Re: [PEIRCE-L] Logical Graphs

[Jon Awbrey]

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


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.


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

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Re: [PEIRCE-L] Thinking in diagrams vs thinking in words

[Jerry LR Chandler]

John:

While the abstractions of mathematics are extremely powerful, 
and have had profound influence on our economic systems,
such abstractions are far less powerful in analysis of complex systems of 
chemistry and biology.
I believe that your statement below is categorically in error.

> On Jul 27, 2021, at 2:55 PM, John F. Sowa  wrote:
> 
>  In his three universes of
> discourse -- possibilities, actualities, and necessities -- mathematics
> is first because it includes every possible pattern of any kind.  That
> includes everything that any human or any living thing of any kind could
> imagine -- plus all the possible patterns that no finite being could
> imagine.

Scientific languages and semiotic grounding of the chemical and genetic symbol 
systems are 
syntactically developed from the epistemology of human sensory interpretations 
and symbolizations.

The illations that connect the chemical and genetic symbol systems are not 
necessarily grounded in mathematics,
 but rather are ground in semiotics and the epistemologies of the natural 
sciences.

In short, the abductive logic used by CSP in the 
illative assertions of the trichotomy is 
relative to the adductive logic of mathematics 
BUT remote from the multiplicative logic of physical philosophy.

Furthermore, at present, no mathematical or physical method exists to calculate 
all possible chemical patterns (isomers) because of the multiplicity of 
branchings associated with concatenations of chemical elements (atomic numbers) 
with valences exceeding 2.

Once again, in my opinion,
 the logical operations of geometrically based mathematical theories are
 insufficient to ground the calculations
 of the semantically grounded and syntactically grounded calculations of number 
theory of chemistry. 

I would urge you to peruse the mathematics of an introductory organic chemistry 
textbook from the perspective of (atomic) number theory and the quanta physics 
of electricity. CSP grasp the essential elements of this obligatory logic a 
century ago and you certainly can too. CSP valued semiotic reasoning higher 
than geometry when he expressed his views on the simplest mathematics. 
(4.240-243).  

Cheers

Jerry 


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Re: [PEIRCE-L] Fwd: Re: RE: Thinking in diagrams vs thinking in words

[Jerry LR Chandler]

Edwinia:

> On Jul 25, 2021, at 12:11 PM, Edwina Taborsky  wrote:
> 
> Yes, of course. I see what you mean. His categories are indeed 'innate 
> semiosic predispositions'...and are indeed necessary initial conditions. 
> Exactly.
> 
> And that's where mathematics comes in - to outline the nature of these 
> categories, which we then use to examine the phaneron.
> 
Your continued development of your substantial capacities is impressive!

An enthusiastic YES! to your assertions.

The next STEP (in the logical diagram) in analysis is to ask the biological 
question, HOW to the mathematical groundings come into existence?

Is it possible that molecular biological dynamics GROUND the innate 
capabilities to which you refer?
Is it possible that the atomic numbers ground the molecular biological dynamics?
Is it possible that the CSP anticipated this chemical grounding of the phaneron?
( Note that this line of formal  associative logics is remote from the set 
theory logic of Husserl’s phenomenology!)

Cheers
Jerry_ _ _ _ _ _ _ _ _ _
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Re: [PEIRCE-L] Fwd: Re: RE: Thinking in diagrams vs thinking in words

[Edwina Taborsky]

 

Jerry, list

Flattery will get you everywhere!

And so, I know that you will say that 'the mathematical groundings
come into existence' via the chemical groundings'.

And I agree. That is, the categories are not 'human constructs'
which would make the nominalistic. They are material, biological-
physico-chemical realities. 

Edwina
 On Thu 29/07/21 10:45 AM , Jerry LR Chandler
jerry_lr_chand...@icloud.com sent:
 Edwinia:
 On Jul 25, 2021, at 12:11 PM, Edwina Taborsky  wrote:
 Yes, of course. I see what you mean. His categories are indeed
'innate semiosic predispositions'...and are indeed necessary initial
conditions. Exactly.

