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

[Helmut Raulien]

 

John, Jon, List,

I have not fully understood the example wit Mary and the camera (in Hamburg it is very late now), but I think, that it would be good to replace the concept of "linguistic turn", which is nominalistic, with a kind of "social turn", see the other thread by Jon, about inquiry being dependent on social communication. This was just a guess, I have not understood the difference between obligatory and optional, sorry, I will try, but not now, I go to sleep.

Best,

Helmut


 08. Mai 2017 um 21:56 Uhr
Von: "John F Sowa" 
 

On 5/8/2017 10:40 AM, Jon Awbrey wrote:
> The question then is whether we keep or lose information in passing
> from a triadic relation to the collection of its dyadic projections.

Linguists use the term 'obligatory'. For example:

Obligatory: "Mary gave Bill a camera."
Optional: "Mary saw Bill with a camera at the party."

In the first sentence 'gave' has three obligatory participants.
If you omit one, its absence can be noticed or inferred:
"Everyone gave Bill a present for his birthday. Mary gave a camera."

In the second sentence, 'saw' has an obligatory object,
but "with a camera" and "at the party" are optional adjuncts.

John



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

[Jon Awbrey]

John, List,

That's interesting.
I'll have to think
on that a while ...

Regards,

Jon

On 5/8/2017 3:56 PM, John F Sowa wrote:

On 5/8/2017 10:40 AM, Jon Awbrey wrote:

The question then is whether we keep or lose information in passing
from a triadic relation to the collection of its dyadic projections.


Linguists use the term 'obligatory'.  For example:

Obligatory:  "Mary gave Bill a camera."
Optional:  "Mary saw Bill with a camera at the party."

In the first sentence 'gave' has three obligatory participants.
If you omit one, its absence can be noticed or inferred:
"Everyone gave Bill a present for his birthday. Mary gave a camera."

In the second sentence, 'saw' has an obligatory object,
but "with a camera" and "at the party" are optional adjuncts.

John



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

[Jon Awbrey]

Helmut, List,

I think the maximum benefit possible at this point
is to be gained from studying those simple examples
of triadic relations and sign relations that I gave.
Once we get used to dealing with small examples like
that we can move on to tackling more complex examples
on the order of those we might encounter in realistic
applications.

The sort of sign relation we normally encounter in practice
will be a subset L of a cartesian product O × S × I, where
the object, sign, and interpretant-sign domains all have
infinitely many members in principle, though of course we
tend to get by with finite samples at any given moment and
it may even be possible to start small and build capacity
over time.

All the objects we need to signify in a given application will go
into the object domain O and all the signs and interpretant-signs
we need to signify these objects will go into the sign domain S
and the interpretant-sign domain I.

There are such things as monadic projections:

proj_O : O × S × I → O

proj_S : O × S × I → S

proj_I : O × S × I → I

For example, proj_O (L) would give all the elements of O
that actually occur as first correlates in L, sometimes
called the O-range.

But I don't get the sense you are talking about that
with your idea of projections with two S's and so on.

There is however an interesting class of relations that take place
internal to the sign domain.  These are the syntactic relations or
parsing relations that relate a complex sign to its component signs.

But again, that's a topic a little ways down the road ...

Regards,

Jon

On 5/8/2017 1:55 PM, Helmut Raulien wrote:

Jon, List,
I guess, that the answer to the question, whether or not information is lost due
to the projection (of a triadic relation towards three dyadic ones), depends on
whether the triadic relation is intransparent, and thus casts three shadow-like
pictures, or is sort of transparent, and thus casts three X-ray-like pictures.
Another problem is, that, as a relation may be upon one set, meaning between a
set and a copy of the same set, then there are not only three, but six
dimensions. But I guess, that only the representamen/sign can have a reasonable
relation with itself, so perhaps there are only four dimensions: S,S,O,I. Or:
S,s,O,I, or sign, representamen, object, interpretant, with sign and
representamen being both identical and different in some mysterious (Re-entry?),
yet to be elaborated, way... Or has Peirce already solved this mystery, but did
not explain it, assuming that it is self-explaining? This hunch is based on the
fact, that he used the term "sign" for both the whole and a part. With which
matter we have problems, but maybe he did not, because for him, the solution to
what for us feels like a paradoxon, felt somehow for granted?
Best,
Helmut
  08. Mai 2017 um 16:40 Uhr
*Von:* "Jon Awbrey" 
Peircers,

Here's the revised, extended edition of my last two posts on this thread:

https://inquiryintoinquiry.com/2017/05/06/icon-index-symbol-%e2%80%a2-16/

Icon Index Symbol • 16
==

Questions Concerning Certain Faculties Claimed For Signs

Re: Peirce List Discussion
JAS:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00196.html
HR:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00200.html

Having lost my train of thought due to a week on the road, I would like to go
back and pick up the thread at the
following exchange:

JAS:
“To be honest, given that the Sign relation is genuinely triadic, I have never
fully understood why Peirce initially
classified Signs on the basis of one correlate and two dyadic relations.”

HR:
“I have a guess about that: I remember from a thread with Jon Awbrey about
relation reduction something like the
following: A triadic relation is called irreducible, because it cannot
compositionally be reduced to three dyadic
relations. Compositional reduction is the real kind of reduction. But there is
another kind of reduction, called
projective (or projectional?) reduction, which is a kind of consolation prize
for people who want to reduce. It is
possible for some triadic relations.”

The course of discussion after that point left a great many of the original
questions about icons, indices, and symbols
unanswered, so I’d like to make another try at addressing them. The relevant
facts about triadic relations and
relational reduction can be found at the following locations:

• Triadic Relations : Examples from Mathematics
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation#Examples_from_mathematics

• Triadic Relations : Examples from Semiotics
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation#Examples_from_semiotics

• Relation Reduction : Projective Reducibility of Triadic Relations
http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction#Projective_reducibility_of_triadic_relations

I introduced two examples of triadic relations from mathematics, two examples of
sign relations from semiotics, and used
them to illustrate the questio

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

[John F Sowa]

On 5/8/2017 10:40 AM, Jon Awbrey wrote:

The question then is whether we keep or lose information in passing
from a triadic relation to the collection of its dyadic projections.


Linguists use the term 'obligatory'.  For example:

Obligatory:  "Mary gave Bill a camera."
Optional:  "Mary saw Bill with a camera at the party."

In the first sentence 'gave' has three obligatory participants.
If you omit one, its absence can be noticed or inferred:
"Everyone gave Bill a present for his birthday. Mary gave a camera."

In the second sentence, 'saw' has an obligatory object,
but "with a camera" and "at the party" are optional adjuncts.

John



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

[Helmut Raulien]

 

Jon, List,

I guess, that the answer to the question, whether or not information is lost due to the projection (of a triadic relation towards three dyadic ones), depends on whether the triadic relation is intransparent, and thus casts three shadow-like pictures, or is sort of transparent, and thus casts three X-ray-like pictures.

Another problem is, that, as a relation may be upon one set, meaning between a set and a copy of the same set, then there are not only three, but six dimensions. But I guess, that only the representamen/sign can have a reasonable relation with itself, so perhaps there are only four dimensions: S,S,O,I. Or: S,s,O,I, or sign, representamen, object, interpretant, with sign and representamen being both identical and different in some mysterious (Re-entry?), yet to be elaborated, way... Or has Peirce already solved this mystery, but did not explain it, assuming that it is self-explaining? This hunch is based on the fact, that he used the term "sign" for both the whole and a part. With which matter we have problems, but maybe he did not, because for him, the solution to what for us feels like a paradoxon, felt somehow for granted?

Best,

Helmut


 08. Mai 2017 um 16:40 Uhr
Von: "Jon Awbrey" 
 

Peircers,

Here's the revised, extended edition of my last two posts on this thread:

https://inquiryintoinquiry.com/2017/05/06/icon-index-symbol-%e2%80%a2-16/

Icon Index Symbol • 16
==

Questions Concerning Certain Faculties Claimed For Signs

Re: Peirce List Discussion
JAS:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00196.html
HR:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00200.html

Having lost my train of thought due to a week on the road, I would like to go back and pick up the thread at the
following exchange:

JAS:
“To be honest, given that the Sign relation is genuinely triadic, I have never fully understood why Peirce initially
classified Signs on the basis of one correlate and two dyadic relations.”

HR:
“I have a guess about that: I remember from a thread with Jon Awbrey about relation reduction something like the
following: A triadic relation is called irreducible, because it cannot compositionally be reduced to three dyadic
relations. Compositional reduction is the real kind of reduction. But there is another kind of reduction, called
projective (or projectional?) reduction, which is a kind of consolation prize for people who want to reduce. It is
possible for some triadic relations.”

The course of discussion after that point left a great many of the original questions about icons, indices, and symbols
unanswered, so I’d like to make another try at addressing them. The relevant facts about triadic relations and
relational reduction can be found at the following locations:

• Triadic Relations : Examples from Mathematics
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation#Examples_from_mathematics

• Triadic Relations : Examples from Semiotics
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation#Examples_from_semiotics

• Relation Reduction : Projective Reducibility of Triadic Relations
http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction#Projective_reducibility_of_triadic_relations

I introduced two examples of triadic relations from mathematics, two examples of sign relations from semiotics, and used
them to illustrate the question of projective reducibility, in another way of putting it, whether the structure of a
triadic relation can be reconstructed from the structures of three dyadic relations derived or “projected” from it.

• In the geometric picture of triadic relations, a dyadic projection is the shadow that a 3-dimensional body casts on
one of the three coordinate planes.

• In terms of relational data tables, a dyadic projection is the result of deleting one of the three columns of the
table and merging any duplicate rows.

• In Peircean terms, a projection is a type of “prescision” operation, abstracting a portion the structure from the
original relation and ignoring the rest.

The question then is whether we keep or lose information in passing from a triadic relation to the collection of its
dyadic projections. If there is no loss of information then the triadic relation is said to be reducible to and
reconstructible from its dyadic projections. Otherwise it is said to be irreducible and irreconstructible in the same vein.

Regards,

Jon

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

[Jon Awbrey]

Peircers,

Here's the revised, extended edition of my last two posts on this thread:

https://inquiryintoinquiry.com/2017/05/06/icon-index-symbol-%e2%80%a2-16/

Icon Index Symbol • 16
==

Questions Concerning Certain Faculties Claimed For Signs

Re: Peirce List Discussion
JAS:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00196.html
HR:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00200.html

Having lost my train of thought due to a week on the road, I would like to go back and pick up the thread at the 
following exchange:


JAS:
“To be honest, given that the Sign relation is genuinely triadic, I have never fully understood why Peirce initially 
classified Signs on the basis of one correlate and two dyadic relations.”


HR:
“I have a guess about that:  I remember from a thread with Jon Awbrey about relation reduction something like the 
following:  A triadic relation is called irreducible, because it cannot compositionally be reduced to three dyadic 
relations.  Compositional reduction is the real kind of reduction.  But there is another kind of reduction, called 
projective (or projectional?) reduction, which is a kind of consolation prize for people who want to reduce.  It is 
possible for some triadic relations.”


The course of discussion after that point left a great many of the original questions about icons, indices, and symbols 
unanswered, so I’d like to make another try at addressing them.  The relevant facts about triadic relations and 
relational reduction can be found at the following locations:


• Triadic Relations : Examples from Mathematics
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation#Examples_from_mathematics

• Triadic Relations : Examples from Semiotics
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation#Examples_from_semiotics

• Relation Reduction : Projective Reducibility of Triadic Relations
http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction#Projective_reducibility_of_triadic_relations

I introduced two examples of triadic relations from mathematics, two examples of sign relations from semiotics, and used 
them to illustrate the question of projective reducibility, in another way of putting it, whether the structure of a 
triadic relation can be reconstructed from the structures of three dyadic relations derived or “projected” from it.


• In the geometric picture of triadic relations, a dyadic projection is the shadow that a 3-dimensional body casts on 
one of the three coordinate planes.


• In terms of relational data tables, a dyadic projection is the result of deleting one of the three columns of the 
table and merging any duplicate rows.


• In Peircean terms, a projection is a type of “prescision” operation, abstracting a portion the structure from the 
original relation and ignoring the rest.


The question then is whether we keep or lose information in passing from a triadic relation to the collection of its 
dyadic projections.  If there is no loss of information then the triadic relation is said to be reducible to and 
reconstructible from its dyadic projections.  Otherwise it is said to be irreducible and irreconstructible in the same vein.


Regards,

Jon

--

inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
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[PEIRCE-L] Re: Laws of Nature as Signs

[Jon Awbrey]

Peircers,

I think Helmut is probably recalling any number of messages or links
I posted on triadic relations and relational reduction, versions of
which can be found at these locations:

http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation#Examples_from_mathematics
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation#Examples_from_semiotics
http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction#Projective_reducibility_of_triadic_relations

I introduced two examples of triadic relations from mathematics,
two examples of sign relations from semiotics, and used them to
illustrate the question of projective reducibility, in another
way of putting it, whether the structure of a triadic relation
can be reconstructed from the structures of dyadic relations
derived or “projected” from it.

In the geometric picture of triadic relations, a dyadic projection is the
shadow that a 3-dimensional body casts on one of the 3 coordinate planes.
In terms of relational data tables, a dyadic projection is the result of
deleting one of the 3 columns of the table and merging any duplicate rows.
In Peircean terms, a projection is a type of prescision operation, in the
sense that it ignores a portion of the structure in the original relation.

