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Sep 18, 2019, 4:20:55 AM9/18/19

to Arisbe List, SysSciWG, Structural Modeling, Ontolog Forum, Laws Of Form Group, Cybernetic Communications

Cf: The Difference That Makes A Difference That Peirce Makes : 20

At: https://inquiryintoinquiry.com/2019/09/17/the-difference-that-makes-a-difference-that-peirce-makes-20/

Cross-paradigm communication, like cross-disciplinary and cross-cultural

communication, can be difficult. Sometimes people do not even recognize the

existence of other paradigms, disciplines, cultures, long before it comes to

the question of their value. Readers of Peirce know he often uses important

words in more primordial senses than later came into fashion. Other times his

usage embodies a distinct analysis of the concept in question. More than once

I've found myself remarking how Peirce "anticipates" some strikingly "modern"

idea in logic, mathematics, or science, only to find its roots lay deep in

the history of thought. Whether he anticipates a future sense or preserves

an ancient sense is not always easy to answer.

Regards,

Jon

At: https://inquiryintoinquiry.com/2019/09/17/the-difference-that-makes-a-difference-that-peirce-makes-20/

Cross-paradigm communication, like cross-disciplinary and cross-cultural

communication, can be difficult. Sometimes people do not even recognize the

existence of other paradigms, disciplines, cultures, long before it comes to

the question of their value. Readers of Peirce know he often uses important

words in more primordial senses than later came into fashion. Other times his

usage embodies a distinct analysis of the concept in question. More than once

I've found myself remarking how Peirce "anticipates" some strikingly "modern"

idea in logic, mathematics, or science, only to find its roots lay deep in

the history of thought. Whether he anticipates a future sense or preserves

an ancient sense is not always easy to answer.

Regards,

Jon

Sep 18, 2019, 4:44:54 PM9/18/19

to Ontolog Forum, John Bottoms, SysSciWG, Structural Modeling, Laws Of Form Group, Cybernetic Communications

John, All ...

Re: The Difference That Makes A Difference That Peirce Makes : 20

At: https://inquiryintoinquiry.com/2019/09/17/the-difference-that-makes-a-difference-that-peirce-makes-20/

That bit of blogging bubbled up from several weeks observing various discussions

around the web where people seemed to spending most of their effort talking past

each other and hardly ever getting any ideas or information out of one skull and

into another. It's not the first time I've noticed belief systems, comfort zones,

conceptual silos, paradigms, whatever we want to call them, operating a lot like

immune systems, insulating our mental metabolisms from any intellectual antigens.

Anyhow, it's a working hypothesis to prime future inquiry ...

As far as Peirce references go, the choices are legion, so I'll just link to

one place I have in mind at the moment, where he sets out a number of truly

radical ideas, ones I view as missed opportunities in that he did not fully

follow up on them in later years.

Peirce's 1870 Logic Of Relatives

================================

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

Resources : https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Resources

Regards,

Jon

On 9/18/2019 11:19 AM, John Bottoms wrote:> JA: Interesting concepts, could you post a couple of references from his work?

>

> -John Bottoms

Re: The Difference That Makes A Difference That Peirce Makes : 20

At: https://inquiryintoinquiry.com/2019/09/17/the-difference-that-makes-a-difference-that-peirce-makes-20/

That bit of blogging bubbled up from several weeks observing various discussions

around the web where people seemed to spending most of their effort talking past

each other and hardly ever getting any ideas or information out of one skull and

into another. It's not the first time I've noticed belief systems, comfort zones,

conceptual silos, paradigms, whatever we want to call them, operating a lot like

immune systems, insulating our mental metabolisms from any intellectual antigens.

Anyhow, it's a working hypothesis to prime future inquiry ...

As far as Peirce references go, the choices are legion, so I'll just link to

one place I have in mind at the moment, where he sets out a number of truly

radical ideas, ones I view as missed opportunities in that he did not fully

follow up on them in later years.

Peirce's 1870 Logic Of Relatives

================================

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

Resources : https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Resources

Regards,

Jon

On 9/18/2019 11:19 AM, John Bottoms wrote:> JA: Interesting concepts, could you post a couple of references from his work?

>

> -John Bottoms

>

> On 9/18/2019 4:20 AM, Jon Awbrey wrote:

>> Cf: The Difference That Makes A Difference That Peirce Makes : 20

>> At: https://inquiryintoinquiry.com/2019/09/17/the-difference-that-makes-a-difference-that-peirce-makes-20/

>>

>> Cross-paradigm communication, like cross-disciplinary and cross-cultural

>> communication, can be difficult.?? Sometimes people do not even recognize the
> On 9/18/2019 4:20 AM, Jon Awbrey wrote:

>> Cf: The Difference That Makes A Difference That Peirce Makes : 20

>> At: https://inquiryintoinquiry.com/2019/09/17/the-difference-that-makes-a-difference-that-peirce-makes-20/

>>

>> Cross-paradigm communication, like cross-disciplinary and cross-cultural

>> existence of other paradigms, disciplines, cultures, long before it comes to

>> the question of their value.?? Readers of Peirce know he often uses important
>> words in more primordial senses than later came into fashion. Other times his

>> usage embodies a distinct analysis of the concept in question. More than once

>> I've found myself remarking how Peirce "anticipates" some strikingly "modern"

>> idea in logic, mathematics, or science, only to find its roots lay deep in

>> the history of thought.?? Whether he anticipates a future sense or preserves
>> usage embodies a distinct analysis of the concept in question. More than once

>> I've found myself remarking how Peirce "anticipates" some strikingly "modern"

>> idea in logic, mathematics, or science, only to find its roots lay deep in

Sep 18, 2019, 7:14:31 PM9/18/19

to structura...@googlegroups.com, Ontolog Forum, John Bottoms, SysSciWG, Laws Of Form Group, Cybernetic Communications

Jon:

Interesting response and material.

One of your referenced sections states:

"What strikes me about the initial installment this time around is its
use of a certain pattern of argument that I can recognize as invoking a *closure principle*, and this is a figure of reasoning that Peirce uses in three other places: his discussion of continuous predicates, his definition of sign relations, and in the pragmatic maxim itself."

Due to the fact that you have a background in computer science and psychology, which kind of closure principle are you addressing?

Closure principle from psychology, closure principle from computer science or both?

Take care and have fun,

Joe

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# “Reasonable people adapt themselves to the world.

# Unreasonable people attempt to adapt the world to themselves.

# All progress, therefore, depends on unreasonable people.”

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Sep 19, 2019, 5:24:19 PM9/19/19

to Arisbe List, SysSciWG, Structural Modeling, Ontolog Forum, Laws Of Form Group, Cybernetic Communications

Cf : The Difference That Makes A Difference That Peirce Makes : 22

At : http://inquiryintoinquiry.com/2019/09/19/the-difference-that-makes-a-difference-that-peirce-makes-22/

Re: Charles S. Peirce Society Facebook Page

At: https://www.facebook.com/groups/peircesociety/

Re: John Corcoran

At: https://www.facebook.com/groups/peircesociety/permalink/1688730107929641/

At: https://www.facebook.com/groups/peircesociety/permalink/1691535687649083/

A discussion -- well, more like a series of posts and counterposts --

arose on the Peirce Society Facebook Page last week, and I've been

going back over it this week because it seemed to invite a useful

re-examination of some old but important issues. There appears to

be some sort of disagreement, or maybe just failure to communicate,

but I'm still having trouble putting my finger on what the source

of the issue might be.

