Re: [PEIRCE-L] Laws of Nature as Signs

[Jerry Rhee]

Dear list:

“the fact that A presents B with gift C...”



“I cannot forget that there are the germs of the *theory of the categories*
which is (if anything is) the gift I make to the world. That is my child.
In it I shall live when oblivion has me — my body”



The surprising fact, *C*, is observed;
But if *A* were true, *C* would be a matter of course,
Hence, there is reason to suspect that *A* is true.  (CP 5.189)

___



Three dyads:

C is B

A is C

B is A;  (middle term C)



Converting and then ordering gives:



middle term *A* (Rule/Result/Case- C B *A*) or,

middle term *B* (Result/Rule/Case- C A *B*)



So, choose:



C A *B* or C B *A *



(triadic relations = three dyads).



Hth,

Jerry Rhee

On Sun, Apr 30, 2017 at 4:43 PM, Jerry LR Chandler <
jerry_lr_chand...@icloud.com> wrote:

> List, Charles:
>
> On Apr 30, 2017, at 2:43 PM, Charles Pyle  wrote:
>
> Many years ago linguists chewed over the issue of whether the semantic
> analysis of three place predicates can be broken down into a series of two
> place predicates and discovered that the two are not semantically or
> grammatically equivalent.
>
> ‘Bob gave a book to Sue' is not equivalent to e.g. ‘Bob caused Sue to have
> a book’
>
> I am not sure how this would impact the argument in formal logic, since
> ordinary language and formal logic often part ways (e.g. ‘Bob is not
> unhappy’ does not equal ‘Bob is happy’), but it seems relevant in
> evaluating Peirce’s claim.
>
> Yes, and CSP recognized this in his views on graph theory.
>
> And, it further necessary to separate the structures of the grammar.
>
> The arrangements of the order of the terms is crucial in determining the
> meaning.
> Three particular nouns can form three dyadic relations - “John gives John
> to John” (Roberts, Fig. 5 p.25).
> Or,
> Four nouns can be arranged in linear order by syncategormatic terms:
> *John* sells a *book* to *Susan* for a *dollar. (For CSP, this is
> represented by four blanks (loose ends)  in the sentence structure)*
>
> Or, more interestingly, is the possibility of a branched structure in
> CSP’s example of the four atoms of ammonia (Roberts, Fig. 6, p.25).  In the
> branched graphic structure of the four atoms of ammonia, one atom is in
> relation to the other three atoms.  In other words, the nitrogen atom is in
> direct dyadic relation with each of the three hydrogen atoms.
>
> In summary,
> 1. No simple rules of grammar exist between integer numbers and icons of
> relations, as you noted.
> 2. And, the grammatical role of syncategormatic words can play a decisive
> role in how the dyadic relations are formed.
> 3. The logic of the concept of a relation is extra-ordinary difficult to
> express exactly because the grammatical meaning of the categorical terms is
> changed by the syncategormatic terms. This was illustrated by the two
> figures in Robert’s book.  Other examples abound.
>
> John S.’s examples are equally relevant.
>
> Cheers
> Jerry
>
>
>
>
>
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>
>
>
>
>
>

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Re: [PEIRCE-L] Laws of Nature as Signs

[Jerry LR Chandler]

List, Charles:

> On Apr 30, 2017, at 2:43 PM, Charles Pyle  wrote:
> 
> Many years ago linguists chewed over the issue of whether the semantic 
> analysis of three place predicates can be broken down into a series of two 
> place predicates and discovered that the two are not semantically or 
> grammatically equivalent.
> 
> ‘Bob gave a book to Sue' is not equivalent to e.g. ‘Bob caused Sue to have a 
> book’
> 
> I am not sure how this would impact the argument in formal logic, since 
> ordinary language and formal logic often part ways (e.g. ‘Bob is not unhappy’ 
> does not equal ‘Bob is happy’), but it seems relevant in evaluating Peirce’s 
> claim.
> 
Yes, and CSP recognized this in his views on graph theory. 

And, it further necessary to separate the structures of the grammar.

The arrangements of the order of the terms is crucial in determining the 
meaning.
Three particular nouns can form three dyadic relations - “John gives John to 
John” (Roberts, Fig. 5 p.25).
Or, 
Four nouns can be arranged in linear order by syncategormatic terms:
John sells a book to Susan for a dollar. (For CSP, this is represented by four 
blanks (loose ends)  in the sentence structure)

Or, more interestingly, is the possibility of a branched structure in CSP’s 
example of the four atoms of ammonia (Roberts, Fig. 6, p.25).  In the branched 
graphic structure of the four atoms of ammonia, one atom is in relation to the 
other three atoms.  In other words, the nitrogen atom is in direct dyadic 
relation with each of the three hydrogen atoms. 