And that's where mathematics comes in - to outline the nature of
these categories, which we then use to examine the phaneron. Your
continued development of your substantial capacities is impressive!
 An enthusiastic YES! to your assertions.
 The next STEP (in the logical diagram) in analysis is to ask the
biological question, HOW to the mathematical groundings come into
existence?
 Is it possible that molecular biological dynamics GROUND the innate
capabilities to which you refer? Is it possible that the atomic
numbers ground the molecular biological dynamics?Is it possible that
the CSP anticipated this chemical grounding of the phaneron?( Note
that this line of formal  associative logics is remote from the set
theory logic of Husserl’s phenomenology!)
 CheersJerry 


Links:
--
[1]
http://webmail.primus.ca/javascript:top.opencompose(\'tabor...@primus.ca\',\'\',\'\',\'\')
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Re: [PEIRCE-L] Thinking in Diagrams vs Thinking in Words

[Jon Awbrey]

Dear Robert,

That was something between idle snark and off-the-cuff remark,
as that's all my current dis-array of interrupredations allow
me right now, but it does touch on pressing issues about the
present reception and comprehension of Peirce's impact which
have been tugging at the edges of my wariness increasingly
over the past couple of decades, so I will try to make my
worries more effable in the fulsome-mess of time ...

But I wouldn't wish to hijack this topic with all that
so I'll came back to it under another subject line ...

Regards,

Jon

On 7/29/2021 10:08 AM, robert marty wrote:

Dear Jon, List,


I know what book you are talking about; today it can be downloaded for
free...
I looked at your diagram... it rejuvenated me... indeed, I was always the
terror of my students because, whenever they presented me with a diagram I
demanded that every single point, every single line be documented... so I
look at your diagram and I see first of all ovals,5 , with words inside...
I wonder if they delimit sets of points of the plane which would represent
each one an object of the extension of each of the labels inscribed in the
oval... the answer is obvious, it's not. So the ovals are just decorative
elements that direct attention to the 5 terms of the language they surround.
I come to the lines ... the graphic conventions in use (signs of law)
strongly suggest to me that they are relationships between concepts ...
perhaps of dependence given the context of communication ... the same
conventions and context suggest that they should be considered top-down
relationships ... I can't go beyond that as I have no information about
these lines and the modes of correspondence they cover ... in advance of
the upcoming debate, I say that if all the lines represent top-down
dependency relationships then this diagram comes into open conflict with
Peirce's classification ... conflict involving debate in the Sciences of
Discovery ...I am ready...

On Thu. Jul 29, 2021 at 2:30 PM, Jon Awbrey  wrote:
Dear Robert, John, Edwina, ...
This discussion reminds me a lot of the time I spent the big bucks
buying a book on "Diagrammatology" which ran to over 500 pages with
many sections in very small print and had just over 50 diagrams in
the whole thing.

So I think the real "versus" here is more like the difference
between people who "think in words about thinking in diagrams"
and people who "think 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.

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

Regardez,

Jon

On 7/29/2021 5:27 AM, robert marty wrote:

Dear John, Edwina, List

Let me clarify my question:

The references in parentheses refer to the classification
<

https://www.academia.edu/5148127/The_outline_of_Peirces_classification_of_sciences_1902_1911_


compiled by Tommi Vehkavaara.

The classification of the Sciences of Discovery places Mathematics (AI)
ex-ante the Phaneroscopy; the whole mathematical activity is per se,
independent of any implementation and does not depend on anything, since

it

incorporates its own mathematics (of Logic) (AIa) as a constituent part

of

itself.

The discrete mathematics (so the algebra) (AIb) depend on it, and then

the

Mathematics of Continuum (AIc) depends on them.

The discrete mathematics (so the algebra) (AIb) depend on it, and then

the

Mathematics of Continuum (AIc) depends on these last ones.

In the ladder of dependencies that penetrate inside the "well of truth"
(Peirce's metaphor is a way of expressing his agreement with Auguste

Comte)

comes the (AII) Cenoscopy - Philosophia prima, which is only a generic
label covering all the positive sciences "which rests upon familiar,
general experience." At the first rank of them, the Phenomenology (AIIa),
the study of Universal Categories "all present in any phenomenon:
Firstness, Secondness, Thirdness." Indeed, any particular science of

nature

is the study of a phenomenology. We can see that it is at this level that
Peirce situates the elaboration of his universal categories.

I will stop here for a moment before addressing the question of the
Normative Sciences (AIIb) because you have referred three Universes of
Discourse.