Still a bit fatigued from travel, so will break here ...

Jon

On 5/5/2017 3:12 PM, Jon Awbrey wrote:

Helmut, Jon, List ...

Having lost my train of thought due to a week on the road,
I would like to go back and pick up the thread again here:

HR:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00200.html
JAS:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00203.html

The direction and pace of discussion after that point left a great many
of the original questions unanswered, so I'd like to make another try
at addressing them.

For now, though, just a note to anchor the thread.

Regards,

Jon


> On 4/13/2017 4:26 PM, Jon Alan Schmidt wrote:
>> Helmut, List:
>>
>> That is a very interesting suggestion, and some quick Googling confirms
>> that Jon Awbrey has written about compositive vs. projective reduction
>> in the past.  He even cited the Sign relation as a specific example
>> of a triadic relation that is "projectively reducible."  I still
>> wonder, though -- did Peirce ever write anything along these lines,
>> or otherwise explaining this aspect of his Sign classifications?
>>
>> By the way, I suspect that the proper "projective reduction" is
>> your first guess -- (S,O), (O,I), (I,S).  The reason why Peirce
>> never discusses the (O,I) relation is that it is always the same
>> as the (S,O) relation.  The first of the three 1903 trichotomies
>> (Qualisign/Sinsign/Legisign) divides the Sign itself as a correlate,
>> not a relation;  the dyadic relation of anything to itself is simply
>> *identity*.
>>
>> Thanks,
>>
>> Jon Alan Schmidt - Olathe, Kansas, USA
>> Professional Engineer, Amateur Philosopher, Lutheran Layman
>> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>>
>> On Thu, Apr 13, 2017 at 2:45 PM, Helmut Raulien  wrote:
>>
>>> Jon, List,
>>> You wrote:
>>> "To be honest, given that the Sign relation is genuinely *triadic*,
>>> I have never fully understood why Peirce initially classified Signs
>>> on the basis of one correlate and two *dyadic *relations.   Perhaps
>>> others on the List can shed some light on that."
>>>
>>> I have a guess about that: I remember from a thread with Jon Awbrey
>>> about relation reduction something like the following:
>>>
>>> A triadic relation is called irreducible, because it cannot composition-
>>> ally be reduced to three dyadic relations.  Compositional reduction is
>>> the real kind of reduction.  But there is another kind of reduction,
>>> called projective (or projectional?) reduction, which is a kind of
>>> consolation prize for people, who want to reduce.  It is possible
>>> for some triadic relations.
>>>
>>> Now a triadic relation, say, (S,O,I) might be reduced
>>> projectionally to (S,O), (O,I), (I,S).
>>>
>>> My guess is now, that Peirce uses another kind of
>>> projectional reduction: (S,S), (S,O), (S,I).
>>>
>>> It is only a guess, because I am not a mathematician.  But at least
>>> I would say, that mathematically a relation wit itself is possible,
>>> so the> representamen relation can be called relation too, instead
>>> of correlate.
>>> Best,
>>> Helmut
>>>
>>
>

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

[Jon Awbrey]

Helmut, Jon, List ...

Having lost my train of thought due to a week on the road,
I would like to go back and pick up the thread again here:

HR:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00200.html
JAS:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00203.html

The direction and pace of discussion after that point left a great many
of the original questions unanswered, so I'd like to make another try
at addressing them.

For now, though, just a note to anchor the thread.

Regards,

Jon

On 4/13/2017 4:26 PM, Jon Alan Schmidt wrote:

Helmut, List:

That is a very interesting suggestion, and some quick Googling confirms
that Jon Awbrey has written about compositive vs. projective reduction in
the past.  He even cited the Sign relation as a specific example of a
triadic relation that is "projectively reducible."  I still wonder,
though--did Peirce ever write anything along these lines, or otherwise
explaining this aspect of his Sign classifications?

By the way, I suspect that the proper "projective reduction" is your first
guess--(S,O), (O,I), (I,S).  The reason why Peirce never discusses the
(O,I) relation is that it is always the same as the (S,O) relation.  The
first of the three 1903 trichotomies (Qualisign/Sinsign/Legisign) divides
the Sign itself as a correlate, not a relation; the dyadic relation of
anything to itself is simply *identity*.

Thanks,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Thu, Apr 13, 2017 at 2:45 PM, Helmut Raulien  wrote:


Jon, List,
You wrote:
"To be honest, given that the Sign relation is genuinely *triadic*, I
have never fully understood why Peirce initially classified Signs on the
basis of one correlate and two *dyadic *relations.  Perhaps others on the
List can shed some light on that."

I have a guess about that: I remember from a thread with Jon Awbrey about
relation reduction something like the following:
A triadic relation is called irreducible, because it cannot
compositionally be reduced to three dyadic relations. Compositional
reduction is the real kind of reduction. But there is another kind of
reduction, called projective (or projectional?) reduction, which is a kind
of consolation prize for people, who want to reduce. It is possible for
some triadic relations.
Now a triadic relation, say, (S,O,I) might be reduced projectionally to
(S,O), (O,I), (I,S).
My guess is now, that Peirce uses another kind of projectional reduction:
(S,S), (S,O), (S,I).
It is only a guess, because I am not a mathematician. But at least I would
say, that mathematically a relation wit itself is possible, so the
representamen relation can be called relation too, instead of correlate.
Best,
Helmut





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

[Jon Awbrey]

Helmut, List ...

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/


HR:
> I guess, that a difference between Peirce's relation theory,
> and his semiotics and category theory, is, that the first
> is about all triadic relations, and the latter only about
> sign relations or representational relations (the special
> kind of triadic relations).

My guess is that Peirce's category theory, when taken at its full promise and broadest historical perspective, will find 
its place in a line of inquiry extending from Aristotle's Categories up through category theory in its present-day 
mathematical sense — and then beyond in certain directions, as guided by its more peircing insight into triadicity.  In 
this view, category theory, the logic of relatives, and the theory of relations all work in tandem toward the same object.


But it's true, the initial focus and inciting application of all three converging operations — Peirce's triple drill bit 
— must be to the matter of signs, information, and inquiry.  Our first imperative (!) is thus to interrogate (?) the 
indicative (.) faculty of signs.  Our experiences of confusion, comprehension, and communication place demands on us 
that only competent theories of inquiry and signs can bring to a close.


Regards,

Jon

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

[Jon Awbrey]

Helmut, List ...

Here are links to my blog rehashes of the last few exchanges on this thread:

https://inquiryintoinquiry.com/2017/04/16/icon-index-symbol-%e2%80%a2-7/
https://inquiryintoinquiry.com/2017/04/17/icon-index-symbol-%e2%80%a2-8/
https://inquiryintoinquiry.com/2017/04/24/icon-index-symbol-%e2%80%a2-9/
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/

Turning now to your next point:

HR:
> Example: The triadic function “x_1 + x_2 = x_3”, with the
> three sets X_1, X_2, X_3 not being classes of any kind,
> at least not of the special kind (whatever that is),
> that would allow representation, and make it having
> to do with the third category.

Mathematics is rife with examples of triadic relations having all three
relational domains the same.  For instance, the binary operation “+”
in “x_1 + x_2 = x_3” is associated with a function fun[+] such that
fun[+] : X × X → X and also with a triadic relation rel[+] such that
rel[+] ⊆ X × X × X.

Semiotics, by contrast, tends to deal with relational domains O, S, I
where the objects in O are distinct in kind from the signs in S and the
interpretant signs in I.  As far as S and I go, it is usually convenient
to lump them all into one big set S = I, even if we have to partition that
set into distinct kinds, say, mental concepts and verbal symbols, or signs
from different languages.  But even if it's how things tend to work out in
practice, as we currently practice it, there does not seem to be anything
in Peirce's most general definition of a sign relation to prevent all the
relational domains from being the same.  So I'll leave that open for now.

Regards,

Jon

On 4/21/2017 4:59 PM, Helmut Raulien wrote:
> Jon, List,
> I am not so sure, if thirdness is about any triadic relation.
> The categories in Peirce's "new list" of them are quality, relation,
> representation.  Maybe "representation" is a very special kind of
> triadic relation.  A simple triadic or n-adic relation, I think,
> belongs to secondness, and has only two modes, the quality, eg.
> function or caprice (intension), and the resulting set of tuples
> (extension).  Example: The triadic function "x_1 + x_2 = x_3",
> with the three sets X_1, X_2, X_3 not being classes of any kind,
> at least not of the special kind (whatever that is), that would
> allow representation, and make it having to do with the third
> category.  I guess, that a difference between Peirce's relation
> theory, and his semiotics and category theory, is, that the
> first is about all triadic relations, and the latter only
> about sign relations or representational relations (the
> special kind of triadic relations).
> Best,
> Helmut

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

[Jon Awbrey]

Helmut, List ...

Short on time tonight so let me just
respond to the next point you raised:

HR:
> A simple triadic or n-adic relation, I think, belongs
> to secondness, and has only two modes, the quality, eg.
> function or caprice (intension), and the resulting set
> of tuples (extension).

There is a kind of secondness involved in any use of set theory,
indeed, there are several kinds of dyadic relations in the mix,
all intimately related.  Letting X be the universe of discourse,
there is the dyadic elementhood or membership relation x ∈ X,
there is the subset relation A ⊆ X, and every subset A ⊆ X has
a “characteristic” or “indicator” function f_A : X → {0, 1} with
f_A(x) = 1 if x ∈ A and f_A(x) = 0 if x ∉ A.  So one could say,
if one wishes, there is secondness afoot in the extensions of
whatever symbols one uses to demarcate or distinguish portions
of the universe.  As it usually turns out, though, if you know
enough to invoke secondness, you usually know enough to say
something more specific about the dyadic relation you have
in mind.

This is a very old theme.  The very word “existence”, whether by
way of folk etymology or not, is said to mean “standing out”, the
way a subset stands out against its ground.  It's a nice image if
nothing else.  In another connection, some take the prevalence of
these set-theoretic dyadic relations, along with their assumption
of set theory's foundational status, as proving all structure to
be ultimately dyadic.

Well, I have my reasons to doubt that,
but that's all the time I have tonight.

Regards,

Jon

On 4/21/2017 4:59 PM, Helmut Raulien wrote:
> Jon, List,
> I am not so sure, if thirdness is about any triadic relation.
> The categories in Peirce's "new list" of them are quality, relation,
> representation.  Maybe "representation" is a very special kind of
> triadic relation.  A simple triadic or n-adic relation, I think,
> belongs to secondness, and has only two modes, the quality, eg.
> function or caprice (intension), and the resulting set of tuples
> (extension).  Example: The triadic function "x_1 + x_2 = x_3",
> with the three sets X_1, X_2, X_3  not being classes of any kind,
> at least not of the special kind (whatever that is), that would
> allow representation, and make it having to do with the third
> category.  I guess, that a difference between Peirce's relation
> theory, and his semiotics and category theory, is, that the
> first is about all triadic relations, and the latter only
> about sign relations or representational relations (the
> special kind of triadic relations).
> Best,
> Helmut

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

[Jerry LR Chandler]

Jeff, List: 

> On Apr 26, 2017, at 10:48 AM, Jeffrey Brian Downard  
> wrote:
> 
>  I wonder why this relation of determination of one being determined after 
> another seemed to him to be so important.

The answer to your question is very very simple, but rather technical for this 
list.

Historically, your question has the logical form of sorites.

Bacon recognized this facet of natural logic (see below).

The Schoolmen approached logical form of your question in terms of 
significatio, suppositio, etc., with the inquiry: what is the meaning of a sign 
(significatio) as a logical term? 

Leibniz presupposed this question in his notion of logic as calculations with 
integers.

 CSP logic is an extension of the Schoolmen’s logic. (As an aside, CSP logic 
can also be linguistically generalized to include the logic of Boole and de 
Morgan.) 

CSP recognized that your question is more than merely “important”, it is 
absolutely essential to the perplex logic of the chemical sciences - chemistry, 
biology and medicine.

In modern chemistry, your question is answered in the logic of concatenation of 
atoms into molecules. That is, in CSP talk, the diagrams that are formed from 
the representations (signs) of things.

The mathematical / scientific basis for your question is also elementary, but 
rather perplex.  In general, the physics of atomic numbers do not follow the 
associative, distributive or commutative of mathematics. Thus, CSP recognized 
that an alternative form of the logic of addition is essential to the logical 
abductions over a set of chemical elements where the order of the copulation of 
predicates is critical to the correspondence relations among the multiplicity 
of signs. In simpler terms, the copulation of two unique chemical elements 
generates a unique chemical bond that is specified by the atomic numbers of the 
two elements. 

Well, perhaps the answer to your question is not so simple, unless one grasps 
CSP usage of the logical terms, symbol, index, and icon in the context of the 
chemical table of elements and the perplex number system. 

Jeff, given the breadth and depth of your assets, (your multiple intellectual 
backgrounds,) I believe that you will find further exploration of your question 
to be extraordinarily profitable.

BTW, your question is intimately associated with the inquiry into the meaning 
of a relational triad!

Have fun in your exploratory syntheses!!!

Cheers

Jerry 





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

[kirstima]

John, list,

The invasion of Big Data into social sciences makes critical views on 
Carnap (& co) utterly important nowadays.


Kirsti

John F Sowa kirjoitti 24.4.2017 04:34:

Helmut, Jeffrey, Jon A, Clark, list,

HR

Not every triadic relation is categorically thirdness. But which are?