One factor seems to be different understandings of the relationship

between Peirce's brand of semiotics and standard first order logic.

One thing I've noticed before is that people who view Peirce's work

through the filter of first order logic are not likely to see what

many of us appreciate in his semiotic approach to logic. There are

commentators on Peirce's logical systems who treat them as nothing

more than first order logics in other syntaxes, but I am not one of

those. There is something more general and powerful going on with

Peirce's conception of "logic as formal semiotic", in other words,

a normative science of signs.

I still see that playing a role in the background of the animadversion

but I'm beginning to think there's probably a much simpler explanation.

Regards,

Jon

At : http://inquiryintoinquiry.com/2019/09/19/the-difference-that-makes-a-difference-that-peirce-makes-22/

Re: Charles S. Peirce Society Facebook Page

At: https://www.facebook.com/groups/peircesociety/

Re: John Corcoran

At: https://www.facebook.com/groups/peircesociety/permalink/1688730107929641/

At: https://www.facebook.com/groups/peircesociety/permalink/1691535687649083/

A discussion -- well, more like a series of posts and counterposts --

arose on the Peirce Society Facebook Page last week, and I've been

going back over it this week because it seemed to invite a useful

re-examination of some old but important issues. There appears to

be some sort of disagreement, or maybe just failure to communicate,

but I'm still having trouble putting my finger on what the source

of the issue might be.

One factor seems to be different understandings of the relationship

between Peirce's brand of semiotics and standard first order logic.

One thing I've noticed before is that people who view Peirce's work

through the filter of first order logic are not likely to see what

many of us appreciate in his semiotic approach to logic. There are

commentators on Peirce's logical systems who treat them as nothing

more than first order logics in other syntaxes, but I am not one of

those. There is something more general and powerful going on with

Peirce's conception of "logic as formal semiotic", in other words,

a normative science of signs.

I still see that playing a role in the background of the animadversion

but I'm beginning to think there's probably a much simpler explanation.

Regards,

Jon

Sep 20, 2019, 6:34:34 PM9/20/19

to structura...@googlegroups.com, Ontolog Forum, John Bottoms, SysSciWG, Laws Of Form Group, Cybernetic Communications

Jon:

As I work through the linked material, I find that there appears to be errors in Part 2 graphic displays when I use Firefox.

However, the errors are not present when I view the material using the Chrome browser.

This is just a note of information if anyone else has an issue reading the linked material.

The Boolean matrices are interesting, what software do you use to make these matrix calculations?

I use the Sage Math system for these types of Boolean matrix calculations, but I was wondering if there are other executable systems that preform the same type of operations.

My plan is to spin up an executable notebook and see if I can reproduce the presents material.

If I am successful, I will share the notebooks with the list.

Take care and have fun,

Joe

On Wed, Sep 18, 2019 at 1:44 PM Jon Awbrey <jaw...@att.net> wrote:

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Sep 21, 2019, 9:08:16 AM9/21/19

to structura...@googlegroups.com, joseph simpson, Ontolog Forum, SysSciWG, Laws Of Form Group, Cybernetic Communications

Cf: The Difference That Makes A Difference That Peirce Makes : 23

At: https://inquiryintoinquiry.com/2019/09/20/the-difference-that-makes-a-difference-that-peirce-makes-23/

Joe, All ...

A fundamental question in applications of mathematical logic is the threshold of

complexity between dyadic (binary) and triadic (ternary) relations, in particular,

whether 2-place relations are universally adequate or whether 3-place relations

are irreducible, minimally adequate, and even sufficient as a basis for all

higher dimensions.

One of Peirce's earliest arguments for the sufficiency of

triadic relative terms occurs at the top of his 1870

"Logic of Relatives".

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

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

Cf: At: https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1#Selection_1

<QUOTE>

The conjugative term involves the conception of "third", the relative that

of second or "other", the absolute term simply considers "an" object. No

fourth class of terms exists involving the conception of "fourth", because

when that of "third" is introduced, since it involves the conception of

bringing objects into relation, all higher numbers are given at once,

inasmuch as the conception of bringing objects into relation is independent

of the number of members of the relationship. Whether this "reason" for

the fact that there is no fourth class of terms fundamentally different

from the third is satisfactory or not, the fact itself is made perfectly

evident by the study of the logic of relatives. (Peirce, CP 3.63).

</QUOTE>

Peirce's argument invokes what is known as a "closure principle",

as I remarked in the following comment:

What strikes me about the initial installment this time around is

its use of a certain pattern of argument I can recognize as invoking

a "closure principle", and this is a figure of reasoning Peirce uses

* https://oeis.org/wiki/Continuous_predicate

* https://oeis.org/wiki/Sign_relation

* https://inquiryintoinquiry.com/2008/08/07/pragmatic-maxim/

In mathematics, a "closure operator" is one whose repeated application

yields the same result as its first application.

If we take an arbitrary operator A, the result of applying A

to an operand x is Ax, the result of applying A again is AAx,

the result of applying A again is AAAx, and so on. In general,

it is perfectly possible each application yields a novel result,

distinct from all previous results.

But a closure operator C is defined by the property CC = C,

so nothing new results beyond the first application.

Regards,

Jon

At: https://inquiryintoinquiry.com/2019/09/20/the-difference-that-makes-a-difference-that-peirce-makes-23/

Joe, All ...

A fundamental question in applications of mathematical logic is the threshold of

complexity between dyadic (binary) and triadic (ternary) relations, in particular,

whether 2-place relations are universally adequate or whether 3-place relations

are irreducible, minimally adequate, and even sufficient as a basis for all

higher dimensions.

One of Peirce's earliest arguments for the sufficiency of

triadic relative terms occurs at the top of his 1870

"Logic of Relatives".

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

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

Cf: At: https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1#Selection_1

<QUOTE>

The conjugative term involves the conception of "third", the relative that

of second or "other", the absolute term simply considers "an" object. No

fourth class of terms exists involving the conception of "fourth", because

when that of "third" is introduced, since it involves the conception of

bringing objects into relation, all higher numbers are given at once,

inasmuch as the conception of bringing objects into relation is independent

of the number of members of the relationship. Whether this "reason" for

the fact that there is no fourth class of terms fundamentally different

from the third is satisfactory or not, the fact itself is made perfectly

evident by the study of the logic of relatives. (Peirce, CP 3.63).

</QUOTE>

Peirce's argument invokes what is known as a "closure principle",

as I remarked in the following comment:

What strikes me about the initial installment this time around is

a "closure principle", and this is a figure of reasoning Peirce uses

in three other places: his discussion of "continuous predicates", his

definition of "sign relations", and in the "pragmatic maxim" itself.
* https://oeis.org/wiki/Continuous_predicate

* https://oeis.org/wiki/Sign_relation

* https://inquiryintoinquiry.com/2008/08/07/pragmatic-maxim/

In mathematics, a "closure operator" is one whose repeated application

yields the same result as its first application.