JS >. " *In his three universes of** discourse -- possibilities,
actualities, and necessities – mathematics is first because it includes
every possible pattern of any kind.*"

In Universe of Discourse | Dictionary | Commens
 there is

a

set of texts in which Peirce expresses himself on his conception of the
Universe of Discourse. I take one of them, which seems to me to be
representative (if this were not the case, you could indicate to me

whether

I am introducing any bias by this choice:

   *"1903 | Graphs, Little Account [R] | MS [R] S27:9-10*

*…if one person is to convey any 

Re: [PEIRCE-L] Thinking in Diagrams vs Thinking in Words

[robert marty]

Dear Jon, List,

> I know what book you are talking about; today it can be downloaded for
> free...
> I looked at your diagram... it rejuvenated me... indeed, I was always the
> terror of my students because, whenever they presented me with a diagram I
> demanded that every single point, every single line be documented... so I
> look at your diagram and I see first of all ovals,5 , with words inside...
> I wonder if they delimit sets of points of the plane which would represent
> each one an object of the extension of each of the labels inscribed in the
> oval... the answer is obvious, it's not. So the ovals are just decorative
> elements that direct attention to the 5 terms of the language they surround.
> I come to the lines ... the graphic conventions in use (signs of law)
> strongly suggest to me that they are relationships between concepts ...
> perhaps of dependence given the context of communication ... the same
> conventions and context suggest that they should be considered top-down
> relationships ... I can't go beyond that as I have no information about
> these lines and the modes of correspondence they cover ... in advance of
> the upcoming debate, I say that if all the lines represent top-down
> dependency relationships then this diagram comes into open conflict with
> Peirce's classification ... conflict involving debate in the Sciences of
> Discovery ...I am ready...
>
> On Thu. Jul 29, 2021 at 2:30 PM, Jon Awbrey  wrote:
> Dear Robert, John, Edwina, ...
> This discussion reminds me a lot of the time I spent the big bucks
> buying a book on "Diagrammatology" which ran to over 500 pages with
> many sections in very small print and had just over 50 diagrams in
> the whole thing.
>
> So I think the real "versus" here is more like the difference
> between people who "think in words about thinking in diagrams"
> and people who "think 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.
>
> https://inquiryintoinquiry.files.wordpress.com/2014/08/peirce-syllabus.jpg
>
> Regardez,
>
> Jon
>
> On 7/29/2021 5:27 AM, robert marty wrote:
> > Dear John, Edwina, List
> >
> > Let me clarify my question:
> >
> > The references in parentheses refer to the classification
> > <
> https://www.academia.edu/5148127/The_outline_of_Peirces_classification_of_sciences_1902_1911_
> >
> > compiled by Tommi Vehkavaara.
> >
> > The classification of the Sciences of Discovery places Mathematics (AI)
> > ex-ante the Phaneroscopy; the whole mathematical activity is per se,
> > independent of any implementation and does not depend on anything, since
> it
> > incorporates its own mathematics (of Logic) (AIa) as a constituent part
> of
> > itself.
> >
> > The discrete mathematics (so the algebra) (AIb) depend on it, and then
> the
> > Mathematics of Continuum (AIc) depends on them.
> >
> > The discrete mathematics (so the algebra) (AIb) depend on it, and then
> the
> > Mathematics of Continuum (AIc) depends on these last ones.
> >
> > In the ladder of dependencies that penetrate inside the "well of truth"
> > (Peirce's metaphor is a way of expressing his agreement with Auguste
> Comte)
> > comes the (AII) Cenoscopy - Philosophia prima, which is only a generic
> > label covering all the positive sciences "which rests upon familiar,
> > general experience." At the first rank of them, the Phenomenology (AIIa),
> > the study of Universal Categories "all present in any phenomenon:
> > Firstness, Secondness, Thirdness." Indeed, any particular science of
> nature
> > is the study of a phenomenology. We can see that it is at this level that
> > Peirce situates the elaboration of his universal categories.
> >
> > I will stop here for a moment before addressing the question of the
> > Normative Sciences (AIIb) because you have referred three Universes of
> > Discourse.
> >
> > JS >. " *In his three universes of** discourse -- possibilities,
> > actualities, and necessities – mathematics is first because it includes
> > every possible pattern of any kind.*"
> >
> > In Universe of Discourse | Dictionary | Commens
> >  there is
> a
> > set of texts in which Peirce expresses himself on his conception of the
> > Universe of Discourse. I take one of them, which seems to me to be
> > representative (if this were not the case, you could indicate to me
> whether
> > I am introducing any bias by this choice:
> >
> >   *"1903 | Graphs, Little Account [R] | MS [R] S27:9-10*
> >
> > *…if one person is to convey any information to another, it must be upon
> > the basis of a common experience. They must not only have this common
> > experience, but each must know the other has it; and not only that but
> each
> > must know the other knows that he knows the other has it; so that when
> one
> > says ‘It is cold’ the other may know that he does not mean 