That's a good question.  Some basic principles:

 1. For each of Peirce's categories, there is a characteristic 
question:

Firstness:   What is it?  What kind of mark?
Secondness:  How does it relate or react to something?
Thirdness:   Why does it relate or react to something?
Answer:  (1) quality; (2) relation or reaction; (3) mediation.
  2. Peirce used the term 'triad', not 'triadic relation'.  You can
represent a verb, such as 'give' as either a triadic relation
or as a nominalized node attached to three dyadic relations.
See the attached give.gif, which shows two ways of mapping the
sentence "Sue gives a child a book" to a graph -- a conceptual
graph, which may be mapped to an existential graphs or to an
algebraic formula.

 3. As give.gif illustrates, a triad in a graph cannot be eliminated
by using dyadic relations.  But a graph with a tetrad, pentad, ...
can always be mapped to and from a graph that has no nodes with
more than 3 links.

 4. A non-degenerate triad always involves something law-like,
intentional, or mental.  That implies some mind or quasi-mind
that does the interpretation.  Nominalists don't like that way
of talking.

 5. Strict nominalists, such as Carnap, deny that abstract entities
exist -- that includes all forms of Thirdness:  laws, intentions,
goals, purposes, or habits.  That is why Carnap insisted that all
laws of science are nothing more than summaries of observations.

HR

Is it reasonable to say that a relation has an intension and an
extension, the intension is firstness, and the extension secondness
(of the relation, which is secondness)?


As Church pointed out, the intension is a rule of correspondence
that determines the extension.  That rule is a law-like entity,
which is a kind of Thirdness.  Note, by the way, that multiple,
independently defined rules may specify the same extension.
Two functions or relations may differ in intension , but be
identical in extension.

JBD

why [do] nominalists such as J.S. Mill and Nelson Goodman strongly
prefer extensional systems--and have significant reservations about
using intensional systems in philosophy


All definitions by intension imply some law-like rule.  That's why
Carnap insisted that laws of science are "summaries of observations".
He would never say "law of nature" -- because (a) the phrase implies
that there exists something called nature, and (b) it also implies
that nature has something called laws.

JA

an extensional definition of a 2-place relation ... can be generalized
to k-place relations and then beyond the finite arity case...  But
there is nothing remotely nominal going on here, as the definition
invokes sets of tuples.  Sets and tuples are the very sorts of
abstract objects nominal thinkers would eschew


Church used sets to define extensions because he had no reason to
avoid sets.  But Lesniewski and other nominalists replaced set
theory with mereology.  If you have a set of N elements, you have
N+1 entities, which consist of the N elements plus an abstract set.

But with mereology, a collection of N elements does not imply
the existence of anything more than the N elements.  Therefore,
a mereologist could say that the elements of an N-tuple are parts
of a whole called an N-tuple.  They would not consider the whole
as something distinct from the sum of its parts.

JA

I have never found going on about Firstness Secondness Thirdness
all that useful in any practical situation.


If you think at those terms as a count of links in a graph, they
don't explain much.  It's better to look at the three kinds of
questions summarized at the top of this note.

JA

until you venture to say exactly *which* monadic, dyadic, or triadic
predicate you have in mind, you haven't really said that much at all.


CG

Glad I’m not alone in thinking that.


I agree that we need to look at specific cases.  For examples of the
kinds of Thirdness that nominalists deliberately ignore, see Section 2
(pp. 3 to 8) of http://www.jfsowa.com/pubs/signproc.pdf .

The title of that section is "A Static, Lifeless, Purposeless World".
Some excerpts:

p. 4:  Einstein criticized Russell's "Angst vor der Metaphysik"
and said “Mach was a good experimental physicist but a miserable
philosopher”; he made “a catalog not a system.”

p. 5:  When introducing Russell for his William James Lectures
at Harvard, Whitehead said “This is my friend Bertrand Russell.
Bertie thinks that I am muddleheaded, but then I think that he
is simpleminded” (Lucas 1989:111).  That remark is consistent with
a statement attributed to Russell:  “I’d rather be narrow minded
than vague and wooly” (Kuntz 1984:50).

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

[Jeffrey Brian Downard]

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 James:


1.  The last class of dyadic relation that Peirce considers in "The Logic of 
Mathematics;..." is that of the productive or poietical dyad (CP 1.468) . In 
this type of dyadic relation, the existence of the patient is dependent on the

agent; e.g., mother produces son. As such, this type of relation involves a 
kind of creation of one thing by another. Do you think that this dyadic kind of 
productive relation is involved--in some way--in process in virtue of which 
something is created in the mind of the interpreter? More generally, do you 
think that genuinely triadic forms of creation involve such dyadic kinds of 
production of one thing by another? My hunch is that the answer is "yes" in 
both cases. If you disagree, I'd be interested in hearing the reasons why.

2. 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.

3. Gary F suggests that we should not think of the determination of sign by 
object as a fait accompli or event preceding the determination of interpretant 
by sign. What he goes on to say about events in a sequence would seem to apply 
to anything that takes places over the course of time. 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. As 
such, any conception of an event as a discrete and separate part of time is an 
incomplete view on the matter--and this applies to processes that involve the 
interpretation of signs in minds as well as those that don't appear to have 
that character.

4. Providing a clearer definition of the relation "A determines B after..." is 
one of the tasks that Peirce says (in MS 612) that we need to take up in order 
to have a clearer understanding of determination. I wonder why this relation of 
determination of one being determined after another seemed to him to be so 
important.

--Jeff


Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354



From: g...@gnusystems.ca 
Sent: Wednesday, April 26, 2017 6:44 AM
To: peirce-l@list.iupui.edu
Subject: RE: [PEIRCE-L] Re: Laws of Nature as Signs


List,



I think John's remarks here are right on target as usual, but also came across 
a Peirce quote today which struck me as relevant to this and other recent 
threads having to do with “determination” and Thirdness. It’s from a 1909 
letter to James:



[[ The Sign creates something in the Mind of the Interpreter, which something, 
in that it has been so created by the sign, has been, in a mediate and relative 
way, also created by the Object of the Sign, although the Object is essentially 
other than the Sign. And this creature of the sign is called the Interpretant. 
It is created by the Sign; but not by the Sign quâ member of whichever of the 
Universes it belongs to; but it has been created by the Sign in its capacity of 
bearing the determination by the Object.]]



This passage is unusual in using the verb “create” as pretty much synonymous 
with “determine.” It’s incorporated into the final chapter of my book Turning 
Signs, which is largely about the role of signs (and especially symbols) in 
both creation and determination; the context is at 
http://www.gnusystems.ca/TS/crn.htm#symbio.



But what popped out at me today is Peirce’s observation that the interpretant 
is not determined by a qualisign, sinsign or legisign as such. In other words, 
we should not think of “determination” as a dyadic action of sign upon 
interpretant (or upon mind). Neither should we think of the determination of 
sign by object as a fait accompli or event preceding the determination of 
interpretant by sign. The sign-action is irreducibly triadic because the 
determination of and by the sign are just two aspects of a single process, not 
successive steps in the process; not events separated in time, but objects 
hypostatically abstracted from its flow.



This is just a new version of an old story, but sometimes it feels right to 
turn the wheel again …



Gary f.



-Original Message-
From: John F Sowa [mailto:s...@bestweb.net]
Sent: 23-Apr-17 21:34
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Re: Laws of Nature as Signs



Helmut, Jeffrey, Jon A, Clark, list,



HR

> Not every triadic relation is categorically thirdness. But which are?



That's a good ques

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

[gnox]

List,

 

I think John's remarks here are right on target as usual, but also came across 
a Peirce quote today which struck me as relevant to this and other recent 
threads having to do with “determination” and Thirdness. It’s from a 1909 
letter to James:

 

[[ The Sign creates something in the Mind of the Interpreter, which something, 
in that it has been so created by the sign, has been, in a mediate and relative 
way, also created by the Object of the Sign, although the Object is essentially 
other than the Sign. And this creature of the sign is called the Interpretant. 
It is created by the Sign; but not by the Sign quâ member of whichever of the 
Universes it belongs to; but it has been created by the Sign in its capacity of 
bearing the determination by the Object.]]

 

This passage is unusual in using the verb “create” as pretty much synonymous 
with “determine.” It’s incorporated into the final chapter of my book Turning 
Signs, which is largely about the role of signs (and especially symbols) in 
both creation and determination; the context is at 
http://www.gnusystems.ca/TS/crn.htm#symbio. 

 

But what popped out at me today is Peirce’s observation that the interpretant 
is not determined by a qualisign, sinsign or legisign as such. In other words, 
we should not think of “determination” as a dyadic action of sign upon 
interpretant (or upon mind). Neither should we think of the determination of 
sign by object as a fait accompli or event preceding the determination of 
interpretant by sign. The sign-action is irreducibly triadic because the 
determination of and by the sign are just two aspects of a single process, not 
successive steps in the process; not events separated in time, but objects 
hypostatically abstracted from its flow.

 

This is just a new version of an old story, but sometimes it feels right to 
turn the wheel again …

 

Gary f.

 

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net] 
Sent: 23-Apr-17 21:34
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Re: Laws of Nature as Signs

 

Helmut, Jeffrey, Jon A, Clark, list,

 

HR

> Not every triadic relation is categorically thirdness. But which are?

 

That's a good question.  Some basic principles:

 

  1. For each of Peirce's categories, there is a characteristic question:

 Firstness:   What is it?  What kind of mark?

 Secondness:  How does it relate or react to something?

 Thirdness:   Why does it relate or react to something?

 Answer:  (1) quality; (2) relation or reaction; (3) mediation.

  

  2. Peirce used the term 'triad', not 'triadic relation'.  You can

 represent a verb, such as 'give' as either a triadic relation

 or as a nominalized node attached to three dyadic relations.

 See the attached give.gif, which shows two ways of mapping the

sentence "Sue gives a child a book" to a graph -- a conceptual

 graph, which may be mapped to an existential graphs or to an

 algebraic formula.

 

  3. As give.gif illustrates, a triad in a graph cannot be eliminated

 by using dyadic relations.  But a graph with a tetrad, pentad, ...

 can always be mapped to and from a graph that has no nodes with

 more than 3 links.

 

  4. A non-degenerate triad always involves something law-like,

 intentional, or mental.  That implies some mind or quasi-mind

 that does the interpretation.  Nominalists don't like that way

 of talking.

 

  5. Strict nominalists, such as Carnap, deny that abstract entities

 exist -- that includes all forms of Thirdness:  laws, intentions,

 goals, purposes, or habits.  That is why Carnap insisted that all

 laws of science are nothing more than summaries of observations.

 

HR

> Is it reasonable to say that a relation has an intension and an 

> extension, the intension is firstness, and the extension secondness 

> (of the relation, which is secondness)?

 

As Church pointed out, the intension is a rule of correspondence that 
determines the extension.  That rule is a law-like entity, which is a kind of 
Thirdness.  Note, by the way, that multiple, independently defined rules may 
specify the same extension.

Two functions or relations may differ in intension , but be identical in 
extension.

 

JBD

> why [do] nominalists such as J.S. Mill and Nelson Goodman strongly 

> prefer extensional systems--and have significant reservations about 

> using intensional systems in philosophy

 

All definitions by intension imply some law-like rule.  That's why Carnap 
insisted that laws of science are "summaries of observations".

He would never say "law of nature" -- because (a) the phrase implies that there 
exists something called nature, and (b) it also implies that nature has 
something called laws.

 

JA

> an extensional definition of a 2-place relation ... can be gen

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

[Jon Awbrey]

On 4/25/2017 4:24 PM, Jon Awbrey wrote:

Helmut, List ...

My mind was a mite muddled toward the end of last week
and I did not track all the parts of your comments and
questions.  I posted the beginnings of a more complete
response on my blog:

Icon Index Symbol • 10
https://inquiryintoinquiry.com/2017/04/25/icon-index-symbol-%e2%80%a2-10/

Regards,

Jon



For convenience, here's a text copy, but
missing a lot of emphasis and formatting:

Icon Index Symbol • 10
==

Questions Concerning Certain Faculties Claimed For Signs

Re: Peirce List Discussion • Helmut Raulien
https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00340.html

HR: I am not so sure, if thirdness is about any triadic relation.

It may be more a matter of exegetic strategy than anything else but it’s convenient to attribute thirdness to all 
triadic relations, differentiating their genus in specific and individual cases according to how generic or genuine 
their triadicity may be.


HR: The categories in Peirce’s “new list” of them are quality, relation, 
representation.

Peirce’s paper “On a New List of Categories” is from 1867, before he had worked out his Logic of Relatives to its full 
strength, and he is still thinking of relation as limited to dyadic relations, as many in some quarters of logic still 
do today.  In his 1870 Logic of Relatives he refers to the “three grand classes” of logical terms as absolute terms, 
simple relative terms, and conjugative terms.


On a New List of Categories
http://www.iupui.edu/~arisbe/menu/library/bycsp/newlist/nl-frame.htm

Use of the Letters
http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives#Use_of_the_Letters



Now logical terms are of three grand classes.

The first embraces those whose logical form involves only the conception of quality, and which therefore represent a 
thing simply as “a ──”.  These discriminate objects in the most rudimentary way, which does not involve any 
consciousness of discrimination.  They regard an object as it is in itself as such (quale);  for example, as horse, 
tree, or man.  These are absolute terms.