If we take an arbitrary operator A, the result of applying A

to an operand x is Ax, the result of applying A again is AAx,

the result of applying A again is AAAx, and so on. In general,

it is perfectly possible each application yields a novel result,

distinct from all previous results.

But a closure operator C is defined by the property CC = C,

so nothing new results beyond the first application.

Regards,

Jon

Sep 22, 2019, 10:22:31 AM9/22/19

to Sys Sci, Jon Awbrey, structura...@googlegroups.com, Ontolog Forum @ GG

Bob:

Interesting point of view.

Jon wrote:

"What strikes me about the initial installment this time around is

its use of a certain pattern of argument I can recognize as invoking

a "closure principle","

its use of a certain pattern of argument I can recognize as invoking

a "closure principle","

It is still not clear to me what type of "closure principle."

The closure principle may be associated with the closure property of set theory (closed set operations) or

the closure principle may be associated with the concept of an idempotent executable operation.

An idempotent operation has the form f(f(x)) = f(x).

This form appears to be similar to the form provided by Jon:

"But a closure operator C is defined by the property CC = C,

so nothing new results beyond the first application."

so nothing new results beyond the first application."

Take care and have fun,

Joe

On Sun, Sep 22, 2019 at 5:14 AM Bob Kenley <ken...@purdue.edu> wrote:

I would not be surprised if someone has investigated the closure operator C using a variant of fixed point theory, which typically is stated using the operand rather than the operator as the fixed term in the relation, I.e., Ax=x for all x.

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Sep 22, 2019, 11:49:02 AM9/22/19

to SysSciWG, Structural Modeling, Ontolog Forum, Cybernetic Communications

Cf: The Difference That Makes A Difference That Peirce Makes : 24

At: https://inquiryintoinquiry.com/2019/09/22/the-difference-that-makes-a-difference-that-peirce-makes-24/

The concepts of "closure" and "idempotence" are closely related.

We usually speak of a "closure operator" in contexts where the objects acted on are

the primary interest, as in topology, where the objects of interest are open sets,

boundaries, closed sets, etc. In contexts where we abstract away from the operand

space, as in algebra, we tend to say "idempotence" for the detached application

CC = C. (If I recall right, it was actually Charles Peirce's father Benjamin

who coined the term "idempotence".)

At any rate, I???ll have to mutate the principle a bit to cover the uses Peirce makes of it.

Regards,

Jon

At: https://inquiryintoinquiry.com/2019/09/22/the-difference-that-makes-a-difference-that-peirce-makes-24/

The concepts of "closure" and "idempotence" are closely related.

We usually speak of a "closure operator" in contexts where the objects acted on are

the primary interest, as in topology, where the objects of interest are open sets,

boundaries, closed sets, etc. In contexts where we abstract away from the operand

space, as in algebra, we tend to say "idempotence" for the detached application

CC = C. (If I recall right, it was actually Charles Peirce's father Benjamin

who coined the term "idempotence".)

At any rate, I???ll have to mutate the principle a bit to cover the uses Peirce makes of it.

Regards,

Jon

Sep 23, 2019, 5:04:48 PM9/23/19

to structura...@googlegroups.com, SysSciWG, Ontolog Forum, Cybernetic Communications

Jon:

Thanks for the additional context.

I think we are closer to a common understanding of the terms use.

Also, it appears that Benjamin Peirce originated the term, idempotence.

Take care and have fun,

Joe

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Sep 25, 2019, 10:40:25 AM9/25/19

to Ontolog Forum, Structural Modeling, SysSciWG, Laws Of Form Group, Cybernetic Communications, John Bottoms

Re: The Difference That Makes A Difference That Peirce Makes : 21

At: https://inquiryintoinquiry.com/2019/09/18/the-difference-that-makes-a-difference-that-peirce-makes-21/

Joe, John, All ...

I'm not seeing any errors from my Firefox, the only browser I use.

Cf: Peirce's 1870 Logic Of Relatives : Part 2

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

Is it a problem with the JPGs or the LaTeX generated images?

The JPGs were exported from LibreOffice Draw five years ago,

so I could try it again with a newer version of LibreOffice,

if that is where the problem lies.

At any rate, I serialized all this content to my blog a while back,

so folks could peruse that as an alternative. I'll post a link on

a separate thread.

Regards,

Jon

At: https://inquiryintoinquiry.com/2019/09/18/the-difference-that-makes-a-difference-that-peirce-makes-21/

Joe, John, All ...

I'm not seeing any errors from my Firefox, the only browser I use.

Cf: Peirce's 1870 Logic Of Relatives : Part 2

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

Is it a problem with the JPGs or the LaTeX generated images?

The JPGs were exported from LibreOffice Draw five years ago,

so I could try it again with a newer version of LibreOffice,

if that is where the problem lies.

At any rate, I serialized all this content to my blog a while back,

so folks could peruse that as an alternative. I'll post a link on

a separate thread.

Regards,

Jon

Oct 13, 2019, 10:05:54 AM10/13/19

to Arisbe List, SysSciWG, Structural Modeling, Ontolog Forum, Laws Of Form Group, Cybernetic Communications

Cf: The Difference That Makes A Difference That Peirce Makes : 25

At: https://inquiryintoinquiry.com/2019/10/13/the-difference-that-makes-a-difference-that-peirce-makes-25/

I've been detecting something approaching a mini-zeitgeist lately.

Ideas and issues popping up in my recent discussions and readings

keep reminding me of themes I first encountered in Peirce's early

work, especially the Lectures on the Logic of Science (1865-1866)

and the 1870 Logic of Relatives. A number of Peirce's potentially

ground-breaking, paradigm-shifting ideas first saw the light of day

in these early ventures. I say "potentially" because what I regard

as his most revolutionary ideas never saw their full development in

Peirce's lifetime, only to arise again in the press of mathematical

and scientific advances later in the 20th Century.

Regards,

Jon

At: https://inquiryintoinquiry.com/2019/10/13/the-difference-that-makes-a-difference-that-peirce-makes-25/

I've been detecting something approaching a mini-zeitgeist lately.

Ideas and issues popping up in my recent discussions and readings

keep reminding me of themes I first encountered in Peirce's early

work, especially the Lectures on the Logic of Science (1865-1866)

and the 1870 Logic of Relatives. A number of Peirce's potentially

ground-breaking, paradigm-shifting ideas first saw the light of day

in these early ventures. I say "potentially" because what I regard

as his most revolutionary ideas never saw their full development in

Peirce's lifetime, only to arise again in the press of mathematical

and scientific advances later in the 20th Century.

Regards,

Jon

Oct 14, 2019, 1:10:33 PM10/14/19

Cf : The Difference That Makes A Difference That Peirce Makes : 26

At : http://inquiryintoinquiry.com/2019/10/14/the-difference-that-makes-a-difference-that-peirce-makes-26/

Questions about Peirce's use of "formal" and "normative" in relation to logic

and semiotic have come up again on the Peirce List, but I have to run off to

another appointment, so for now I'll just post a link to a relevant previous

discussion.

* The Difference That Makes A Difference That Peirce Makes : 19

https://inquiryintoinquiry.com/2017/11/18/the-difference-that-makes-a-difference-that-peirce-makes-19/

In other recurring discussions, as far as my personal usage goes,

I've always suggested there is a place for descriptive semiotics,

whether of not that was Peirce's way of drawing the distinctions.