In summary, 
1. No simple rules of grammar exist between integer numbers and icons of 
relations, as you noted. 
2. And, the grammatical role of syncategormatic words can play a decisive role 
in how the dyadic relations are formed.
3. The logic of the concept of a relation is extra-ordinary difficult to 
express exactly because the grammatical meaning of the categorical terms is 
changed by the syncategormatic terms. This was illustrated by the two figures 
in Robert’s book.  Other examples abound.
 
John S.’s examples are equally relevant.

Cheers
Jerry

 


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Re: [PEIRCE-L] Re: Laws of Nature as Signs

[Charles Pyle]

I can't tell who wrote the following quote, so I am not sure who to address 
here.

Many years ago linguists chewed over the issue of whether the semantic analysis 
of three place predicates can be broken down into a series of two place 
predicates and discovered that the two are not semantically or grammatically 
equivalent.


‘Bob gave a book to Sue' is not equivalent to e.g. ‘Bob caused Sue to have a 
book’


I am not sure how this would impact the argument in formal logic, since 
ordinary language and formal logic often part ways (e.g. ‘Bob is not unhappy’ 
does not equal ‘Bob is happy’), but it seems relevant in evaluating Peirce’s 
claim.


---begin quote---

Many logicians have correctly observed
that you can replace any triadic relation by three dyadic relations
plus an additional quantified variable. In a graph, the node thatte 
represents the variable will be linked to the three dyadic relations.

For example, consider the following sentence and its translation
to two different formulas in predicate calculus:

x gives y to z.
∃x ∃y ∃z gives(x,y,z).
∃x ∃y ∃z ∃w (give(w) & agent(w,x) & theme(w,y) & recipient(w,z))

---end quote---

> 
> On April 30, 2017 at 1:51 PM John F Sowa  wrote:
> 
> Jon and Jerry,
> 
> JA
> 
> > > 
> > triadic relations extend across a threshold of complexity, such that
> > relations of all higher adicities can be analyzed in terms of 
> > 1-adic,
> > 2-adic, and 3-adic relations.
> > 
> > > 
> No. Peirce never said that. Many logicians have correctly observed
> that you can replace any triadic relation by three dyadic relations
> plus an additional quantified variable. In a graph, the node that
> represents the variable will be linked to the three dyadic relations.
> 
> For example, consider the following sentence and its translation
> to two different formulas in predicate calculus:
> 
> x gives y to z.
> ∃x ∃y ∃z gives(x,y,z).
> ∃x ∃y ∃z ∃w (give(w) & agent(w,x) & theme(w,y) & recipient(w,z)).
> 
> The second formula has a new entity named w, which is linked to three
> dyadic relations. There is still an implicit triad in the formula.
> 
> In an earlier note, I showed the sentence "Sue gives a child a book"
> as two different conceptual graphs. In the attached giveEGCG.jpg,
> I show that sentence translated to the same two conceptual graphs
> and to their translations as existential graphs.
> 
> To show the mappings to the algebraic formulas, I also annotated
> the lines of identity: x, y, and z represent the same lines in
> both EGs. But w represents a ligature of *four* lines of identity
> that are connected at a "tetra-identity".
> 
> What Peirce showed is that any connection of four or more lines may
> be replaced by connections of just three lines (called teridentities).
> In the diagram giveEGCG.jpg, you can replace the ligature labeled w
> with a ligature of 5 lines of identity linked by two teridentities.
> 
> JA
> 
> > > 
> > In mathematics, category theory is largely based on the prevalence
> > of functions in mathematical practice, and functions are dyadic
> > relations.
> > 
> > > 
> Not just "largely based", but "completely based". And note that the
> "functions" of plus, minus, times, and divide map two arguments to
> a single value. For generality, mathematicians say that functions
> map elements from one domain to another, but those elements may
> be pairs, N-tuples, or structures of any kind.
> 
> I agree with Jerry:
> 
> JLRC
> 
> > > 
> > The mappings may represent a vast range of mathematical structures
> > and be constrained to oriented graphs.
> > 
> > > 
> Yes. Graphs are convenient because they can show some logical
> connections more clearly than a linear notation. But the basic
> principles are independent of notation.
> 
> John
> 
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Re: [PEIRCE-L] Re: Laws of Nature as Signs

[John F Sowa]

Jon and Jerry,

JA

triadic relations extend across a threshold of complexity, such that
relations of all higher adicities can be analyzed in terms of 1-adic,
2-adic, and 3-adic relations.


No.  Peirce never said that.  Many logicians have correctly observed
that you can replace any triadic relation by three dyadic relations
plus an additional quantified variable.  In a graph, the node that
represents the variable will be linked to the three dyadic relations.