Re: [PEIRCE-L] Thinking in Diagrams vs Thinking in Words

[Edwina Taborsky]

 

 BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px;
}Jon, list

Hmm. Does this claim, 

" the difference 
  between people who "think in words about thinking in diagrams" 
  and people who "think in words about thinking in words". 

1]..not lead to the problem where it will be claimed that X-people
or X-person couldn't think about the situation because they didn't
have the vocabulary to do so?

I am aware that such a claim is made about certain languages  but I
am not convinced of its validity. 

2] I think that languages are flexible and the people can come up
with new terms for experiences.

3] But, on the other hand, there are people who prefer taxonomic
analysis, where each situation and event is classified and labelled
into a niche of purity.

Edwina
 On Thu 29/07/21  8:30 AM , Jon Awbrey jawb...@att.net sent:
 Dear Robert, John, Edwina, ... 
 This discussion reminds me a lot of the time I spent the big bucks 
 buying a book on "Diagrammatology" which ran to over 500 pages with 
 many sections in very small print and had just over 50 diagrams in 
 the whole thing. 
 So I think the real "versus" here is more like the difference 
 between people who "think in words about thinking in diagrams" 
 and people who "think 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. 

https://inquiryintoinquiry.files.wordpress.com/2014/08/peirce-syllabus.jpg
[1] 
 Regardez, 
 Jon 
 On 7/29/2021 5:27 AM, robert marty wrote: 
 > Dear John, Edwina, List 
 >  
 > Let me clarify my question: 
 >  
 > The references in parentheses refer to the classification 
 > <
https://www.academia.edu/5148127/The_outline_of_Peirces_classification_of_sciences_1902_1911
[2]_ > 
 > compiled by Tommi Vehkavaara. 
 >  
 > The classification of the Sciences of Discovery places Mathematics
(AI) 
 > ex-ante the Phaneroscopy; the whole mathematical activity is per
se, 
 > independent of any implementation and does not depend on anything,
since it 
 > incorporates its own mathematics (of Logic) (AIa) as a constituent
part of 
 > itself. 
 >  
 > The discrete mathematics (so the algebra) (AIb) depend on it, and
then the 
 > Mathematics of Continuum (AIc) depends on them. 
 >  
 > The discrete mathematics (so the algebra) (AIb) depend on it, and
then the 
 > Mathematics of Continuum (AIc) depends on these last ones. 
 >  
 > In the ladder of dependencies that penetrate inside the "well of
truth" 
 > (Peirce's metaphor is a way of expressing his agreement with
Auguste Comte) 
 > comes the (AII) Cenoscopy - Philosophia prima, which is only a
generic 
 > label covering all the positive sciences "which rests upon
familiar, 
 > general experience." At the first rank of them, the Phenomenology
(AIIa), 
 > the study of Universal Categories "all present in any phenomenon: 
 > Firstness, Secondness, Thirdness." Indeed, any particular science
of nature 
 > is the study of a phenomenology. We can see that it is at this
level that 
 > Peirce situates the elaboration of his universal categories. 
 >  
 > I will stop here for a moment before addressing the question of
the 
 > Normative Sciences (AIIb) because you have referred three
Universes of 
 > Discourse. 
 >  
 > JS >. " *In his three universes of** discourse -- possibilities, 
 > actualities, and necessities – mathematics is first because it
includes 
 > every possible pattern of any kind.*" 
 >  
 > In Universe of Discourse | Dictionary | Commens 
 >  [3] there is a 
 > set of texts in which Peirce expresses himself on his conception
of the 
 > Universe of Discourse. I take one of them, which seems to me to be