Regards,

Jon

At : http://inquiryintoinquiry.com/2019/10/14/the-difference-that-makes-a-difference-that-peirce-makes-26/

Questions about Peirce's use of "formal" and "normative" in relation to logic

and semiotic have come up again on the Peirce List, but I have to run off to

another appointment, so for now I'll just post a link to a relevant previous

discussion.

* The Difference That Makes A Difference That Peirce Makes : 19

https://inquiryintoinquiry.com/2017/11/18/the-difference-that-makes-a-difference-that-peirce-makes-19/

In other recurring discussions, as far as my personal usage goes,

I've always suggested there is a place for descriptive semiotics,

whether of not that was Peirce's way of drawing the distinctions.

Regards,

Jon

Oct 15, 2019, 8:00:19 AM10/15/19

Returning to the matter of form ...

Cf: The Difference That Makes A Difference That Peirce Makes : 27

At: https://inquiryintoinquiry.com/2019/10/14/the-difference-that-makes-a-difference-that-peirce-makes-27/

It's been my observation over many decades that people invoke

the "ethics of terminology" mainly to inveigh against everyone's

innovations but their own, so these days I've shifted more of my

attention to the "pragmatics of communication", the critical case

being communication across the boundaries and through the filters

of diverse communities of usage. In that spirit, I'll copy here

my last best attempt to devise a bridge between Peirce's special

sense of "formal" and the more generic brands we likely know.

Cf: Definition and Determination : 8

At: https://inquiryintoinquiry.com/2012/06/13/definition-and-determination-8/

<QUOTE>

The most general meaning of "formal" is "concerned with form",

but the Latin "forma" can mean "beauty" in addition to "form",

so perhaps a normative "goodness of form" enters at this root.

The Latin word "norma" literally means a "carpenter's square".

The Greek "gnomon" is a sundial pointer taking a similar form.

The most general meaning of "normative" is "having to do with

what a person ought to do", but a pragmatic interpretation of

ethical imperatives tends to treat that as "having to do with

what a person ought to do in order to achieve a given object",

so another formula might be "relating to the good that befits

a being of our kind, what must be done in order to bring that

good into being, and how to tell the signs that show the way".

Defining logic as formal or normative semiotic differentiates

logic from other species of semiotic under the general theory

of signs, leaving a niche open for descriptive semiotic, just

to mention the obvious branch. This brings us to the question:

How does a concern with form, or goodness of form, along with

the question of what is required to achieve an object, modify

our perspective on sign relations in a way that duly marks it

as a logical point of view?

</QUOTE>

Regards,

Jon

Cf: The Difference That Makes A Difference That Peirce Makes : 27

At: https://inquiryintoinquiry.com/2019/10/14/the-difference-that-makes-a-difference-that-peirce-makes-27/

It's been my observation over many decades that people invoke

the "ethics of terminology" mainly to inveigh against everyone's

innovations but their own, so these days I've shifted more of my

attention to the "pragmatics of communication", the critical case

being communication across the boundaries and through the filters

of diverse communities of usage. In that spirit, I'll copy here

my last best attempt to devise a bridge between Peirce's special

sense of "formal" and the more generic brands we likely know.

Cf: Definition and Determination : 8

At: https://inquiryintoinquiry.com/2012/06/13/definition-and-determination-8/

<QUOTE>

The most general meaning of "formal" is "concerned with form",

but the Latin "forma" can mean "beauty" in addition to "form",

so perhaps a normative "goodness of form" enters at this root.

The Latin word "norma" literally means a "carpenter's square".

The Greek "gnomon" is a sundial pointer taking a similar form.

The most general meaning of "normative" is "having to do with

what a person ought to do", but a pragmatic interpretation of

ethical imperatives tends to treat that as "having to do with

what a person ought to do in order to achieve a given object",

so another formula might be "relating to the good that befits

a being of our kind, what must be done in order to bring that

good into being, and how to tell the signs that show the way".

Defining logic as formal or normative semiotic differentiates

logic from other species of semiotic under the general theory

of signs, leaving a niche open for descriptive semiotic, just

to mention the obvious branch. This brings us to the question:

How does a concern with form, or goodness of form, along with

the question of what is required to achieve an object, modify

our perspective on sign relations in a way that duly marks it

as a logical point of view?

</QUOTE>

Regards,

Jon

Oct 15, 2019, 4:16:19 PM10/15/19

On 9/18/2019 4:20 AM, Jon Awbrey wrote:

> Cf: The Difference That Makes A Difference That Peirce Makes : 20

> At: https://inquiryintoinquiry.com/2019/09/17/the-difference-that-makes-a-difference-that-peirce-makes-20/

>

> Cross-paradigm communication, like cross-disciplinary and cross-cultural

> communication, can be difficult.?? Sometimes people do not even recognize the
> At: https://inquiryintoinquiry.com/2019/09/17/the-difference-that-makes-a-difference-that-peirce-makes-20/

>

> Cross-paradigm communication, like cross-disciplinary and cross-cultural

> existence of other paradigms, disciplines, cultures, long before it comes to

> the question of their value.?? Readers of Peirce know he often uses important
> words in more primordial senses than later came into fashion.?? Other times his

> usage embodies a distinct analysis of the concept in question.?? More than once

> I've found myself remarking how Peirce "anticipates" some strikingly "modern"

> idea in logic, mathematics, or science, only to find its roots lay deep in

> the history of thought.?? Whether he anticipates a future sense or preserves
> idea in logic, mathematics, or science, only to find its roots lay deep in

> an ancient sense is not always easy to answer.

>

> Regards,

>

> Jon

>

I had to go back a bit to remind myself why I restarted this thread,
>

> Regards,

>

> Jon

>

but at least it supplies plenty of material for future study on the

difficulties of cross-paradigm communication.

At any rate, while I still have them in mind, I wanted to add to the record

a few exhibits on Peirce's definition of logic as "formal semiotic" and in

another place his description of logic as "semiotic, the quasi-necessary,

or formal, doctrine of signs".

Here's two variants of a paragraph where Peirce defines logic as "formal semiotic".

Selections from C.S. Peirce, "Carnegie Application" (1902)

==========================================================

Cf: C.S. Peirce : On the Definition of Logic

At: https://inquiryintoinquiry.com/2012/06/01/c-s-peirce-%e2%80%a2-on-the-definition-of-logic/

<QUOTE>

No. 12. On the Definition of Logic

Logic will here be defined as formal semiotic. A definition

of a sign will be given which no more refers to human thought

than does the definition of a line as the place which a particle

occupies, part by part, during a lapse of time. Namely, a sign

is something, A, which brings something, B, its interpretant sign

determined or created by it, into the same sort of correspondence

with something, C, its object, as that in which itself stands to C.

It is from this definition, together with a definition of "formal",

that I deduce mathematically the principles of logic. I also make

a historical review of all the definitions and conceptions of logic,

and show, not merely that my definition is no novelty, but that my

non-psychological conception of logic has virtually been quite

generally held, though not generally recognized. (NEM 4, 20-21).