The second class embraces terms whose logical form involves the conception of relation, and which require the addition 
of another term to complete the denotation.  These discriminate objects with a distinct consciousness of discrimination. 
 They regard an object as over against another, that is as relative;  as father of, lover of, or servant of.  These are 
simple relative terms.


The third class embraces terms whose logical form involves the conception of bringing things into relation, and which 
require the addition of more than one term to complete the denotation.  They discriminate not only with consciousness of 
discrimination, but with consciousness of its origin.  They regard an object as medium or third between two others, that 
is as conjugative;  as giver of ── to ──, or buyer of ── for ── from ──.  These may be termed conjugative terms.


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 of not, the fact itself is made perfectly evident by the study of the logic of relatives.

(CP 3.63).



HR: Maybe representation is a very special kind of triadic relation.

If representation refers to the class of sign relations then those are marked out from the general class of triadic 
relations by a definition that specifies the roles that signs, their interpretant signs, and their objects play within 
the bounds of a sign relation.  Not too incidentally, Peirce gives one of his more consequential definitions of a sign 
relation in the process of defining logic:


C.S. Peirce • On the Definition of Logic
https://inquiryintoinquiry.com/2012/06/01/c-s-peirce-%e2%80%a2-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 m

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

[Jon Awbrey]

Helmut, List ...

My mind was a mite muddled toward the end of last week
and I did not track all the parts of your comments and
questions.  I posted the beginnings of a more complete
response on my blog:

Icon Index Symbol • 10
https://inquiryintoinquiry.com/2017/04/25/icon-index-symbol-%e2%80%a2-10/

Regards,

Jon

On 4/21/2017 8:36 PM, Jon Awbrey wrote:

Helmut, List,

The New List of Categories is 1867, before Peirce has worked out his
Logic of Relatives to its full strength, and he is still thinking of
“relation” as limited to dyadic relations, as many in some quarters
of logic still do today.  In his 1870 Logic of Relatives he refers
to the third category of relative terms as “conjugative terms”.

Peirce's 1870 Logic Of Relatives
http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives#Use_of_the_Letters



Now logical terms are of three grand classes.

The first embraces those whose logical form involves only the conception of 
quality, and which therefore represent a
thing simply as “a ——”.  These discriminate objects in the most rudimentary 
way, which does not involve any
consciousness of discrimination.  They regard an object as it is in itself as 
such (quale); for example, as horse, tree,
or man.  These are absolute terms.

The second class embraces terms whose logical form involves the conception of 
relation, and which require the addition
of another term to complete the denotation. These discriminate objects with a 
distinct consciousness of discrimination.
They regard an object as over against another, that is as relative; as father 
of, lover of, or servant of. These are
simple relative terms.

The third class embraces terms whose logical form involves the conception of 
bringing things into relation, and which
require the addition of more than one term to complete the denotation.  They 
discriminate not only with consciousness of
discrimination, but with consciousness of its origin.  They regard an object as 
medium or third between two others, that
is as conjugative; as giver of —— to ——, or buyer of —— for —— from ——.  These 
may be termed conjugative terms.

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 of not, the fact itself is made perfectly evident by the 
study of the logic of relatives.

(Peirce, CP 3.63).



On 4/21/2017 4:59 PM, Helmut Raulien wrote:

Jon, List,
I am not so sure, if thirdness is about any triadic relation. The categories in
Peirces "new list" of them are quality, relation, representation. Maybe
"representation" is a very special kind of triadic relation. A simple triadic or
n-adic relation, I think, belongs to secondness, and has only two modes, the
quality, eg. function or caprice (intension), and the resulting set of tuples
(extension). Example: The triadic function "x_1 + x_2 = x_3", with the three
sets X_1, X_2, X_3  not being classes of any kind, at least not of the special
kind (whatever that is), that would allow representation, and make it having to
do with the third category.
I guess, that a difference between Peirces relation theory, and his semiotics
and category theory, is, that the first is about all triadic relations, and the
latter only about sign relations or representational relations (the special kind
of triadic relations).
Best,
Helmut




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

[John F Sowa]

Helmut, Jeffrey, Jon A, Clark, list,

HR

Not every triadic relation is categorically thirdness. But which are?


That's a good question.  Some basic principles:

 1. For each of Peirce's categories, there is a characteristic question:
Firstness:   What is it?  What kind of mark?
Secondness:  How does it relate or react to something?
Thirdness:   Why does it relate or react to something?
Answer:  (1) quality; (2) relation or reaction; (3) mediation.

 2. Peirce used the term 'triad', not 'triadic relation'.  You can
represent a verb, such as 'give' as either a triadic relation
or as a nominalized node attached to three dyadic relations.
See the attached give.gif, which shows two ways of mapping the
sentence "Sue gives a child a book" to a graph -- a conceptual
graph, which may be mapped to an existential graphs or to an
algebraic formula.

 3. As give.gif illustrates, a triad in a graph cannot be eliminated
by using dyadic relations.  But a graph with a tetrad, pentad, ...
can always be mapped to and from a graph that has no nodes with
more than 3 links.

 4. A non-degenerate triad always involves something law-like,
intentional, or mental.  That implies some mind or quasi-mind
that does the interpretation.  Nominalists don't like that way
of talking.

 5. Strict nominalists, such as Carnap, deny that abstract entities
exist -- that includes all forms of Thirdness:  laws, intentions,
goals, purposes, or habits.  That is why Carnap insisted that all
laws of science are nothing more than summaries of observations.

HR

Is it reasonable to say that a relation has an intension and an
extension, the intension is firstness, and the extension secondness
(of the relation, which is secondness)?


As Church pointed out, the intension is a rule of correspondence
that determines the extension.  That rule is a law-like entity,
which is a kind of Thirdness.  Note, by the way, that multiple, 
independently defined rules may specify the same extension.

Two functions or relations may differ in intension , but be
identical in extension.

JBD

why [do] nominalists such as J.S. Mill and Nelson Goodman strongly
prefer extensional systems--and have significant reservations about
using intensional systems in philosophy


All definitions by intension imply some law-like rule.  That's why
Carnap insisted that laws of science are "summaries of observations".
He would never say "law of nature" -- because (a) the phrase implies
that there exists something called nature, and (b) it also implies
that nature has something called laws.

JA

an extensional definition of a 2-place relation ... can be generalized
to k-place relations and then beyond the finite arity case...  But
there is nothing remotely nominal going on here, as the definition
invokes sets of tuples.  Sets and tuples are the very sorts of
abstract objects nominal thinkers would eschew


Church used sets to define extensions because he had no reason to
avoid sets.  But Lesniewski and other nominalists replaced set
theory with mereology.  If you have a set of N elements, you have
N+1 entities, which consist of the N elements plus an abstract set.

But with mereology, a collection of N elements does not imply
the existence of anything more than the N elements.  Therefore,
a mereologist could say that the elements of an N-tuple are parts
of a whole called an N-tuple.  They would not consider the whole
as something distinct from the sum of its parts.

JA

I have never found going on about Firstness Secondness Thirdness
all that useful in any practical situation.


If you think at those terms as a count of links in a graph, they
don't explain much.  It's better to look at the three kinds of
questions summarized at the top of this note.

JA

until you venture to say exactly *which* monadic, dyadic, or triadic
predicate you have in mind, you haven't really said that much at all.


CG

Glad I’m not alone in thinking that.


I agree that we need to look at specific cases.  For examples of the
kinds of Thirdness that nominalists deliberately ignore, see Section 2
(pp. 3 to 8) of http://www.jfsowa.com/pubs/signproc.pdf .

The title of that section is "A Static, Lifeless, Purposeless World".
Some excerpts:

p. 4:  Einstein criticized Russell's "Angst vor der Metaphysik"
and said “Mach was a good experimental physicist but a miserable
philosopher”; he made “a catalog not a system.”

p. 5:  When introducing Russell for his William James Lectures
at Harvard, Whitehead said “This is my friend Bertrand Russell.
Bertie thinks that I am muddleheaded, but then I think that he
is simpleminded” (Lucas 1989:111).  That remark is consistent with
a statement attributed to Russell:  “I’d rather be narrow minded
than vague and wooly” (Kuntz 1984:50).

p. 5:  While reviewing Quine’s Word and Object, [Rescher] was struck
by the absence of any discussion of events, processes, actions, and
change.  After reviewing the l

Aw: [PEIRCE-L] Re: Laws of Nature as Signs (Edited)

[Helmut Raulien]

Jerry, List,

I think, this evaluation does relate to firstness, secondness, thirdness. I was wrong with assuming, that the logic of relations is not about the categories. But I still have problems with comparing the mathematical concept of triadic relations with the logic of relations. Eg "father of" is secondness and a genitive term, as you have written. Thank you for this and the other clarifications! Translated into mathematics, is this genitiveness a trait of all elements of the second set "X_2", making X_2 a subset of the class of genitive terms, or is it a part of the function? I have no idea.

The only thing I am still quite sure about is, that not all triadic relations are categorically thirdness. Example: The function "x_1 = x_2 = x_3", upon the three sets X_1 = X_2 = X_3 = natural numbers from 1 to 10. This would  be something like: "Alice, Bob, and Celia are taking a walk". This has to do with the number three, but not with thirdness. It is secondness. Genitively spoken: "The group´s (A,B,C) walk".

That was my point: Not every triadic relation is categorically thirdness. But which are? I have no idea. Neither, whether I am overestimating the relevance of this question.

Best,

Helmut

 

23. April 2017 um 02:31 Uhr
Von: "Jerry LR Chandler" 
 



(This post corrects and adds to the previous post)  JLRC )

 
Helmut, List: 

 


On Apr 21, 2017, at 3:59 PM, Helmut Raulien  wrote:
 

I am not so sure, if thirdness is about any triadic relation. The categories in Peirces "new list" of them are quality, relation, representation. Maybe "representation" is a very special kind of triadic relation. A simple triadic or n-adic relation, I think, belongs to secondness, and has only two modes, the quality, eg. function or caprice (intension), and the resulting set of tuples (extension). Example: The triadic function "x_1 + x_2 = x_3", with the three sets X_1, X_2, X_3  not being classes of any kind, at least not of the special kind (whatever that is), that would allow representation, and make it having to do with the third category.




From your perspective, how important is it parse the distinctions among philosophical terms that express the concept of “trine” or “three-fold” or “trinity”?  (I select these words because they all express the count of verbal objects without using CSP’s favorite word-objects to express analogous or similar notions of the count of an integer.)

 

Jon’s post cite’s 3.363 with respect to classes of LOGICAL TERMS, namely:


 "logical terms are of three grand classes.”


 

In other words, in this early phase of his writings, CSP was focused on the sorts or kinds of logical terms.  To quote  3.363,

"The first embraces those whose logical form involves only the conception of quality, and which therefore represent a thing simply as “a ——”. “

 

"The second class embraces terms whose logical form involves the conception of relation, and which require the addition of another term to complete the denotation.”

 

"The third class embraces terms whose logical form involves the conception of bringing things into relation, and which require the addition of more than one term to complete the denotation.”

 

The grammatical examples of the classes of terms of 3.363 are:

1. ...for example, as horse, tree, or man.

2. … father of, lover of, or servant of. 

3. ...giver of —— to ——, or buyer of —— for —— from ——

 

Note that the first class of terms are simple nouns.

Note that the second class of terms are genitive cases of nouns.

Note that the third class of terms includes multiple nouns, multiple syncategormatic  terms.

 

(Edit: I omitted the crucial observation that the third class of terms is CONSTRAINED "TO  COMPLETE THE DENOTATION”.  This constraint limits the “three grand classes” of terms to denotative arguments!   Thus, CSP infers that his grand classes of terms excludes non-denotative terms.  The constraint excludes most linguistic terms sense denotation is an extremely restrictive constraint on common usages of logic propositions. For example, connotative terms and arguments are excluded. Thus, the connotation of “things”, “representations” and “forms” form a different class of terms.  This does not imply that CSP’s “grand terms” are not completely useless.) 

 

As classes of terms, these examples do not include any hint of propositions or conclusions.  One could, perhaps, say that these examples are antecedents to propositions or syllogisms or partial assertions…

 

Helmut, does this evaluation of CSP 3.363 relate to triadicity(?) or triadic relations (?) or trichotomy(?)  or firstness, secondness or thirdness?

 

Does the logical term, “triadic relations” implicitly or intentionally imply three “valences"?  How would it relate to last of the examples listed above?

 

It seems to me that CSP is drawing a sharp distinction of his thinking from the classification of terms used in logica moderna - significatio, suppositio, and related properties of te

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

[Jerry LR Chandler]

(This post corrects and adds to the previous post)  JLRC )

Helmut, List: 

> On Apr 21, 2017, at 3:59 PM, Helmut Raulien  > wrote:
> 
> I am not so sure, if thirdness is about any triadic relation. The categories 
> in Peirces "new list" of them are quality, relation, representation. Maybe 
> "representation" is a very special kind of triadic relation. A simple triadic 
> or n-adic relation, I think, belongs to secondness, and has only two modes, 
> the quality, eg. function or caprice (intension), and the resulting set of 
> tuples (extension). Example: The triadic function "x_1 + x_2 = x_3", with the 
> three sets X_1, X_2, X_3  not being classes of any kind, at least not of the 
> special kind (whatever that is), that would allow representation, and make it 
> having to do with the third category.

>From your perspective, how important is it parse the distinctions among 
>philosophical terms that express the concept of “trine” or “three-fold” or 
>“trinity”?  (I select these words because they all express the count of verbal 
>objects without using CSP’s favorite word-objects to express analogous or 
>similar notions of the count of an integer.)