For example, consider the following sentence and its translation
to two different formulas in predicate calculus:

  x gives y to z.
  ∃x ∃y ∃z gives(x,y,z).
  ∃x ∃y ∃z ∃w (give(w) & agent(w,x) & theme(w,y) & recipient(w,z)).

The second formula has a new entity named w, which is linked to three
dyadic relations.  There is still an implicit triad in the formula.

In an earlier note, I showed the sentence "Sue gives a child a book"
as two different conceptual graphs.  In the attached giveEGCG.jpg,
I show that sentence translated to the same two conceptual graphs
and to their translations as existential graphs.

To show the mappings to the algebraic formulas, I also annotated
the lines of identity:  x, y, and z represent the same lines in
both EGs.  But w represents a ligature of *four* lines of identity
that are connected at a "tetra-identity".

What Peirce showed is that any connection of four or more lines may
be replaced by connections of just three lines (called teridentities).
In the diagram giveEGCG.jpg, you can replace the ligature labeled w
with a ligature of 5 lines of identity linked by two teridentities.

JA

In mathematics, category theory is largely based on the prevalence
of functions in mathematical practice, and functions are dyadic
relations.


Not just "largely based", but "completely based".  And note that the
"functions" of plus, minus, times, and divide map two arguments to
a single value.  For generality, mathematicians say that functions
map elements from one domain to another, but those elements may
be pairs, N-tuples, or structures of any kind.

I agree with Jerry:

JLRC

The mappings may represent a vast range of mathematical structures
and be constrained to oriented graphs.


Yes.  Graphs are convenient because they can show some logical
connections more clearly than a linear notation.  But the basic
principles are independent of notation.

John

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RE: [PEIRCE-L] Re: Determination and Creation in Sign-Action (was Laws of Nature as Signs)

[gnox]

Jeff, Jon S,

 

Sorry, I'm a bit late following up on this thread - but I only have a few
comments to add anyway.

 

JS: Peirce obviously endorsed analyzing the Sign-Object relation as dyadic
by excluding the Interpretant.

GF: Yes, in a way, but he did not exclude the Interpretant in his definition
of the symbol, the third in that trichotomy. And that's why the other two
are relatively "degenerate," according to Peirce, despite their necessary
involvement in any informational symbol.

 

JD: It is one thing to say that we should not think of "determination" as a
dyadic action of sign upon interpretant (or upon mind) at all, and saying
that we should not think of the process as solely a matter of such dyadic
action. Are you advocating one of these options? Given all of the different
classes of dyadic relations that Peirce considers, I tend to think that the
latter way of putting the matter is closer to what Peirce is suggesting.

GF: I think I agree with you . what I had in mind was something like this:

[[ The merchant in the Arabian Nights threw away a datestone which struck
the eye of a Jinnee. This was purely mechanical, and there was no genuine
triplicity. The throwing and the striking were independent of one another.
But had he aimed at the Jinnee's eye, there would have been more than merely
throwing away the stone. There would have been genuine triplicity, the stone
being not merely thrown, but thrown at the eye. Here, intention, the mind's
action, would have come in. Intellectual triplicity, or Mediation, is my
third category. ]]  - CP 2.86 (1902)

 

JD: On Peirce's account, the change of things over the course of time is
itself a process that involves a general law--where that law has a monadic,
dyadic and a triadic clause.

GF: Well, not every change involves a general law according to Peirce; he
does allow for spontaneous changes. I don't know about your "clauses," but I
do think that wherever there is a continuous process there is Thirdness.

 

Gary f.

 

From: Jeffrey Brian Downard [mailto:jeffrey.down...@nau.edu] 
Sent: 26-Apr-17 13:03



 

Jon S, Gary F, John S, List, 

 

Regarding #1, does Peirce ever identify a class of triadic relation that is
similarly "productive or poietical"?  Or is creation in this context an
inherently dyadic relation as a matter of 2ns?

 

Peirce talks about creation and procreation as well as production and
reproduction in the context of the semiotic theory. For instance, we create
abstractions such as diagrams by hypostatic abstraction (e.g., CP 2.341,
4.531). I take this to imply that some genuine triadic relations are
creative in character.

 

Regarding #2, Peirce obviously endorsed analyzing the Sign-Object relation
as dyadic by excluding the Interpretant; thus it seems to me that the
question is whether we can likewise fruitfully analyze the Sign-Interpretant
relation as dyadic by excluding the Object.  I used to think so, in
accordance with the received view that the third 1903 trichotomy is based on
this dyadic relation; but now I am not so sure, since I have recently come
to view that trichotomy as based instead on the triadic
Object-Sign-Interpretant relation.