No. 12. On the Definition of Logic [Earlier Draft]

Logic is formal semiotic. A sign is something, A, which brings

something, B, its interpretant sign, determined or created by it,

into the same sort of correspondence (or a lower implied sort) with

something, C, its object, as that in which itself stands to C. This

definition no more involves any reference to human thought than does

the definition of a line as the place within which a particle lies

during a lapse of time. It is from this definition that I deduce the

principles of logic by mathematical reasoning, and by mathematical

reasoning that, I aver, will support criticism of Weierstrassian

severity, and that is perfectly evident. The word "formal" in

the definition is also defined. (NEM 4, 54).

</QUOTE>

Charles S. Peirce (1902), "Parts of Carnegie Application" (L 75), published in

Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce,

vol. 4, 13-73. http://www.iupui.edu/~arisbe/menu/library/bycsp/L75/l75.htm

Here's a passage where Peirce explains his sense of "formal" or "quasi-necessary".

Selection from C.S. Peirce, "Ground, Object, and Interpretant" (c. 1897)

========================================================================

Cf: C.S. Peirce : Logic as Semiotic

At: https://inquiryintoinquiry.com/2012/06/04/c-s-peirce-%E2%80%A2-logic-as-semiotic/

<QUOTE>

Logic, in its general sense, is, as I believe I have shown,

only another name for semiotic (...), the quasi-necessary,

or formal, doctrine of signs. By describing the doctrine

as "quasi-necessary", or formal, I mean that we observe

the characters of such signs as we know, and from such an

observation, by a process which I will not object to naming

Abstraction, we are led to statements, eminently fallible,

and therefore in one sense by no means necessary, as to what

must be the characters of all signs used by a "scientific"

intelligence, that is to say, by an intelligence capable of

learning by experience. As to that process of abstraction,

it is itself a sort of observation.

The faculty which I call abstractive observation is one which

ordinary people perfectly recognize, but for which the theories

of philosophers sometimes hardly leave room. It is a familiar

experience to every human being to wish for something quite

beyond his present means, and to follow that wish by the question,

"Should I wish for that thing just the same, if I had ample means

to gratify it?" To answer that question, he searches his heart,

and in doing so makes what I term an abstractive observation.

He makes in his imagination a sort of skeleton diagram, or outline

sketch, of himself, considers what modifications the hypothetical

state of things would require to be made in that picture, and then

examines it, that is, observes what he has imagined, to see whether

the same ardent desire is there to be discerned. By such a process,

which is at bottom very much like mathematical reasoning, we can reach

conclusions as to what would be true of signs in all cases, so long as

the intelligence using them was scientific.

</QUOTE>

C.S. Peirce, Collected Papers, CP 2.227

From an unidentified fragment, c. 1897

Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1-6,

Charles Hartshorne and Paul Weiss (eds.), vols. 7-8, Arthur W. Burks (ed.),

Harvard University Press, Cambridge, MA, 1931-1935, 1958. Volume 2 :

Elements of Logic, 1932.

Oct 16, 2019, 2:15:11 PM10/16/19

to Arisbe List, SysSciWG, Structural Modeling, Ontolog Forum, Laws Of Form Group, Cybernetic Communications, Peirce List

Dear Mihai,

Thanks for your paper, "The Logic of Vagueness and The Category of Synechism".

There is much subtlety there. In my applied life these days I'd be satisfied,

or at least satisficed, just to make my ideas clear about the applications of

triadic sign relations to simple logic, along with getting my programs up and

running far enough again to finally get plain vanilla propositional logic out

of first gear, where our chop-logic school books have kept it for many a year.

But fuzzy logic and fuzzy sets were something I explored way back during my

first foundational crisis when I was exploring all the alternatives I could

find to standard set theory. As I got to know Peirce's theory of relations

better I saw a way to understand fuzzy sets within the framework of certain

triadic relations. I think I posted some comments about that somewhere, so

I'll try to dig them up ...

Regards,

Jon

On Tuesday, October 15, 2019 at 4:27:25 PM UTC-4, Mihai Nadin wrote:

>

> There is a bit more to Peirce:

> The Logic of Vagueness and The Category of Synechism

>

> https://academic.oup.com/monist/article-abstract/63/3/351/973996?redirectedFrom=fulltext

>

> Mihai Nadin

>

Thanks for your paper, "The Logic of Vagueness and The Category of Synechism".

There is much subtlety there. In my applied life these days I'd be satisfied,

or at least satisficed, just to make my ideas clear about the applications of

triadic sign relations to simple logic, along with getting my programs up and

running far enough again to finally get plain vanilla propositional logic out

of first gear, where our chop-logic school books have kept it for many a year.

But fuzzy logic and fuzzy sets were something I explored way back during my

first foundational crisis when I was exploring all the alternatives I could

find to standard set theory. As I got to know Peirce's theory of relations

better I saw a way to understand fuzzy sets within the framework of certain

triadic relations. I think I posted some comments about that somewhere, so

I'll try to dig them up ...

Regards,

Jon

On Tuesday, October 15, 2019 at 4:27:25 PM UTC-4, Mihai Nadin wrote:

>

> There is a bit more to Peirce:

> The Logic of Vagueness and The Category of Synechism

>

> https://academic.oup.com/monist/article-abstract/63/3/351/973996?redirectedFrom=fulltext

>

> Mihai Nadin

>

Oct 17, 2019, 7:00:25 AM10/17/19

to Arisbe List, SysSciWG, Structural Modeling, Laws Of Form Group, Cybernetic Communications

Cf : The Difference That Makes A Difference That Peirce Makes : 29

At : http://inquiryintoinquiry.com/2019/10/17/the-difference-that-makes-a-difference-that-peirce-makes-29/

We are called to recall Peirce's deeper meanings

of ideas like Form (think Platonic Ideas and the

way Aristotle compounded Form and Matter). When

we come to Sentiment, by any other word, Feeling,

that is the medium of Aesthetics, which concerns

Beauty in no merely skin-deep sense but all that

embodies and manifests "the admirable in itself",

thus every form of life worth living. So Peirce

stands the normative science of Logic on grounds

within the pale of Ethics and fixes the sight of

Ethics on the prize Aesthetics picks to steer by.

Regards,

Jon

At : http://inquiryintoinquiry.com/2019/10/17/the-difference-that-makes-a-difference-that-peirce-makes-29/

We are called to recall Peirce's deeper meanings

of ideas like Form (think Platonic Ideas and the

way Aristotle compounded Form and Matter). When

we come to Sentiment, by any other word, Feeling,

that is the medium of Aesthetics, which concerns

Beauty in no merely skin-deep sense but all that

embodies and manifests "the admirable in itself",

thus every form of life worth living. So Peirce

stands the normative science of Logic on grounds

within the pale of Ethics and fixes the sight of

Ethics on the prize Aesthetics picks to steer by.

Regards,

Jon

Oct 18, 2019, 10:45:16 AM10/18/19

to Helmut Raulien, Arisbe List, SysSciWG, Structural Modeling, Ontolog Forum, Laws Of Form Group, Cybernetic Communications, Peirce List

Helmut, Mihai, All ...