Jon’s post cite’s 3.363 with respect to classes of LOGICAL TERMS, namely:
>  "logical terms are of three grand classes.”


In other words, in this early phase of his writings, CSP was focused on the 
sorts or kinds of logical terms.  To quote  3.363,
"The first embraces those whose logical form involves only the conception of 
quality, and which therefore represent a thing simply as “a ——”. “

"The second class embraces terms whose logical form involves the conception of 
relation, and which require the addition of another term to complete the 
denotation.”

"The third class embraces terms whose logical form involves the conception of 
bringing things into relation, and which require the addition of more than one 
term to complete the denotation.”

The grammatical examples of the classes of terms of 3.363 are:
1. ...for example, as horse, tree, or man.
2. … father of, lover of, or servant of. 
3. ...giver of —— to ——, or buyer of —— for —— from ——

Note that the first class of terms are simple nouns.
Note that the second class of terms are genitive cases of nouns.
Note that the third class of terms includes multiple nouns, multiple 
syncategormatic  terms.

(Edit: I omitted the crucial observation that the third class of terms is 
CONSTRAINED "TO  COMPLETE THE DENOTATION”.  This constraint limits the “three 
grand classes” of terms to denotative arguments!   Thus, CSP infers that his 
grand classes of terms excludes non-denotative terms.  The constraint excludes 
most linguistic terms sense denotation is an extremely restrictive constraint 
on common usages of logic propositions. For example, connotative terms and 
arguments are excluded. Thus, the connotation of “things”, “representations” 
and “forms” form a different class of terms.  This does not imply that CSP’s 
“grand terms” are not completely useless.) 

As classes of terms, these examples do not include any hint of propositions or 
conclusions.  One could, perhaps, say that these examples are antecedents to 
propositions or syllogisms or partial assertions…

Helmut, does this evaluation of CSP 3.363 relate to triadicity(?) or triadic 
relations (?) or trichotomy(?)  or firstness, secondness or thirdness?

Does the logical term, “triadic relations” implicitly or intentionally imply 
three “valences"?  How would it relate to last of the examples listed above?

It seems to me that CSP is drawing a sharp distinction of his thinking from the 
classification of terms used in logica moderna - significatio, suppositio, and 
related properties of terms such as 
copulation, appellation, implication, restriction and distribution. 

Cheers

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

[Jerry LR Chandler]

Helmut, List: 

> On Apr 21, 2017, at 3:59 PM, Helmut Raulien  wrote:
> 
> I am not so sure, if thirdness is about any triadic relation. The categories 
> in Peirces "new list" of them are quality, relation, representation. Maybe 
> "representation" is a very special kind of triadic relation. A simple triadic 
> or n-adic relation, I think, belongs to secondness, and has only two modes, 
> the quality, eg. function or caprice (intension), and the resulting set of 
> tuples (extension). Example: The triadic function "x_1 + x_2 = x_3", with the 
> three sets X_1, X_2, X_3  not being classes of any kind, at least not of the 
> special kind (whatever that is), that would allow representation, and make it 
> having to do with the third category.

>From your perspective, how important is it parse the distinctions among 
>philosophical terms that express the concept of “trine” or “three-fold” or 
>“trinity”?  (I select these words because they all express the count of verbal 
>objects without using CSP’s favorite word-objects to express analogous or 
>similar notions of the count of an integer.)

Jon’s post cite’s 3.363 with respect to classes of LOGICAL TERMS, namely:
>  "logical terms are of three grand classes.”


In other words, in this early phase of his writings, CSP was focused on the 
sorts or kinds of logical terms.  To quote  3.363,
"The first embraces those whose logical form involves only the conception of 
quality, and which therefore represent a thing simply as “a ——”. “

"The second class embraces terms whose logical form involves the conception of 
relation, and which require the addition of another term to complete the 
denotation.”

"The third class embraces terms whose logical form involves the conception of 
bringing things into relation, and which require the addition of more than one 
term to complete the denotation.”

The grammatical examples of the classes of terms of 3.363 are:
1. ...for example, as horse, tree, or man.
2. … father of, lover of, or servant of. 
3. ...giver of —— to ——, or buyer of —— for —— from ——

Note that the first class of terms are simple nouns.
Note that the second class of terms are genitive cases of nouns.
Note that the third class of terms includes multiple nouns, multiple 
syncategormatic  terms 

As classes of terms, these examples do not include any hint of propositions or 
conclusions.  One could, perhaps, say that these examples are antecedents to 
propositions or syllogisms or partial assertions…

Helmut, does this evaluation of CSP 3.363 does not relate to triadicity or 
triadic relations or triadicity or trichotomy or firstness, secondness or 
thirdness?

Does the logical term, “triadic relations” implicitly or intentionally imply 
three “valences"?  How would it relate to last of the examples listed above?

It seems to me that CSP is drawing a sharp distinction of his thinking from the 
classification of terms used in logica moderna - significatio, suppositio, and 
related properties of terms such as 
copulation, appellation, implication, restriction and distribution. 

Cheers

Jerry







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

[Helmut Raulien]

Jon, List,

Thank you, Jon! So I was wrong assuming that Peirces relation theory is not about the categories, it is too.


The three classes of terms, quale, relative, conjugative, to me seem somehow to corrobate my guess that a triadic relation, for being a representational, or thirdness-involving one, requires three sets of certain classes. But how to reconstruct linguistic concepts like "quale", "relative" and "conjugative" with mathematics? A relative is an element that anticipates two things (or consists of two things). A conjugative three, a quale one. I dont know. Prime numbers for quales? Complex numbers for relatives? Maybe better not and move on to something completely different.

Best,

Helmut


 22. April 2017 um 02:36 Uhr
Von: "Jon Awbrey" 
 

Helmut, List,

The New List of Categories is 1867, before Peirce has worked out his
Logic of Relatives to its full strength, and he is still thinking of
“relation” as limited to dyadic relations, as many in some quarters
of logic still do today. In his 1870 Logic of Relatives he refers
to the third category of relative terms as “conjugative terms”.

Peirce's 1870 Logic Of Relatives
http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives#Use_of_the_Letters



Now logical terms are of three grand classes.

The first embraces those whose logical form involves only the conception of quality, and which therefore represent a
thing simply as “a ——”. These discriminate objects in the most rudimentary way, which does not involve any
consciousness of discrimination. They regard an object as it is in itself as such (quale); for example, as horse, tree,
or man. These are absolute terms.

The second class embraces terms whose logical form involves the conception of relation, and which require the addition
of another term to complete the denotation. These discriminate objects with a distinct consciousness of discrimination.
They regard an object as over against another, that is as relative; as father of, lover of, or servant of. These are
simple relative terms.

The third class embraces terms whose logical form involves the conception of bringing things into relation, and which
require the addition of more than one term to complete the denotation. They discriminate not only with consciousness of
discrimination, but with consciousness of its origin. They regard an object as medium or third between two others, that
is as conjugative; as giver of —— to ——, or buyer of —— for —— from ——. These may be termed conjugative terms.

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 of not, the fact itself is made perfectly evident by the study of the logic of relatives.

(Peirce, CP 3.63).



On 4/21/2017 4:59 PM, Helmut Raulien wrote:
> Jon, List,
> I am not so sure, if thirdness is about any triadic relation. The categories in
> Peirces "new list" of them are quality, relation, representation. Maybe
> "representation" is a very special kind of triadic relation. A simple triadic or
> n-adic relation, I think, belongs to secondness, and has only two modes, the
> quality, eg. function or caprice (intension), and the resulting set of tuples
> (extension). Example: The triadic function "x_1 + x_2 = x_3", with the three
> sets X_1, X_2, X_3 not being classes of any kind, at least not of the special
> kind (whatever that is), that would allow representation, and make it having to
> do with the third category.
> I guess, that a difference between Peirces relation theory, and his semiotics
> and category theory, is, that the first is about all triadic relations, and the
> latter only about sign relations or representational relations (the special kind
> of triadic relations).
> Best,
> Helmut

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

[Jon Awbrey]

Helmut, List,

The New List of Categories is 1867, before Peirce has worked out his
Logic of Relatives to its full strength, and he is still thinking of
“relation” as limited to dyadic relations, as many in some quarters
of logic still do today.  In his 1870 Logic of Relatives he refers
to the third category of relative terms as “conjugative terms”.

Peirce's 1870 Logic Of Relatives
http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives#Use_of_the_Letters



Now logical terms are of three grand classes.

The first embraces those whose logical form involves only the conception of quality, and which therefore represent a 
thing simply as “a ——”.  These discriminate objects in the most rudimentary way, which does not involve any 
consciousness of discrimination.  They regard an object as it is in itself as such (quale); for example, as horse, tree, 
or man.  These are absolute terms.


The second class embraces terms whose logical form involves the conception of relation, and which require the addition 
of another term to complete the denotation. These discriminate objects with a distinct consciousness of discrimination. 
They regard an object as over against another, that is as relative; as father of, lover of, or servant of. These are 
simple relative terms.


The third class embraces terms whose logical form involves the conception of bringing things into relation, and which 
require the addition of more than one term to complete the denotation.  They discriminate not only with consciousness of 
discrimination, but with consciousness of its origin.  They regard an object as medium or third between two others, that 
is as conjugative; as giver of —— to ——, or buyer of —— for —— from ——.  These may be termed conjugative terms.


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 of not, the fact itself is made perfectly evident by the study of the logic of relatives.


(Peirce, CP 3.63).



On 4/21/2017 4:59 PM, Helmut Raulien wrote:

Jon, List,
I am not so sure, if thirdness is about any triadic relation. The categories in
Peirces "new list" of them are quality, relation, representation. Maybe
"representation" is a very special kind of triadic relation. A simple triadic or
n-adic relation, I think, belongs to secondness, and has only two modes, the
quality, eg. function or caprice (intension), and the resulting set of tuples
(extension). Example: The triadic function "x_1 + x_2 = x_3", with the three
sets X_1, X_2, X_3  not being classes of any kind, at least not of the special
kind (whatever that is), that would allow representation, and make it having to
do with the third category.
I guess, that a difference between Peirces relation theory, and his semiotics
and category theory, is, that the first is about all triadic relations, and the
latter only about sign relations or representational relations (the special kind
of triadic relations).
Best,
Helmut


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

[Helmut Raulien]

Jon, List,

I am not so sure, if thirdness is about any triadic relation. The categories in Peirces "new list" of them are quality, relation, representation. Maybe "representation" is a very special kind of triadic relation. A simple triadic or n-adic relation, I think, belongs to secondness, and has only two modes, the quality, eg. function or caprice (intension), and the resulting set of tuples (extension). Example: The triadic function "x_1 + x_2 = x_3", with the three sets X_1, X_2, X_3  not being classes of any kind, at least not of the special kind (whatever that is), that would allow representation, and make it having to do with the third category.

I guess, that a difference between Peirces relation theory, and his semiotics and category theory, is, that the first is about all triadic relations, and the latter only about sign relations or representational relations (the special kind of triadic relations).

Best,

Helmut

 

 21. April 2017 um 05:32 Uhr
Von: "Jon Awbrey" 
 

Helmut, John, List ...

I'll answer Helmut's question first as I can think of something
right off to say about it, whereas JFS and I have had this same
discussion every 3 or 4 years for going on the last 20 and I'll
need a while to see if I can think of anything new to say on it.



I confess I have never found going on about Firstness Secondness Thirdness
all that useful in any practical situation. Firstness means one has some
monadic predicate in mind as relevant to a phenomenon, problem, or other
subject matter, Secondness means one has a dyadic relation in mind to
the same end, and Thirdness means one has a triadic relation in mind
as bearing on the situation at hand. After that one can consider
the fine points of generic versus degenerate cases, and that is
all well and good, but until you venture to say exactly *which*
monadic, dyadic, or triadic predicate you have in mind, you
haven't really said that much at all.



What I really think is interesting in all this is the fact that Peirce,
from 1865 on, maintains in the background of his thought the idea that
information is the solid substance born by concepts and symbols, while
comprehension and extension are its complementary aspects, its shadows.

I have been studying this integration of comprehension and extension
in the form of information for quite a while, and there is my set of
excerpts and comments on this page:

Information = Comprehension × Extension
http://intersci.ss.uci.edu/wiki/index.php/Information_%3D_Comprehension_%C3%97_Extension

But I just ran across a shorter sketch of the main ideas
that I must have begun some time ago but not yet finished:

Peirce's Logic Of Information
http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_Logic_Of_Information

It has the advantage of having a nicely self-explanatory figure right up front.
At any rate, try taking a look at that ...

Regards,

Jon

On 4/20/2017 4:47 PM, Helmut Raulien wrote:
> Jon, John, List,
> Is it reasonable to say that a relation has an intension and an extension, the
> intension is firstness, and the extension secondness (of the relation, which is
> secondness)?
> Best,
> Helmut
> 20. April 2017 um 15:14 Uhr
> *Von:* "John F Sowa" 
> Jon,
>
> That is an extensional definition of a relation:
>
>> Following the pattern of the functional case, let the notation
>> “L ⊆ X × Y” bring to mind a mathematical object specified by
>> three pieces of data, the set X, the set Y, and a particular
>> subset of their cartesian product X × Y. As before we have
>> two choices, either let L = (X, Y, graph(L)) or let “L” denote
>> graph(L) and choose another name for the triple.
>
> Nominalists prefer extensional definitions. But Peirce would
> usually state intensional definitions (rules) for the functions
> or relations he was considering.
>
> Alonzo Church (1941) stated the intensional definition:
>> A function is a rule of correspondence by which when anything is
>> given (as argument) another thing (the value of the function for
>> that argument) may be obtained. That is, a function is an operation
>> which may be applied on one thing (the argument) to yield another
>> thing (the value of the function).
>
> For further discussion of the distinction between intensions
> extensions, see pp. 1 to 3 of Church's book:
> http://www.jfsowa.com/logic/alonzo.htm
>
> By the way, Church was not a nominalist. See the transcript of his
> talk "On the ontological status of women and abstract entities":
> http://www.jfsowa.com/ontology/church.htm
>
> John
>

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

[Jon Awbrey]

John, List ...