 

For my part, I put great weight on passages where he says that triadic
action involves dyadic action. For example, see CP. 6.323-4, where he says:

 

a) "But a triadic relationship is of an essentially higher nature than a
dyadic relationship, in the sense that while it involves three dyadic
relationships, it is not constituted by them."

 

b) "The triadic fact takes place in thought. I do not say in anybody's
thinking, but in pure abstract thought; while the dyadic fact is
existential. With that comparison plainly before them, our minds perversely
regard the dyadic fact as superior in reality to the "mere" relation of
thought which is the triadic fact. We forget that thinking implies
existential action, though it does not consist in that;..."(emphasis added)

 

For my part, I would add "solely" to the last clause to make the point
clearer:  "though it does not consist solely in that;..."

 

Regarding #4, on which specific page(s) of MS 611-615 at
https://www.fromthepage.com/display/read_work?work_id=149 does Peirce
discuss the relation "A determines B after ..."?

 

See the pages just before and after 49:
https://www.fromthepage.com/display/display_page?page_id=7790


  49 (C. S.
Peirce Manuscripts, MS 611-15) | FromThePage

www.fromthepage.com  

49 (C. S. Peirce Manuscripts, MS 611-15) - page overview. 1908 Nov 12 Logic
32 I have been so careful in defining 'Determination', for the reason that I
have to use it in defining an even more...

Yours,

 

Jeff

 

 

On Wed, Apr 26, 2017 at 10:48 AM, Jeffrey Brian Downard
mailto:jeffrey.down...@nau.edu> > wrote:

Gary F, John S, List,

Here are a few quick observations about the points Gary F is making about
the passage from the 1909 letter to 

Re: [PEIRCE-L] Laws of Nature as Signs

[Jerry LR Chandler]

List:

> On Apr 29, 2017, at 10:41 PM, John F Sowa  wrote:
> 
> Re mathematical category theory:  Many mathematicians believe that
> the term 'category theory' was a poor choice.  The focus of category
> theory is on the mappings or morphisms.  The things that are mapped
> could be mathematical structures of any kind.  Some mathematicians
> call it a "theory of arrows" -- the symbols that represent the maps.

John’s assertions here are spot on.
If anything, these assertions are rather weak relative to what could be said. 

And, I will add a simple example to John’s semantic framework.
Pure mathematics is an artificial idealization of symbols constructed by human 
minds.
Such mathematical symbols must be free of any encumbering significations of 
nature because the scientific (real) significations of nature are antecedent to 
natural consequences of nature.

And, I will add a simple caveat to John’s assertion that: 
> The things that are mapped
> could be mathematical structures of any kind.

The mappings may represent a vast range of mathematical structures and be 
constrained to oriented graphs.

Cheers

jerry 


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[PEIRCE-L] Re: Laws of Nature as Signs

[Jon Awbrey]

Re: ( https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00340.html )
( https://inquiryintoinquiry.com/2017/04/25/icon-index-symbol-%e2%80%a2-10/ )
( https://inquiryintoinquiry.com/2017/04/27/icon-index-symbol-%e2%80%a2-11/ )
( https://inquiryintoinquiry.com/2017/04/28/icon-index-symbol-%e2%80%a2-12/ )
( https://inquiryintoinquiry.com/2017/04/29/icon-index-symbol-%e2%80%a2-13/ )

Helmut, List ...

Let me sum up the main points of the above exchange before moving on:

Mathematics is useful in our present endeavor because it covers relations
in general.  In addition — and multiplication, too — mathematics is chock
full of well-studied examples of triadic relations.  When it comes to the
job of analyzing sign relations and teasing out their relevant structures
we could save ourselves a lot of trouble and trial and error by examining
this record of prior art and adapting its methods to cover sign relations.

On the other hand, there are hints in Peirce's work that triadic relations
extend across a threshold of complexity, such that relations of all higher
adicities can be analyzed in terms of 1-adic, 2-adic, and 3-adic relations.
This is the point where the analogy with mathematical category theory both
forms and breaks.  In mathematics, category theory is largely based on the
prevalence of functions in mathematical practice, and functions are dyadic
relations.  Still, triadic relations pervade the background of the subject,
visible in the triadic composition relation and in the concept of what are
called “natural transformations”, the clarification of which notion is one
of the original motivations of the subject.  Bringing the triadic roots of
category theory into higher relief is one of motives for bringing about an
encounter with Peirce's categories, a task to which I have given not a few
years of thought.

That brings us to the case of sign relations proper.  I think it's clear
that these types of triadic relations form our first stepping stones and
also our first stumbling blocks in the inquiry into inquiry, and I think
I gave some indications already of why that might be true.  I don't know
if I can do any better than that at this time, but I'll think on it more
after that all-essential secondness of caffeination.

Regards,

Jon

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