Peirce's take on the twin topics of generality and vagueness

does bear a relationship to what I've been posting lately on

the Precursors of Category Theory and the Logic of Relatives,

so it may be worth the candle to throw better light on those

connections. Looks like it'll be next week before I can get

back to it, though. Meanwhile, here's a good entry point --

Peirce (CP 5.447)

https://oeis.org/wiki/User:Jon_Awbrey/Peircean_Pragmata#Excerpt_5._Peirce_.28CP_5.447.29

<QUOTE>

Accurate writers have apparently made a distinction between

the definite and the determinate. A subject is determinate in

respect to any character which inheres in it or is (universally

and affirmatively) predicated of it, as well as in respect to

the negative of such character, these being the very same respect.

In all other respects it is indeterminate. The definite shall be

defined presently.

A sign (under which designation I place every kind of thought,

and not alone external signs), that is in any respect objectively

indeterminate (i.e., whose object is undetermined by the sign itself)

is objectively 'general' in so far as it extends to the interpreter

the privilege of carrying its determination further.

Example: "Man is mortal." To the question, What man? the reply is

that the proposition explicitly leaves it to you to apply its assertion

to what man or men you will.

A sign that is objectively indeterminate in any respect is objectively

vague in so far as it reserves further determination to be made in some

other conceivable sign, or at least does not appoint the interpreter as

its deputy in this office.

Example: "A man whom I could mention seems to be a little conceited."

The suggestion here is that the man in view is the person addressed;

but the utterer does not authorize such an interpretation or any other

application of what she says. She can still say, if she likes, that

she does not mean the person addressed.

Every utterance naturally leaves the right of further exposition

in the utterer; and therefore, in so far as a sign is indeterminate,

it is vague, unless it is expressly or by a well-understood convention

rendered general.

C.S. Peirce, Collected Papers, CP 5.447

</QUOTE>

On 10/16/2019 8:41 PM, Helmut Raulien wrote:

> Jon, Mihai, List,

> the unity of vagueness and continuum seems very reasonable to me. So vagueness

> is not (merely) a matter of inexact language, but of nature. Inexact language

> problems are not (always) vagueness, but instead e.g. ambiguity or misdenotation

> (so I understand the text). I guess, whether two elements are separated by a

> clear or fuzzy border depends on scales. Example: On a normal taxonomic scale,

> horse and donkey are two different species, because they cannot interbreed

> fertile offspring (in case this would be the definition for species). But on a

> smaller scale, maybe it is impossible to identify an exact time or a single

> genetic mutation, from which on the species have separated, and separation has

> been continuous, making it gradually more and more unlikely to interbreed

> fertile offspring. (?)

> To say, that scales are only a matter of observation however would lead back to

> language and representation, and away from naturalistic or realistic

> interpretation. To solve this problem, I guess that scale differences work

> together in nature, recreating a continuum even of discreteness: A single gene

> mutation is discrete, but for species separation, other influences on other

> scales may play a role too, such as epigenetics, culture, individual preference.

> Best,

> Helmut

Peirce's take on the twin topics of generality and vagueness

does bear a relationship to what I've been posting lately on

the Precursors of Category Theory and the Logic of Relatives,

so it may be worth the candle to throw better light on those

connections. Looks like it'll be next week before I can get

back to it, though. Meanwhile, here's a good entry point --

Peirce (CP 5.447)

https://oeis.org/wiki/User:Jon_Awbrey/Peircean_Pragmata#Excerpt_5._Peirce_.28CP_5.447.29

<QUOTE>

Accurate writers have apparently made a distinction between

the definite and the determinate. A subject is determinate in

respect to any character which inheres in it or is (universally

and affirmatively) predicated of it, as well as in respect to

the negative of such character, these being the very same respect.

In all other respects it is indeterminate. The definite shall be

defined presently.

A sign (under which designation I place every kind of thought,

and not alone external signs), that is in any respect objectively

indeterminate (i.e., whose object is undetermined by the sign itself)

is objectively 'general' in so far as it extends to the interpreter

the privilege of carrying its determination further.

Example: "Man is mortal." To the question, What man? the reply is

that the proposition explicitly leaves it to you to apply its assertion

to what man or men you will.

A sign that is objectively indeterminate in any respect is objectively

vague in so far as it reserves further determination to be made in some

other conceivable sign, or at least does not appoint the interpreter as

its deputy in this office.

Example: "A man whom I could mention seems to be a little conceited."

The suggestion here is that the man in view is the person addressed;

but the utterer does not authorize such an interpretation or any other

application of what she says. She can still say, if she likes, that

she does not mean the person addressed.

Every utterance naturally leaves the right of further exposition

in the utterer; and therefore, in so far as a sign is indeterminate,

it is vague, unless it is expressly or by a well-understood convention

rendered general.

C.S. Peirce, Collected Papers, CP 5.447

</QUOTE>

On 10/16/2019 8:41 PM, Helmut Raulien wrote:

> Jon, Mihai, List,

> the unity of vagueness and continuum seems very reasonable to me. So vagueness

> is not (merely) a matter of inexact language, but of nature. Inexact language

> problems are not (always) vagueness, but instead e.g. ambiguity or misdenotation

> (so I understand the text). I guess, whether two elements are separated by a

> clear or fuzzy border depends on scales. Example: On a normal taxonomic scale,

> horse and donkey are two different species, because they cannot interbreed

> fertile offspring (in case this would be the definition for species). But on a

> smaller scale, maybe it is impossible to identify an exact time or a single

> genetic mutation, from which on the species have separated, and separation has

> been continuous, making it gradually more and more unlikely to interbreed

> fertile offspring. (?)

> To say, that scales are only a matter of observation however would lead back to

> language and representation, and away from naturalistic or realistic

> interpretation. To solve this problem, I guess that scale differences work

> together in nature, recreating a continuum even of discreteness: A single gene

> mutation is discrete, but for species separation, other influences on other

> scales may play a role too, such as epigenetics, culture, individual preference.

> Best,

> Helmut

Oct 19, 2019, 9:16:36 AM10/19/19

to Arisbe List, SysSciWG, Structural Modeling, Ontolog Forum, Laws Of Form Group, Cybernetic Communications, Peirce List

Cf: The Difference That Makes A Difference That Peirce Makes : 30

At: https://inquiryintoinquiry.com/2019/10/18/the-difference-that-makes-a-difference-that-peirce-makes-30/

Peirce on "General" & "Vague" ...

I added a remark by way of context and corrected a typo.

(See the linked blog post for a better formatted copy.)

***

I first encountered Peirce's dimensions of generality and vagueness --

two measures of determinacy on sign relations telling how well objects

are determined by signs and interpretant signs -- while exploring the

closely related subjects of definition and determination.

* https://oeis.org/wiki/User:Jon_Awbrey/Peircean_Pragmata#Definition

* https://oeis.org/wiki/User:Jon_Awbrey/Peircean_Pragmata#Determination_2

Lately I've noticed Peirce's treatment of objectively indeterminate signs has

a bearing on my approach to Category Theory through the Logic of Relatives --

* https://inquiryintoinquiry.com/2015/05/15/survey-of-precursors-of-category-theory-%E2%80%A2-1/

* https://inquiryintoinquiry.com/2019/09/24/peirces-1870-logic-of-relatives-%e2%80%a2-overview/

so it looks worth paying attention to their potential relationships.