That is indeed an extensional definition of a 2-place relation.
It can be generalized to k-place relations and then beyond the
finite arity case, but k-place relations are enough to cover
the triadic case of principal interest to us in semiotics.

But there is nothing remotely nominal going on here, as the
definition invokes sets of tuples.  Sets and tuples are the
very sorts of abstract objects nominal thinkers would eschew
if they could — we know they can't but they think they can —
which is why they are always inventing square wheels like
Russell's no-class theory or Leśniewski's mereology.

The more interesting polarity that does arise in this setting of sets
is not the one between nominalism and realism but the one that ranges
over different cognitive styles or intellectual inclinations, namely,
the empiricist and rationalist tendencies of mind.  The question is,
not which is best, but how best to integrate these dual capacities
within the practice of inquiry.

Regards,

Jon

On 4/20/2017 9:14 AM, John F Sowa wrote:
> Jon,
>
> That is an extensional definition of a relation:
>
>> Following the pattern of the functional case, let the notation
>> “L ⊆ X × Y” bring to mind a mathematical object specified by
>> three pieces of data, the set X, the set Y, and a particular
>> subset of their cartesian product X × Y.  As before we have
>> two choices, either let L = (X, Y, graph(L)) or let “L”
>> denote graph(L) and choose another name for the triple.
>
> Nominalists prefer extensional definitions.  But Peirce would
> usually state intensional definitions (rules) for the functions
> or relations he was considering.
>
> Alonzo Church (1941) stated the intensional definition:
>> A function is a rule of correspondence by which when anything is
>> given (as argument) another thing (the value of the function for
>> that argument) may be obtained.  That is, a function is an operation
>> which may be applied on one thing (the argument) to yield another
>> thing (the value of the function).
>
> For further discussion of the distinction between
> intensions and extensions, see pp. 1 to 3 of Church's book:
> http://www.jfsowa.com/logic/alonzo.htm
>
> By the way, Church was not a nominalist.  See the transcript of his
> talk "On the ontological status of women and abstract entities":
> http://www.jfsowa.com/ontology/church.htm
>
> John
>

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

[Jon Awbrey]

Helmut, John, List ...

I'll answer Helmut's question first as I can think of something
right off to say about it, whereas JFS and I have had this same
discussion every 3 or 4 years for going on the last 20 and I'll
need a while to see if I can think of anything new to say on it.



I confess I have never found going on about Firstness Secondness Thirdness
all that useful in any practical situation.  Firstness means one has some
monadic predicate in mind as relevant to a phenomenon, problem, or other
subject matter, Secondness means one has a dyadic relation in mind to
the same end, and Thirdness means one has a triadic relation in mind
as bearing on the situation at hand.  After that one can consider
the fine points of generic versus degenerate cases, and that is
all well and good, but until you venture to say exactly *which*
monadic, dyadic, or triadic predicate you have in mind, you
haven't really said that much at all.



What I really think is interesting in all this is the fact that Peirce,
from 1865 on, maintains in the background of his thought the idea that
information is the solid substance born by concepts and symbols, while
comprehension and extension are its complementary aspects, its shadows.

I have been studying this integration of comprehension and extension
in the form of information for quite a while, and there is my set of
excerpts and comments on this page:

Information = Comprehension × Extension
http://intersci.ss.uci.edu/wiki/index.php/Information_%3D_Comprehension_%C3%97_Extension

But I just ran across a shorter sketch of the main ideas
that I must have begun some time ago but not yet finished:

Peirce's Logic Of Information
http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_Logic_Of_Information

It has the advantage of having a nicely self-explanatory figure right up front.
At any rate, try taking a look at that ...

Regards,

Jon

On 4/20/2017 4:47 PM, Helmut Raulien wrote:
> Jon, John, List,
> Is it reasonable to say that a relation has an intension and an extension, the
> intension is firstness, and the extension secondness (of the relation, which 
is
> secondness)?
> Best,
> Helmut
> 20. April 2017 um 15:14 Uhr
> *Von:* "John F Sowa" 
> Jon,
>
> That is an extensional definition of a relation:
>
>> Following the pattern of the functional case, let the notation
>> “L ⊆ X × Y” bring to mind a mathematical object specified by
>> three pieces of data, the set X, the set Y, and a particular
>> subset of their cartesian product X × Y.  As before we have
>> two choices, either let L = (X, Y, graph(L)) or let “L” denote
>> graph(L) and choose another name for the triple.
>
> Nominalists prefer extensional definitions.  But Peirce would
> usually state intensional definitions (rules) for the functions
> or relations he was considering.
>
> Alonzo Church (1941) stated the intensional definition:
>> A function is a rule of correspondence by which when anything is
>> given (as argument) another thing (the value of the function for
>> that argument) may be obtained. That is, a function is an operation
>> which may be applied on one thing (the argument) to yield another
>> thing (the value of the function).
>
> For further discussion of the distinction between intensions
> extensions, see pp. 1 to 3 of Church's book:
> http://www.jfsowa.com/logic/alonzo.htm
>
> By the way, Church was not a nominalist. See the transcript of his
> talk "On the ontological status of women and abstract entities":
> http://www.jfsowa.com/ontology/church.htm
>
> John
>

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

[Jeffrey Brian Downard]

Hi John,

Thank you for sending the links to the excerpts from Church's work in logic. 
His explanation of the assumptions behind extensional approaches in formal 
logic and the philosophical theory of logic are remarkably clear. If you have 
additional thoughts to add that help to explain why it is that nominalists such 
as J.S. Mill and Nelson Goodman strongly prefer extensional systems--and have 
significant reservations about using intensional systems in philosophy--I'd be 
interested to hear what you think. In particular, I'd like to hear more about 
the connections that you see between (1) the motives for developing intensional 
systems, (2) Church's remarks about the treatment of things such as functions 
and relations as objects in these systems (e.g., in the lambda operator), and 
(3)  the treatment of the infinite character of some collections and the 
continuity of some operations at both the object level and the meta-level 
within intensional systems.

--Jeff

Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354

From: John F Sowa 
Sent: Thursday, April 20, 2017 6:14 AM
To: peirce-l@list.iupui.edu; Jon Awbrey
Subject: Re: [PEIRCE-L] Re: Laws of Nature as Signs

Jon,

That is an extensional definition of a relation:

> Following the pattern of the functional case, let the notation
> “L ⊆ X × Y” bring to mind a mathematical object specified by
> three pieces of data, the set X, the set Y, and a particular
> subset of their cartesian product X × Y}.  As before we have
> two choices, either let L = (X, Y, graph(L)) or let “L” denote
> graph(L) and choose another name for the triple.

Nominalists prefer extensional definitions.  But Peirce would
usually state intensional definitions (rules) for the functions
or relations he was considering.

Alonzo Church (1941) stated the intensional definition:
> A function is a rule of correspondence by which when anything is
> given (as argument) another thing (the value of the function for
> that argument) may be obtained. That is, a function is an operation
> which may be applied on one thing (the argument) to yield another
> thing (the value of the function).

For further discussion of the distinction between intensions
extensions, see pp. 1 to 3 of Church's book:
http://www.jfsowa.com/logic/alonzo.htm

By the way, Church was not a nominalist.  See the transcript of his
talk "On the ontological status of women and abstract entities":
http://www.jfsowa.com/ontology/church.htm

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

[Helmut Raulien]

Jon, John, List,

Is it reasonable to say that a relation has an intension and an extension, the intension is firstness, and the extension secondness (of the relation, which is secondness)?

Best,

Helmut

 

20. April 2017 um 15:14 Uhr
Von: "John F Sowa" 
 

Jon,

That is an extensional definition of a relation:

> Following the pattern of the functional case, let the notation
> “L ⊆ X × Y” bring to mind a mathematical object specified by
> three pieces of data, the set X, the set Y, and a particular
> subset of their cartesian product X × Y}. As before we have
> two choices, either let L = (X, Y, graph(L)) or let “L” denote
> graph(L) and choose another name for the triple.

Nominalists prefer extensional definitions. But Peirce would
usually state intensional definitions (rules) for the functions
or relations he was considering.

Alonzo Church (1941) stated the intensional definition:
> A function is a rule of correspondence by which when anything is
> given (as argument) another thing (the value of the function for
> that argument) may be obtained. That is, a function is an operation
> which may be applied on one thing (the argument) to yield another
> thing (the value of the function).

For further discussion of the distinction between intensions
extensions, see pp. 1 to 3 of Church's book:
http://www.jfsowa.com/logic/alonzo.htm

By the way, Church was not a nominalist. See the transcript of his
talk "On the ontological status of women and abstract entities":
http://www.jfsowa.com/ontology/church.htm

John

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

[Edwina Taborsky]

 

 BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px;
}The Church definition of a function is exactly why I define the
semiosic  triadic process as a function, where the Object [Argument] 
is mediated by the Representamen/Function to provide the Interpretant
[value].

Edwina
 -- 
 This message is virus free, protected by Primus - Canada's 
 largest alternative telecommunications provider. 
 http://www.primus.ca 
 On Thu 20/04/17  9:14 AM , John F Sowa s...@bestweb.net sent:
 Jon, 
 That is an extensional definition of a relation: 
 > Following the pattern of the functional case, let the notation 
 > “L ⊆ X × Y” bring to mind a mathematical object specified
by 
 > three pieces of data, the set X, the set Y, and a particular 
 > subset of their cartesian product X × Y}.  As before we have 
 > two choices, either let L = (X, Y, graph(L)) or let “L” denote

 > graph(L) and choose another name for the triple. 
 Nominalists prefer extensional definitions.  But Peirce would 
 usually state intensional definitions (rules) for the functions 
 or relations he was considering. 
 Alonzo Church (1941) stated the intensional definition: 
 > A function is a rule of correspondence by which when anything is 
 > given (as argument) another thing (the value of the function for 
 > that argument) may be obtained. That is, a function is an
operation 
 > which may be applied on one thing (the argument) to yield another 
 > thing (the value of the function). 
 For further discussion of the distinction between intensions 
 extensions, see pp. 1 to 3 of Church's book: 
 http://www.jfsowa.com/logic/alonzo.htm [1] 
 By the way, Church was not a nominalist.  See the transcript of his 
 talk "On the ontological status of women and abstract entities":  
 http://www.jfsowa.com/ontology/church.htm [2] 
 John 


Links:
--
[1]
http://webmail.primus.ca/parse.php?redirect=http%3A%2F%2Fwww.jfsowa.com%2Flogic%2Falonzo.htm
[2]
http://webmail.primus.ca/parse.php?redirect=http%3A%2F%2Fwww.jfsowa.com%2Fontology%2Fchurch.htm

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

[John F Sowa]

Jon,

That is an extensional definition of a relation:


Following the pattern of the functional case, let the notation
“L ⊆ X × Y” bring to mind a mathematical object specified by
three pieces of data, the set X, the set Y, and a particular
subset of their cartesian product X × Y}.  As before we have
two choices, either let L = (X, Y, graph(L)) or let “L” denote
graph(L) and choose another name for the triple.


Nominalists prefer extensional definitions.  But Peirce would
usually state intensional definitions (rules) for the functions
or relations he was considering.

Alonzo Church (1941) stated the intensional definition:

A function is a rule of correspondence by which when anything is
given (as argument) another thing (the value of the function for
that argument) may be obtained. That is, a function is an operation
which may be applied on one thing (the argument) to yield another
thing (the value of the function).


For further discussion of the distinction between intensions
extensions, see pp. 1 to 3 of Church's book:
http://www.jfsowa.com/logic/alonzo.htm

By the way, Church was not a nominalist.  See the transcript of his
talk "On the ontological status of women and abstract entities": 
http://www.jfsowa.com/ontology/church.htm


John

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

[Jon Awbrey]

Helmut, List,

That's not really supposed to be a recursive definition.
It's just my sloppy notation or lack thereof that makes
it seem so.  I wrote it more precisely in my article on
Relation Theory:

http://intersci.ss.uci.edu/wiki/index.php/Relation_theory



Following the pattern of the functional case, let the notation
“L ⊆ X × Y” bring to mind a mathematical object specified by
three pieces of data, the set X, the set Y, and a particular
subset of their cartesian product X × Y}.  As before we have
two choices, either let L = (X, Y, graph(L)) or let “L” denote
graph(L) and choose another name for the triple.



For a k-place relation, then, we let “L” denote the (k+1)-tuple
and use a new name “graph(L)” for the subset of X_1 × ... × X_k,
yielding L = (X_1, ..., X_k, graph(L)).