 > representative (if this were not the case, you could indicate to
me whether 
 > I am introducing any bias by this choice: 
 >  
 >   *"1903 | Graphs, Little Account [R] | MS [R] S27:9-10* 
 >  
 > *…if one person is to convey any information to another, it must
be upon 
 > the basis of a common experience. They must not only have this
common 
 > experience, but each must know the other has it; and not only that
but each 
 > must know the other knows that he knows the other has it; so that
when one 
 > says ‘It is cold’ the other may know that he does not mean
that it is cold 
 > in Iceland or in Laputa, but right here. In short it must be
thoroughly 
 > understood between them that they are talking about objects of a
collection 
 > with which both have some familiarity. **The collection of objects
to which 
 > it is mutually understood that the propositions refer is called by
exact 
 > logicians the universe of discourse." *[emphasize mine] 
 >  
 > Then you consider the three universes of discourse which are
possibilities, 
 > actualities, and necessities. In other words, the universe of
discourse 
 > discussed above is now divided into 3 collections of objects. It
remains to 
 

Re: [PEIRCE-L] Thinking in Diagrams vs Thinking in Words

[Jon Awbrey]

Dear Robert, John, Edwina, ...

This discussion reminds me a lot of the time I spent the big bucks
buying a book on "Diagrammatology" which ran to over 500 pages with
many sections in very small print and had just over 50 diagrams in
the whole thing.

So I think the real "versus" here is more like the difference
between people who "think in words about thinking in diagrams"
and people who "think 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.

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

Regardez,

Jon

On 7/29/2021 5:27 AM, robert marty wrote:

Dear John, Edwina, List

Let me clarify my question:

The references in parentheses refer to the classification
< 
https://www.academia.edu/5148127/The_outline_of_Peirces_classification_of_sciences_1902_1911_
 >
compiled by Tommi Vehkavaara.

The classification of the Sciences of Discovery places Mathematics (AI)
ex-ante the Phaneroscopy; the whole mathematical activity is per se,
independent of any implementation and does not depend on anything, since it
incorporates its own mathematics (of Logic) (AIa) as a constituent part of
itself.

The discrete mathematics (so the algebra) (AIb) depend on it, and then the
Mathematics of Continuum (AIc) depends on them.

The discrete mathematics (so the algebra) (AIb) depend on it, and then the
Mathematics of Continuum (AIc) depends on these last ones.

In the ladder of dependencies that penetrate inside the "well of truth"
(Peirce's metaphor is a way of expressing his agreement with Auguste Comte)
comes the (AII) Cenoscopy - Philosophia prima, which is only a generic
label covering all the positive sciences "which rests upon familiar,
general experience." At the first rank of them, the Phenomenology (AIIa),
the study of Universal Categories "all present in any phenomenon:
Firstness, Secondness, Thirdness." Indeed, any particular science of nature
is the study of a phenomenology. We can see that it is at this level that
Peirce situates the elaboration of his universal categories.

I will stop here for a moment before addressing the question of the
Normative Sciences (AIIb) because you have referred three Universes of
Discourse.

JS >. " *In his three universes of** discourse -- possibilities,
actualities, and necessities – mathematics is first because it includes
every possible pattern of any kind.*"

In Universe of Discourse | Dictionary | Commens
 there is a
set of texts in which Peirce expresses himself on his conception of the
Universe of Discourse. I take one of them, which seems to me to be
representative (if this were not the case, you could indicate to me whether
I am introducing any bias by this choice:

  *"1903 | Graphs, Little Account [R] | MS [R] S27:9-10*

*…if one person is to convey any information to another, it must be upon
the basis of a common experience. They must not only have this common
experience, but each must know the other has it; and not only that but each
must know the other knows that he knows the other has it; so that when one
says ‘It is cold’ the other may know that he does not mean that it is cold
in Iceland or in Laputa, but right here. In short it must be thoroughly
understood between them that they are talking about objects of a collection
with which both have some familiarity. **The collection of objects to which
it is mutually understood that the propositions refer is called by exact
logicians the universe of discourse." *[emphasize mine]

Then you consider the three universes of discourse which are possibilities,
actualities, and necessities. In other words, the universe of discourse
discussed above is now divided into 3 collections of objects. It remains to
know how this division occurs.