To get things rolling, here's a good entry point:

C.S. Peirce, Collected Papers, CP 5.447

</QUOTE>

Regards,

Jon

inquiry into inquiry: https://inquiryintoinquiry.com/

academia: https://independent.academia.edu/JonAwbrey

oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey

isw: http://intersci.ss.uci.edu/wiki/index.php/JLA

facebook page: https://www.facebook.com/JonnyCache

At: https://inquiryintoinquiry.com/2019/10/18/the-difference-that-makes-a-difference-that-peirce-makes-30/

Peirce on "General" & "Vague" ...

I added a remark by way of context and corrected a typo.

(See the linked blog post for a better formatted copy.)

***

I first encountered Peirce's dimensions of generality and vagueness --

two measures of determinacy on sign relations telling how well objects

are determined by signs and interpretant signs -- while exploring the

closely related subjects of definition and determination.

* https://oeis.org/wiki/User:Jon_Awbrey/Peircean_Pragmata#Definition

* https://oeis.org/wiki/User:Jon_Awbrey/Peircean_Pragmata#Determination_2

Lately I've noticed Peirce's treatment of objectively indeterminate signs has

a bearing on my approach to Category Theory through the Logic of Relatives --

* https://inquiryintoinquiry.com/2015/05/15/survey-of-precursors-of-category-theory-%E2%80%A2-1/

* https://inquiryintoinquiry.com/2019/09/24/peirces-1870-logic-of-relatives-%e2%80%a2-overview/

so it looks worth paying attention to their potential relationships.

To get things rolling, here's a good entry point:

</QUOTE>

Regards,

Jon

inquiry into inquiry: https://inquiryintoinquiry.com/

academia: https://independent.academia.edu/JonAwbrey

oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey

isw: http://intersci.ss.uci.edu/wiki/index.php/JLA

facebook page: https://www.facebook.com/JonnyCache

Oct 21, 2019, 7:54:15 AM10/21/19

to Arisbe List, SysSciWG, Structural Modeling, Ontolog Forum, Laws Of Form Group, Cybernetic Communications, Peirce List

All,

One of the more disconcerting developments, I might even say "devolutions",

I've observed over the last 20 years has been the general slippage back to

absolutist and dyadic ways of thinking, all of it due to the stubborn pull

of unchecked reductionism, a failure to comprehend the relational paradigm,

especially triadic relations, their irreducibility, and its consequences.

With all that in mind, I'll return to a point in our earlier discussions,

add a bit more on the concept of closure, and continue from there to its

bearing on the pragmatic maxim.

> Cf: The Difference That Makes A Difference That Peirce Makes : 23

> At: https://inquiryintoinquiry.com/2019/09/20/the-difference-that-makes-a-difference-that-peirce-makes-23/

One of the more disconcerting developments, I might even say "devolutions",

I've observed over the last 20 years has been the general slippage back to

absolutist and dyadic ways of thinking, all of it due to the stubborn pull

of unchecked reductionism, a failure to comprehend the relational paradigm,

especially triadic relations, their irreducibility, and its consequences.

With all that in mind, I'll return to a point in our earlier discussions,

add a bit more on the concept of closure, and continue from there to its

bearing on the pragmatic maxim.

> Cf: The Difference That Makes A Difference That Peirce Makes : 23

> At: https://inquiryintoinquiry.com/2019/09/20/the-difference-that-makes-a-difference-that-peirce-makes-23/

>

> A fundamental question in applications of mathematical logic

> is the threshold of complexity between dyadic (binary) and

> triadic (ternary) relations, in particular, whether 2-place

> relations are universally adequate or whether 3-place relations

> are irreducible, minimally adequate, and even sufficient as

> a basis for all higher dimensions.

>

> One of Peirce's earliest arguments for the sufficiency

> of triadic relative terms occurs at the top of his

> 1870 "Logic of Relatives".

>

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

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

> Cf: https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1#Selection_1
> A fundamental question in applications of mathematical logic

> is the threshold of complexity between dyadic (binary) and

> triadic (ternary) relations, in particular, whether 2-place

> relations are universally adequate or whether 3-place relations

> are irreducible, minimally adequate, and even sufficient as

> a basis for all higher dimensions.

>

> One of Peirce's earliest arguments for the sufficiency

> of triadic relative terms occurs at the top of his

> 1870 "Logic of Relatives".

>

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

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

>

> <QUOTE>

>

> The conjugative term involves the conception of "third",

> the relative that of second or "other", the absolute term

> simply considers "an" object. No fourth class of terms exists

> involving the conception of "fourth", because when that of "third"

> is introduced, since it involves the conception of bringing objects

> into relation, all higher numbers are given at once, inasmuch as the

> conception of bringing objects into relation is independent of the

> number of members of the relationship. Whether this "reason" for the

> fact that there is no fourth class of terms fundamentally different

> from the third is satisfactory or not, the fact itself is made

> perfectly evident by the study of the logic of relatives.

> (Peirce, CP 3.63).

>

> </QUOTE>

>

> Peirce's argument invokes what is known as a "closure principle",

> as I remarked in the following comment:

>

> <QUOTE>

>

> The conjugative term involves the conception of "third",

> the relative that of second or "other", the absolute term

> simply considers "an" object. No fourth class of terms exists

> involving the conception of "fourth", because when that of "third"

> is introduced, since it involves the conception of bringing objects

> into relation, all higher numbers are given at once, inasmuch as the

> conception of bringing objects into relation is independent of the

> number of members of the relationship. Whether this "reason" for the

> fact that there is no fourth class of terms fundamentally different

> from the third is satisfactory or not, the fact itself is made

> perfectly evident by the study of the logic of relatives.

> (Peirce, CP 3.63).

>

> </QUOTE>

>

> Peirce's argument invokes what is known as a "closure principle",

> as I remarked in the following comment:

>

> What strikes me about the initial installment this time around is

> its use of a certain pattern of argument I can recognize as invoking

> its use of a certain pattern of argument I can recognize as invoking

> a "closure principle", and this is a figure of reasoning Peirce uses

> in three other places: his discussion of "continuous predicates", his

> definition of "sign relations", and in the "pragmatic maxim" itself.

>

> * https://oeis.org/wiki/Continuous_predicate

> * https://oeis.org/wiki/Sign_relation

> * https://inquiryintoinquiry.com/2008/08/07/pragmatic-maxim/

>

> In mathematics, a "closure operator" is one whose repeated application

> yields the same result as its first application.

>

> If we take an arbitrary operator A, the result of applying A

> to an operand x is Ax, the result of applying A again is AAx,

> the result of applying A again is AAAx, and so on. In general,

> it is perfectly possible each application yields a novel result,

> distinct from all previous results.

>

> in three other places: his discussion of "continuous predicates", his

> definition of "sign relations", and in the "pragmatic maxim" itself.

>

> * https://oeis.org/wiki/Continuous_predicate

> * https://oeis.org/wiki/Sign_relation

> * https://inquiryintoinquiry.com/2008/08/07/pragmatic-maxim/

>

> In mathematics, a "closure operator" is one whose repeated application

> yields the same result as its first application.

>

> If we take an arbitrary operator A, the result of applying A

> to an operand x is Ax, the result of applying A again is AAx,

> the result of applying A again is AAAx, and so on. In general,

> it is perfectly possible each application yields a novel result,

> distinct from all previous results.