Regards,

Jon


On 4/19/2017 4:24 PM, Helmut Raulien wrote:

Jon, List,
interesting! I have a guess, regarding the possible bridge between the "strong
typing" relation concept in mathematics, and semiotics and other theories. I
know this is anticipation towards much later, and we dont want to do this now,
but first talk about mathematics only. So, it is  merely to create a holding
power for people who read this, by showing that indeed mathematics might be able
to contribute much to semiotics and other theories:
The k+1-tuple reminds me of the re-entry concept by Spencer Brown, and also of
the term "sign" being used by Peirce for both the triad and a part of it, the
representamen, and also the concept of "self-reference" in systems theories: In
the k+1-tuple, there is also the whole thing (the relation "L") a part of 
itself.
The term "quality" in the context you have used it (fourth-last line) reminds me
of secondness having two modes, firstness and secondness of secondness: In
Peirces "On a new List of Categories" "Relation" is the second category, so it
should have two modes. Maybe the quality (which is the first category in (On a
new list...") of a relation (eg. "smaller than", or "random" is the firstness of
the relation, and the actual subset (plus the relation, or plus the domains, or
neither) is secondness (of the secondness, the relation). Just guesses!
Best,
Helmut
17. April 2017 um 16:05 Uhr

Helmut, List ...

The difference between the two definitions is sometimes
described as “decontextualized” versus “contextualized”
or, in computerese, “weak typing” versus “strong typing”.
The second definition is typically expressed by means of
a peculiar mathematical idiom that starts out as follows:

“A k-place relation is a k+1-tuple (X_1, …, X_k, L) …”

That way of defining relations is a natural generalization
of the way functions are defined in the mathematical subject
of category theory, where the “domain” X and the “codomain” Y
share in defining the “type” X → Y of the function f : X → Y.

The threshold between “arbitrary”, “artificial”, “random” kinds of
relations and those selected for due consideration as “reasonable”,
“proper”, “natural” kinds tends to shift from context to context.
We usually have in mind some property or quality that marks the
latter class as “proper” objects of contemplation relative to
the end in view, and so this relates to the intensional view
of subject matters.

Regards,

Jon




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

[Helmut Raulien]

Jon, List,

interesting! I have a guess, regarding the possible bridge between the "strong typing" relation concept in mathematics, and semiotics and other theories. I know this is anticipation towards much later, and we dont want to do this now, but first talk about mathematics only. So, it is  merely to create a holding power for people who read this, by showing that indeed mathematics might be able to contribute much to semiotics and other theories:

The k+1-tuple reminds me of the re-entry concept by Spencer Brown, and also of the term "sign" being used by Peirce for both the triad and a part of it, the representamen, and also the concept of "self-reference" in systems theories: In the k+1-tuple, there is also the whole thing (the relation "L") a part of itself.


The term "quality" in the context you have used it (fourth-last line) reminds me of secondness having two modes, firstness and secondness of secondness: In Peirces "On a new List of Categories" "Relation" is the second category, so it should have two modes. Maybe the quality (which is the first category in (On a new list...") of a relation (eg. "smaller than", or "random" is the firstness of the relation, and the actual subset (plus the relation, or plus the domains, or neither) is secondness (of the secondness, the relation). Just guesses!

Best,

Helmut


17. April 2017 um 16:05 Uhr
"Jon Awbrey" 
 

Helmut, List ...

The difference between the two definitions is sometimes
described as “decontextualized” versus “contextualized”
or, in computerese, “weak typing” versus “strong typing”.
The second definition is typically expressed by means of
a peculiar mathematical idiom that starts out as follows:

“A k-place relation is a k+1-tuple (X_1, …, X_k, L) …”

That way of defining relations is a natural generalization
of the way functions are defined in the mathematical subject
of category theory, where the “domain” X and the “codomain” Y
share in defining the “type” X → Y of the function f : X → Y.

The threshold between “arbitrary”, “artificial”, “random” kinds of
relations and those selected for due consideration as “reasonable”,
“proper”, “natural” kinds tends to shift from context to context.
We usually have in mind some property or quality that marks the
latter class as “proper” objects of contemplation relative to
the end in view, and so this relates to the intensional view
of subject matters.

Regards,

Jon

On 4/15/2017 2:49 PM, Helmut Raulien wrote:
> Jon, List,
> Thank you, Jon! Your point No. 2 is new to me, that some
> define relation not only as the subset of the domains'
> cartesian product, but as that plus a list of the domains.
>
> In case the subset is not a random one, but a consequence
> of some reasonable classification, eg. in a dyadic relation:
> "x_1 < x_2", what is this term "x_1 < x_2" called then?
> I am asking, because I think, that in common language this
> is what people might understand as relation. I had called
> it "relation reason" before.
> Best,
> Helmut
>
> 15 April 2017 um 16:30 Uhr
>> "Jon Awbrey"  wrote:
>> Helmut, List,
>>
>> Looking over those articles with fresh eyes this morning
>> I see they are rather thick with abstract generalities at
>> the beginning and it would be better to skip down to the
>> concrete examples on a first run-through. I promise to
>> keep that in mind the next time I rewrite them. At any
>> rate, we can always go through the material in a more
>> leisurely fashion on the List.
>>
>> Looking back over many previous discussions, I think one
>> of the main things keeping people from being on the same
>> page, or even being able to understand what others write
>> on their individual pages, is the question of what makes
>> a relation.
>>
>> There's a big difference between a single ordered tuple, say,
>> (x_1, x_2, ..., x_k), and a whole set of ordered tuples that
>> it takes to make up a k-place relation. The language we use
>> to get a handle on the structure of relations goes like this:
>>
>> Say the variable x_1 ranges over the set X_1,
>> and the variable x_2 ranges over the set X_2,
>> ...
>> and the variable x_k ranges over the set X_k.
>>
>> Then the set of all possible k-tuples (x_1, x_2, ..., x_k)
>> ranges over a set that is notated as X_1 × X_2 × ... × X_k,
>> called the “cartesian product” of the “domains” X_1 to X_k.
>>
>> There are two different ways of defining
>> a k-place relation that are in common use:
>>
>> 1. Some define a relation L on the domains X_1 to X_k
>> as a subset of the cartesian product X_1 × ... × X_k,
>> in symbols, L ⊆ X_1 × ... × X_k.
>>
>> 2. Others like to make the domains of the relation
>> an explicit part of the definition, saying that
>> a relation L is a list of domains plus a subset
>> of their cartesian product.
>>
>> Sounds like a mess but it's usually pretty easy to
>> translate between the two conventions, so long as
>> one remains aware of difference.
>>
>> By way of a geometric image, we can picture the
>> cartesian product X_1 × ...

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

[kirstima]

Tom,list,

Well put, well put, indeed!

Also, I wish to remind you all, that CSP did not view lawa of nature as 
eternally unchangable. To his mind, tehy do change, albeit mostly very, 
very slowly.


Think about climate change. With it very, very slow changes meet changes 
with other time-scales.


Mother nature does not work  exaclty in the same ways it did by the time 
of our ancients.


Do remember CSP's work on the pendulum, as well.

Best regars,

Kirsti Määttänen



Thomas903 kirjoitti 17.4.2017 20:18:

Group ~

Going back to the original question, I believe a "law of nature" is
characterized differently, in terms of Sign relationships, depending
upon one of three ('ness) perspectives from which the "law of nature"
is being considered:

1 - To Peirce-Emerson-The Sphinx:  Existence consists solely of: (a)
objects which (b) behave logically. To Peirce, behaving logically is
the ONLY law of nature.  It is the unifying element of all of
existence, and represents ultimate Truth.

From this perspective (of ultimate Truth), phenomena labeled by Man as
"laws of nature" (such as the law of gravity) are physical potentials
of existence (firstness), which do not necessarily occur everywhere,
or in all times.

2 - To an object, like Man, affected by but unable to affect a "law of
nature," the law is a physical regularity in its environment that can
be counted on without fail.  It enters the Man's logic-decision
calculus as an object or brute force (secondness).

3 - Finally, the objects comprising the environment (i.e., the
environment responsible for the "law of nature" that Man perceives)
are themselves engaged in habitual-optimizing behaviors (thirdness).

These alternating perspectives for perceiving-assigning Signs carry
over to other objects, apart from "laws of nature."

For example, subatomic particles that obey Pragmatic Logic will in
certain environmental settings evolve into a uranium atom. In other
environments, those particles would have evolved into something else.
From this perspective, a "uranium atom" is a potential (firstness
Sign) of a universe of logical particles.

To Man, the uranium atom has specific-fixed physical qualities,
including decaying at a certain fixed/predictable rate. Here, the
uranium atom is an object, with a secondness Sign.

From the perspective of the particles comprising the uranium atom,
presently they are experiencing the optimizing relationship that
earlier evolved between them (thirdness).  However, having landed on
earth, the particles comprising the uranium atom find themselves in an
inhospitable environment (relative to that of the u-atom's "birth").
Therefore, the original habits of the particles are no longer optimal.
 The decay of the uranium atom represents a transition phase
(secondness activities), where the particles seek new optimizing
actives appropriate for their earth environment (thirdness).

Regards,
Tom Wyrick


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

[Thomas903]

Group ~

Going back to the original question, I believe a "law of nature" is
characterized differently, in terms of Sign relationships, depending upon
one of three ('ness) perspectives from which the "law of nature" is being
considered:

1 - To Peirce-Emerson-The Sphinx:  Existence consists solely of: (a)
objects which (b) behave logically. To Peirce, behaving logically is the
ONLY law of nature.  It is the unifying element of all of existence, and
represents ultimate Truth.

>From this perspective (of ultimate Truth), phenomena labeled by Man as
"laws of nature" (such as the law of gravity) are physical potentials of
existence (firstness), which do not necessarily occur everywhere, or in all
times.


2 - To an object, like Man, affected by but unable to affect a "law of
nature," the law is a physical regularity in its environment that can be
counted on without fail.  It enters the Man's logic-decision calculus as an
object or brute force (secondness).

3 - Finally, the objects comprising the environment (i.e., the environment
responsible for the "law of nature" that Man perceives) are themselves
engaged in habitual-optimizing behaviors (thirdness).


These alternating perspectives for perceiving-assigning Signs carry over to
other objects, apart from "laws of nature."

For example, subatomic particles that obey Pragmatic Logic will in certain
environmental settings evolve into a uranium atom. In other environments,
those particles would have evolved into something else.  From this
perspective, a "uranium atom" is a potential (firstness Sign) of a universe
of logical particles.

To Man, the uranium atom has specific-fixed physical qualities, including
decaying at a certain fixed/predictable rate. Here, the uranium atom is an
object, with a secondness Sign.

>From the perspective of the particles comprising the uranium atom,
presently they are experiencing the optimizing relationship that earlier
evolved between them (thirdness).  However, having landed on earth, the
particles comprising the uranium atom find themselves in an inhospitable
environment (relative to that of the u-atom's "birth").  Therefore, the
original habits of the particles are no longer optimal.  The decay of the
uranium atom represents a transition phase (secondness activities), where
the particles seek new optimizing actives appropriate for their earth
environment (thirdness).


Regards,
Tom Wyrick


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

[Jon Awbrey]

Helmut, List ...

The difference between the two definitions is sometimes
described as “decontextualized” versus “contextualized”
or, in computerese, “weak typing” versus “strong typing”.
The second definition is typically expressed by means of
a peculiar mathematical idiom that starts out as follows:

“A k-place relation is a k+1-tuple (X_1, …, X_k, L) …”

That way of defining relations is a natural generalization
of the way functions are defined in the mathematical subject
of category theory, where the “domain” X and the “codomain” Y
share in defining the “type” X → Y of the function f : X → Y.

The threshold between “arbitrary”, “artificial”, “random” kinds of
relations and those selected for due consideration as “reasonable”,
“proper”, “natural” kinds tends to shift from context to context.
We usually have in mind some property or quality that marks the
latter class as “proper” objects of contemplation relative to
the end in view, and so this relates to the intensional view
of subject matters.