Peirce gives us a well-known (but not exclusive) answer, as one could do in
any observational science:

* "** Phaneroscopy is the description of the phaneron; and by the phaneron
I mean the collective total of all that is in any way or in any sense
present to the mind, quite regardless of whether it corresponds to any real
thing or not. If you ask present when, and to whose mind, I reply that I
leave these questions unanswered, never having entertained a doubt that
those features of the phaneron that I have found in my mind are present at
all times and to all minds. So far as I have developed this science of
phaneroscopy, it is occupied with the formal elements of the phaneron*"(CP
1.284) [emphasize mine]

It is well specified further on:

*" What I term phaneroscopy is that study which, supported by the direct
observation of **phanerons and generalizing its observations, signalizes
several very broad classes of **phanerons; describes the features of each**;
shows that although they are so **inextricably mixed together that no one
can be isolated, yet it is manifest that 

Re: [PEIRCE-L] Thinking in diagrams vs thinking in words

[Edwina Taborsky]

 

 BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px;
}Robert, list

1] If I understand your question correctly - is it 

- our first experience is: the phaneron. This is essentially the
qualisign experience of one material entity with its surroundings.
I'd say this compares with Peirce's outline of cosmology - see 1.412
and 6.217 and 6.191,..200 ie, from the vague to the definite'. , a
state of being 'before logic'..."the utter vagueness of completely
undetermined and dimensionless potentiality" 6.193.

See also his famous blackboard example 6.203..where Peirce outlines
the development of the three categories, or 'modes of being'. And
points out that Thirdness, or habit-formation' ..'must have its
origin in the original continuity which is inherent in potentiality.
Continuity, as generality, is inherent in potentiality, which is
essentially general" 6.204.

- understanding this phaneron is based upon reasoning about
it...which involves diagrammatic reasoning about relations - ie,
mathematics.

2] Your question posed to John Sowa. if I understand it correctly,
refers to his locating mathematical reasoning within the universe of
Firstness while you locate it within the universe of Thirdness??

Edwina
 On Thu 29/07/21  5:27 AM , robert marty robert.mart...@gmail.com
sent:
Dear John, Edwina, List  
Let me clarify my question: 
The references in parentheses refer to the  classification compiled
by Tommi Vehkavaara. 
The classification of the Sciences of Discovery places Mathematics
(AI) ex-ante the Phaneroscopy; the whole mathematical activity is per
se, independent of any implementation and does not depend on anything,
since it incorporates its own mathematics (of Logic) (AIa) as a
constituent part of itself. 

The discrete mathematics (so the algebra) (AIb) depend on it, and
then the Mathematics of Continuum (AIc) depends on them.  
The discrete mathematics (so the algebra) (AIb) depend on it, and
then the Mathematics of Continuum (AIc) depends on these last ones.  
In the ladder of dependencies that penetrate inside the "well of
truth" (Peirce's metaphor is a way of expressing his agreement with
Auguste Comte) comes the (AII) Cenoscopy - Philosophia prima, which
is only a generic label covering all the positive sciences "which
rests upon familiar, general experience." At the first rank of them,
the Phenomenology (AIIa), the study of Universal Categories "all
present in any phenomenon: Firstness, Secondness, Thirdness." Indeed,
any particular science of nature is the study of a phenomenology. We
can see that it is at this level that Peirce situates the elaboration
of his universal categories.  

I will stop here for a moment before addressing the question of the
Normative Sciences (AIIb) because you have referred three Universes
of Discourse.  
JS >. " In his three universes of discourse -- possibilities,
actualities, and necessities – mathematics is first because it
includes every possible pattern of any kind." 
In Universe of Discourse | Dictionary | Commens there is a set of
texts in which Peirce expresses himself on his conception of the
Universe of Discourse. I take one of them, which seems to me to be
representative (if this were not the case, you could indicate to me
whether I am introducing any bias by this choice: 
 "1903 | Graphs, Little Account [R] | MS [R] S27:9-10 

…if one person is to convey any information to another, it must be
upon the basis of a common experience. They must not only have this
common experience, but each must know the other has it; and not only
that but each must know the other knows that he knows the other has
it; so that when one says ‘It is cold’ the other may know that he
does not mean that it is cold in Iceland or in Laputa, but right here.
In short it must be thoroughly understood between them that they are
talking about objects of a collection with which both have some
familiarity. The collection of objects to which it is mutually
understood that the propositions refer is called by exact logicians
the universe of discourse." [emphasize mine] 

Then you consider the three universes of discourse which are
possibilities, actualities, and necessities. In other words, the
universe of discourse discussed above is now divided into 3
collections of objects. It remains to know how this division occurs. 
Peirce gives us a well-known (but not exclusive) answer, as one
could do in any observational science:   
 " Phaneroscopy is the description of the phaneron; and by the 
phaneron I mean the collective total of all that is in any way or in
any sense present to the mind, quite regardless of whether it
corresponds to any real thing or not. If you ask present when, and to
whose mind, I reply that I leave these questions unanswered, never
having entertained a doubt that those features of the 

Re: [PEIRCE-L] Thinking in diagrams vs thinking in words

[robert marty]

Dear John, Edwina, List



Let me clarify my question:



The references in parentheses refer to the classification

compiled by Tommi Vehkavaara.