>

> But a closure operator C is defined by the property CC = C,

> so nothing new results beyond the first application.

>

> so nothing new results beyond the first application.

>

Cf: The Difference That Makes A Difference That Peirce Makes : 24

At: https://inquiryintoinquiry.com/2019/09/22/the-difference-that-makes-a-difference-that-peirce-makes-24/

The concepts of "closure" and "idempotence" are closely related.

We usually speak of a "closure operator" in contexts where the

objects acted on are the primary interest, as in topology, where

the objects of interest are open sets, boundaries, closed sets,

etc. In contexts where we abstract away from the operand space,

as in algebra, we tend to say "idempotence" for the detached

application CC = C. (If I recall right, it was actually Charles

Peirce's father Benjamin who coined the term "idempotence".)

At any rate, I'll have to mutate the principle a bit
At: https://inquiryintoinquiry.com/2019/09/22/the-difference-that-makes-a-difference-that-peirce-makes-24/

The concepts of "closure" and "idempotence" are closely related.

We usually speak of a "closure operator" in contexts where the

objects acted on are the primary interest, as in topology, where

the objects of interest are open sets, boundaries, closed sets,

etc. In contexts where we abstract away from the operand space,

as in algebra, we tend to say "idempotence" for the detached

application CC = C. (If I recall right, it was actually Charles

Peirce's father Benjamin who coined the term "idempotence".)

Oct 27, 2019, 2:00:49 PM10/27/19

to Peirce List, SysSciWG, Structural Modeling, Ontolog Forum, Cybernetic Communications

Cf : The Difference That Makes A Difference That Peirce Makes : 32

At : http://inquiryintoinquiry.com/2019/10/27/the-difference-that-makes-a-difference-that-peirce-makes-32/

Re: FB | Foundations of Mathematics

At: https://www.facebook.com/groups/563574553770077/

Re: John Corcoran

At: https://www.facebook.com/groups/563574553770077/permalink/2383887155072132/ )

There was a huge -- and of course ultimately futile -- discussion

of truth theories back in 2005 when the Wikipediot article on Truth

was under development. Pragmatists of one stripe or another from

the Peirce List ventured in vain to explain the difference between

(1) "classical" correspondence theories, (2) consensus or "social"

theories, and (3) Peircean pragmatic -- I'm guessing what Tarski

meant by "utilitarian" -- theories of truth. I'll dig up some

links and forks when I get a chance.

Regards,

Jon

At : http://inquiryintoinquiry.com/2019/10/27/the-difference-that-makes-a-difference-that-peirce-makes-32/

Re: FB | Foundations of Mathematics

At: https://www.facebook.com/groups/563574553770077/

Re: John Corcoran

At: https://www.facebook.com/groups/563574553770077/permalink/2383887155072132/ )

There was a huge -- and of course ultimately futile -- discussion

of truth theories back in 2005 when the Wikipediot article on Truth

was under development. Pragmatists of one stripe or another from

the Peirce List ventured in vain to explain the difference between

(1) "classical" correspondence theories, (2) consensus or "social"

theories, and (3) Peircean pragmatic -- I'm guessing what Tarski

meant by "utilitarian" -- theories of truth. I'll dig up some

links and forks when I get a chance.

Regards,

Jon

Oct 20, 2021, 11:20:25 AM10/20/21

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

Cf: The Difference That Makes A Difference That Peirce Makes • 33

https://inquiryintoinquiry.com/2021/10/20/the-difference-that-makes-a-difference-that-peirce-makes-33/

Re: Ontolog Forum

https://groups.google.com/g/ontolog-forum/c/IRa-uP9FUow

::: William Frank

https://groups.google.com/g/ontolog-forum/c/IRa-uP9FUow/m/4WiZr44hAgAJ

William Frank asked a question about propositional attitudes and presuppositions.

<QUOTE WF:>

Are there any formal languages, such as Common Logic,

that adequately represent statements about propositions —

statements from which, in natural reasoning, one can draw

conclusions about the elements of the embedded proposition?

</QUOTE>

Dear William,

Propositional attitudes and presuppositions were hot topics in the 80s —

scanning an old bib I see:

• Salmon, N.U., and Soames, S. (eds., 1988), Propositions and Attitudes,

Oxford University Press, New York, NY.

And everyone was reading:

• Barwise and Perry, Situations and Attitudes

https://web.stanford.edu/group/cslipublications/cslipublications/site/1575861933.shtml

But the roots of the problem go way back, and of course it can't be

rooted out till more people read and comprehend and apply Peirce's

theory of triadic sign relations.

At this point in time, however, the gravitational pull

of Russell's Planet and its inconstant satellite Quine

continue to weigh against any real progress being made.

But even Russell almost, barely, just not completely broke orbit

at one of those critical branch points of intellectual history —

it appears it was only Wittgenstein who pulled him back from the

brink of 3-adicity and back to the two-folds of dyadic relations.

I discussed all these issues in some detail in the

old Standard Upper Ontology (SUO) group and its kin.

Here's a few pertinent fragments I archived at my

current haunts:

• Russell's Theory Of Knowledge

https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#RTOK._Russell.27s_Theory_Of_Knowledge

• Russell's Philosophy Of Logical Atomism

https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#POLA._Philosophy_Of_Logical_Atomism

• Note 25

https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#POLA._Note_25

Regards,

Jon

https://inquiryintoinquiry.com/2021/10/20/the-difference-that-makes-a-difference-that-peirce-makes-33/

Re: Ontolog Forum

https://groups.google.com/g/ontolog-forum/c/IRa-uP9FUow

::: William Frank

https://groups.google.com/g/ontolog-forum/c/IRa-uP9FUow/m/4WiZr44hAgAJ

William Frank asked a question about propositional attitudes and presuppositions.

<QUOTE WF:>

Are there any formal languages, such as Common Logic,

that adequately represent statements about propositions —

statements from which, in natural reasoning, one can draw

conclusions about the elements of the embedded proposition?

</QUOTE>

Dear William,

Propositional attitudes and presuppositions were hot topics in the 80s —

scanning an old bib I see:

• Salmon, N.U., and Soames, S. (eds., 1988), Propositions and Attitudes,

Oxford University Press, New York, NY.

And everyone was reading:

• Barwise and Perry, Situations and Attitudes

https://web.stanford.edu/group/cslipublications/cslipublications/site/1575861933.shtml

But the roots of the problem go way back, and of course it can't be

rooted out till more people read and comprehend and apply Peirce's

theory of triadic sign relations.

At this point in time, however, the gravitational pull

of Russell's Planet and its inconstant satellite Quine

continue to weigh against any real progress being made.

But even Russell almost, barely, just not completely broke orbit

at one of those critical branch points of intellectual history —

it appears it was only Wittgenstein who pulled him back from the

brink of 3-adicity and back to the two-folds of dyadic relations.

I discussed all these issues in some detail in the

old Standard Upper Ontology (SUO) group and its kin.

Here's a few pertinent fragments I archived at my

current haunts:

• Russell's Theory Of Knowledge

https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#RTOK._Russell.27s_Theory_Of_Knowledge

• Russell's Philosophy Of Logical Atomism

https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#POLA._Philosophy_Of_Logical_Atomism

• Note 25

https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#POLA._Note_25

Regards,

Jon

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