and mathematics than ever mined before and thus undermining

the fundamental nominalism of First Order Logic as we know it.

Regards.

Jon

https://inquiryintoinquiry.com/2021/08/01/logical-graphs-discussion-4/

Re: Category Theory

https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/logical.20graphs

https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/logical.20graphs/near/245454945

<QUOTE HS:>

Evan Patterson's “Knowledge Representation in Bicategories of Relations”

( https://arxiv.org/abs/1706.00526 ) is also drawn up in terms of string

diagrams, as a way of explaining the W3C RDF and OWL standards. So it

looks like we have a nice route from Peirce to RDF via string diagrams.

Or the other way around: whichever route one prefers to travel.

</QUOTE>

Dear Henry,

I opened a topic on Zulip | Relation Theory

https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/relation.20theory

to discuss the logic of relative terms and the mathematics of relations

as they develop from Peirce’s first breakthroughs (1865–1870). As I keep

telling people, there are radical innovations in this work, probing deeper

strata of logic and mathematics than ever mined before and thus undermining

the fundamental nominalism of First Order Logic as we know it.

Regards.

Jon

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