The classification of the Sciences of Discovery places Mathematics (AI)
ex-ante the Phaneroscopy; the whole mathematical activity is per se,
independent of any implementation and does not depend on anything, since it
incorporates its own mathematics (of Logic) (AIa) as a constituent part of
itself.

The discrete mathematics (so the algebra) (AIb) depend on it, and then the
Mathematics of Continuum (AIc) depends on them.



The discrete mathematics (so the algebra) (AIb) depend on it, and then the
Mathematics of Continuum (AIc) depends on these last ones.



In the ladder of dependencies that penetrate inside the "well of truth"
(Peirce's metaphor is a way of expressing his agreement with Auguste Comte)
comes the (AII) Cenoscopy - Philosophia prima, which is only a generic
label covering all the positive sciences "which rests upon familiar,
general experience." At the first rank of them, the Phenomenology (AIIa),
the study of Universal Categories "all present in any phenomenon:
Firstness, Secondness, Thirdness." Indeed, any particular science of nature
is the study of a phenomenology. We can see that it is at this level that
Peirce situates the elaboration of his universal categories.

I will stop here for a moment before addressing the question of the
Normative Sciences (AIIb) because you have referred three Universes of
Discourse.



JS >. " *In his three universes of** discourse -- possibilities,
actualities, and necessities – mathematics is first because it includes
every possible pattern of any kind.*"



In Universe of Discourse | Dictionary | Commens
 there is a
set of texts in which Peirce expresses himself on his conception of the
Universe of Discourse. I take one of them, which seems to me to be
representative (if this were not the case, you could indicate to me whether
I am introducing any bias by this choice:



 *"1903 | Graphs, Little Account [R] | MS [R] S27:9-10*

*…if one person is to convey any information to another, it must be upon
the basis of a common experience. They must not only have this common
experience, but each must know the other has it; and not only that but each
must know the other knows that he knows the other has it; so that when one
says ‘It is cold’ the other may know that he does not mean that it is cold
in Iceland or in Laputa, but right here. In short it must be thoroughly
understood between them that they are talking about objects of a collection
with which both have some familiarity. **The collection of objects to which
it is mutually understood that the propositions refer is called by exact
logicians the universe of discourse." *[emphasize mine]

Then you consider the three universes of discourse which are possibilities,
actualities, and necessities. In other words, the universe of discourse
discussed above is now divided into 3 collections of objects. It remains to
know how this division occurs.



Peirce gives us a well-known (but not exclusive) answer, as one could do in
any observational science:



* "** Phaneroscopy is the description of the phaneron; and by the phaneron
I mean the collective total of all that is in any way or in any sense
present to the mind, quite regardless of whether it corresponds to any real
thing or not. If you ask present when, and to whose mind, I reply that I
leave these questions unanswered, never having entertained a doubt that
those features of the phaneron that I have found in my mind are present at
all times and to all minds. So far as I have developed this science of
phaneroscopy, it is occupied with the formal elements of the phaneron*"(CP
1.284) [emphasize mine]



It is well specified further on:



*" What I term phaneroscopy is that study which, supported by the direct
observation of **phanerons and generalizing its observations, signalizes
several very broad classes of **phanerons; describes the features of each**;
shows that although they are so **inextricably mixed together that no one
can be isolated, yet it is manifest that their **characters are quite
disparate; then proves, beyond question, that a certain very short **list
comprises all of these broadest categories of phanerons there are; and
finally **proceeds to the laborious and difficult task of enumerating the
principal subdivisions **of those categories. *(CP 1.286, 1902) [emphasize
mine]



That this answer is not exclusive, he showed it himself by having recourse
to justify it, on many occasions, to the triadic reduction of polyadic
relations that he did not really establish himself. It was established
later, notably by Herzberger, Burch and more recently by Dau F., Correia
J.H. (2006 )



*" A