Regards,

Jon

On 4/15/2017 2:49 PM, Helmut Raulien wrote:
> Jon, List,
> Thank you, Jon! Your point No. 2 is new to me, that some
> define relation not only as the subset of the domains'
> cartesian product, but as that plus a list of the domains.
>
> In case the subset is not a random one, but a consequence
> of some reasonable classification, eg. in a dyadic relation:
> "x_1 < x_2", what is this term "x_1 < x_2" called then?
> I am asking, because I think, that in common language this
> is what people might understand as relation.  I had called
> it "relation reason" before.
> Best,
> Helmut
>
> 15 April 2017 um 16:30 Uhr
>> "Jon Awbrey"  wrote:
>> Helmut, List,
>>
>> Looking over those articles with fresh eyes this morning
>> I see they are rather thick with abstract generalities at
>> the beginning and it would be better to skip down to the
>> concrete examples on a first run-through. I promise to
>> keep that in mind the next time I rewrite them. At any
>> rate, we can always go through the material in a more
>> leisurely fashion on the List.
>>
>> Looking back over many previous discussions, I think one
>> of the main things keeping people from being on the same
>> page, or even being able to understand what others write
>> on their individual pages, is the question of what makes
>> a relation.
>>
>> There's a big difference between a single ordered tuple, say,
>> (x_1, x_2, ..., x_k), and a whole set of ordered tuples that
>> it takes to make up a k-place relation. The language we use
>> to get a handle on the structure of relations goes like this:
>>
>> Say the variable x_1 ranges over the set X_1,
>> and the variable x_2 ranges over the set X_2,
>> ...
>> and the variable x_k ranges over the set X_k.
>>
>> Then the set of all possible k-tuples (x_1, x_2, ..., x_k)
>> ranges over a set that is notated as X_1 × X_2 × ... × X_k,
>> called the “cartesian product” of the “domains” X_1 to X_k.
>>
>> There are two different ways of defining
>> a k-place relation that are in common use:
>>
>> 1. Some define a relation L on the domains X_1 to X_k
>> as a subset of the cartesian product X_1 × ... × X_k,
>> in symbols, L ⊆ X_1 × ... × X_k.
>>
>> 2. Others like to make the domains of the relation
>> an explicit part of the definition, saying that
>> a relation L is a list of domains plus a subset
>> of their cartesian product.
>>
>> Sounds like a mess but it's usually pretty easy to
>> translate between the two conventions, so long as
>> one remains aware of difference.
>>
>> By way of a geometric image, we can picture the
>> cartesian product X_1 × ... × X_k as a space in
>> which many different relations reside, each one
>> cutting a different figure in that space.
>>
>> To be continued ...
>>
>> Jon
>>
>> On 4/15/2017 12:00 AM, Jon Awbrey wrote:
>>> Helmut, List,
>>>
>>> I think it would be a good idea to continue reviewing basic concepts
>>> and get better acquainted with the relational context that is needed
>>> to ground all the higher order functions, properties, and structures
>>> we might wish to think about. Once we understand what relations are
>>> then we can narrow down to triadic relations and then sign relations
>>> will fall more easily within our grasp.
>>>
>>> I've written up intros to these topics many times before, and you
>>> can find my latest editions, if still very much works in progress,
>>> on the InterSciWiki site, though in this case it may be preferable
>>> to take them up in order from special to general:
>>>
>>> Sign Relations
>>> http://intersci.ss.uci.edu/wiki/index.php/Sign_relation
>>>
>>> Triadic Relations
>>> http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation
>>>
>>> Relation Theory
>>> http://intersci.ss.uci.edu/wiki/index.php/Relation_theory
>>>
>>> I think most of the material you mentioned on Relational Reducibility,
>>> Compositional and Projective, is summarized in the following article:
>>>
>>> Relation Reduction
>>> http://intersci.ss.uci.edu/wiki/index.php/Rel

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

[Helmut Raulien]

Jon, List,

Thank you, Jon! Your point No. 2 is new to me, that some define relation not only as the subset of the domainses´ cartesian product, but as that plus a list of the domains.

In case the subset is not a random one, but a consequence of some reasonable classification, eg. in a dyadic relation: "x_1 < x_2", what is this term "x_1 < x_2" called then? I am asking, because I think, that in common language this is what people might understand as relation. I had called it "relation reason" before.

Best,

Helmut

 

 15. April 2017 um 16:30 Uhr
 "Jon Awbrey"  wrote:
 

Helmut, List,

Looking over those articles with fresh eyes this morning
I see they are rather thick with abstract generalities at
the beginning and it would be better to skip down to the
concrete examples on a first run-through. I promise to
keep that in mind the next time I rewrite them. At any
rate, we can always go through the material in a more
leisurely fashion on the List.

Looking back over many previous discussions, I think one
of the main things keeping people from being on the same
page, or even being able to understand what others write
on their individual pages, is the question of what makes
a relation.

There's a big difference between a single ordered tuple, say,
(x_1, x_2, ..., x_k), and a whole set of ordered tuples that
it takes to make up a k-place relation. The language we use
to get a handle on the structure of relations goes like this:

Say the variable x_1 ranges over the set X_1,
and the variable x_2 ranges over the set X_2,
and ...
and the variable x_k ranges over the set X_k.

Then the set of all possible k-tuples (x_1, x_2, ..., x_k)
ranges over a set that is notated as X_1 × X_2 × ... × X_k,
called the “cartesian product” of the “domains” X_1 to X_k.

There are two different ways of defining
a k-place relation that are in common use:

1. Some define a relation L on the domains X_1 to X_k
as a subset of the cartesian product X_1 × ... × X_k,
in symbols, L ⊆ X_1 × ... × X_k.

2. Others like to make the domains of the relation
an explicit part of the definition, saying that
a relation L is a list of domains plus a subset
of their cartesian product.

Sounds like a mess but it's usually pretty easy to
translate between the two conventions, so long as
one remains aware of difference.

By way of a geometric image, we can picture the
cartesian product X_1 × ... × X_k as a space in
which many different relations reside, each one
cutting a different figure in that space.

To be continued ...

Jon

On 4/15/2017 12:00 AM, Jon Awbrey wrote:
> Helmut, List,
>
> I think it would be a good idea to continue reviewing basic concepts
> and get better acquainted with the relational context that is needed
> to ground all the higher order functions, properties, and structures
> we might wish to think about. Once we understand what relations are
> then we can narrow down to triadic relations and then sign relations
> will fall more easily within our grasp.
>
> I've written up intros to these topics many times before, and you
> can find my latest editions, if still very much works in progress,
> on the InterSciWiki site, though in this case it may be preferable
> to take them up in order from special to general:
>
> Sign Relations
> http://intersci.ss.uci.edu/wiki/index.php/Sign_relation
>
> Triadic Relations
> http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation
>
> Relation Theory
> http://intersci.ss.uci.edu/wiki/index.php/Relation_theory
>
> I think most of the material you mentioned on Relational Reducibility,
> Compositional and Projective, is summarized in the following article:
>
> Relation Reduction
> http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction
>
> Regards,
>
> Jon
>

--

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

[Jon Awbrey]

Helmut, List,

Looking over those articles with fresh eyes this morning
I see they are rather thick with abstract generalities at
the beginning and it would be better to skip down to the
concrete examples on a first run-through.  I promise to
keep that in mind the next time I rewrite them.  At any
rate, we can always go through the material in a more
leisurely fashion on the List.

Looking back over many previous discussions, I think one
of the main things keeping people from being on the same
page, or even being able to understand what others write
on their individual pages, is the question of what makes
a relation.

There's a big difference between a single ordered tuple, say,
(x_1, x_2, ..., x_k), and a whole set of ordered tuples that
it takes to make up a k-place relation.  The language we use
to get a handle on the structure of relations goes like this:

Say the variable x_1 ranges over the set X_1,
and the variable x_2 ranges over the set X_2,
and ...
and the variable x_k ranges over the set X_k.

Then the set of all possible k-tuples (x_1, x_2, ..., x_k)
ranges over a set that is notated as X_1 × X_2 × ... × X_k,
called the “cartesian product” of the “domains” X_1 to X_k.

There are two different ways of defining
a k-place relation that are in common use:

1.  Some define a relation L on the domains X_1 to X_k
as a subset of the cartesian product X_1 × ... × X_k,
in symbols, L ⊆ X_1 × ... × X_k.

2.  Others like to make the domains of the relation
an explicit part of the definition, saying that
a relation L is a list of domains plus a subset
of their cartesian product.

Sounds like a mess but it's usually pretty easy to
translate between the two conventions, so long as
one remains aware of difference.

By way of a geometric image, we can picture the
cartesian product X_1 × ... × X_k as a space in
which many different relations reside, each one
cutting a different figure in that space.

To be continued ...

Jon

On 4/15/2017 12:00 AM, Jon Awbrey wrote:

Helmut, List,

I think it would be a good idea to continue reviewing basic concepts
and get better acquainted with the relational context that is needed
to ground all the higher order functions, properties, and structures
we might wish to think about.  Once we understand what relations are
then we can narrow down to triadic relations and then sign relations
will fall more easily within our grasp.

I've written up intros to these topics many times before, and you
can find my latest editions, if still very much works in progress,
on the InterSciWiki site, though in this case it may be preferable
to take them up in order from special to general:

Sign Relations
http://intersci.ss.uci.edu/wiki/index.php/Sign_relation

Triadic Relations
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation

Relation Theory
http://intersci.ss.uci.edu/wiki/index.php/Relation_theory

I think most of the material you mentioned on Relational Reducibility,
Compositional and Projective, is summarized in the following article:

Relation Reduction
http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction

Regards,

Jon



--

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

[Jon Awbrey]

Helmut, List,

I think it would be a good idea to continue reviewing basic concepts
and get better acquainted with the relational context that is needed
to ground all the higher order functions, properties, and structures
we might wish to think about.  Once we understand what relations are
then we can narrow down to triadic relations and then sign relations
will fall more easily within our grasp.

I've written up intros to these topics many times before, and you
can find my latest editions, if still very much works in progress,
on the InterSciWiki site, though in this case it may be preferable
to take them up in order from special to general:

Sign Relations
http://intersci.ss.uci.edu/wiki/index.php/Sign_relation

Triadic Relations
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation

Relation Theory
http://intersci.ss.uci.edu/wiki/index.php/Relation_theory

I think most of the material you mentioned on Relational Reducibility,
Compositional and Projective, is summarized in the following article:

Relation Reduction
http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction

Regards,

Jon

On 4/14/2017 8:59 AM, Helmut Raulien wrote:

Jon, List,
Thank you for having found the thread from long ago!  I think,
what often is confusing, that we, when we read "relation", think
of a connection merely, like a spoke of the triad.  But in the case
of sign relations, I think, "relation" means:  Kind of connection.  So
"legisign" is a kind of connection of the representamen/sign with itself.
Perhaps this may also be said like:  A kind of representamen/sign.
"Symbol" is a kind of connection between the representamen/sign
and the object, usually called "object relation of the sign".
Best,
Helmut


14. April 2017 um 05:48 Uhr
"Jon Awbrey"  wrote:
Helmut, List ...

Given that sign relations are special cases of triadic relations,
we can get significant insight into the structures of both cases
by examining a few simple examples of triadic relations, without
getting distracted by all the extra features that come into play
with sign relations.

When I'm talking about a k-place relation L I will always be
thinking about a set of k-tuples. Each k-tuple has the form:

(x_1, x_2, ..., x_(k-1), x_k),

or, as Peirce often wrote them:

x_1 : x_2 : ... : x_(k-1) : x_k.

Of course, L could be a set of 1 k-tuple,
but that would be counted a trivial case.

That sums up the extensional view of k-place relations.

Using a single letter like “L” to refer to that set of
k-tuples is already the genesis of an intensional view,
since we now think of the elements of L as having some
property in common, even if it's only their membership
in L. When we turn to devising some sort of formalism
for working with relations in general, whether it's an
algebra, logical calculus, or graph-theoretic notation,
it's in the nature of the task to “unify the manifold”,
to represent a many as a one, to express a set of many
tuples by means of a single sign. That can be a great
convenience, producing formalisms of significant power,
but failing to discern the many in the one can lead to
no end of confusion.

It's late ...
more later ...

Jon

On 4/13/2017 8:08 PM, Jon Awbrey wrote:


Helmut, List,

Yes, I think that something in that vicinity might be
what's causing people so much trouble with this topic.

Let me just review a few things ...

One thing I always say at these junctures is that people really ought
to take Peirce's advice and study his logic of relative terms and its
relation to what most math and computer sci folks these days would call
the mathematical theory of relations. Personally I find his 1870 Logic
of Relatives very instructive, partly because he gives such concrete and
simple examples of every abstract abstrusity and (2) because he maintains
a healthy balance between the extensional and intensional views of things,
drawing on both our empiricist and rationalist ways of thinking. Thereby
hangs another problem people often have with understanding Peirce's logic
and semiotics. We have what might be called diverse “cognitive styles” or
“intellectual inclinations” that range or swing between the above two poles.
I doubt if there's anything like pure types in the human arena, but thinkers
do tend to lean in one direction or the other, at least, at any given moment.
As a rule, though, we are almost always operating at two different levels of
abstraction, whether we are aware of it or not, and our task is to get better
at doing that, through increased awareness of how thought works. There is the
level of intension, or rational concepts, and there is the level of extension,
or empirical cases.

Well, the striking of the grandfather clock tells me
it's time for Big Bang Theory, so I'll have to break ...

Regards,

Jon

On 4/13/2017 3:45 PM, Helmut Raulien wrote:

Jon [A. Schmidt], List,

You wrote:

“To be honest, given that the Sign relation
is genuinely /triadic/, I have never fully
understood why Peirce initially classified
Signs on the

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

[Helmut Raulien]

Jon, List,

Thank you for having found the thread from long ago!

I think, what often is confusing, that we, when we read "relation", think of a connection merely, like a spoke of the triad. But in the case of sign relations, I think, "relation" means: Kind of connection. So "legisign" is a kind of connection of the representamen/sign with itself. Perhaps this may also be said like: A kind of representamen/sign. "Symbol" is a kind of connection between the representamen/sign and the object, usually called "object relation of the sign".


Best,

Helmut


 14. April 2017 um 05:48 Uhr
 "Jon Awbrey"  wrote:
 

Helmut, List ...

Given that sign relations are special cases of triadic relations,
we can get significant insight into the structures of both cases
by examining a few simple examples of triadic relations, without
getting distracted by all the extra features that come into play
with sign relations.

When I'm talking about a k-place relation L I will always be
thinking about a set of k-tuples. Each k-tuple has the form:

(x_1, x_2, ..., x_(k-1), x_k),

or, as Peirce often wrote them:

x_1 : x_2, ..., x_(k-1) : x_k.

Of course, L could be a set of 1 k-tuple,
but that would be counted a trivial case.

That sums up the extensional view of k-place relations.

Using a single letter like “L” to refer to that set of
k-tuples is already the genesis of an intensional view,
since we now think of the elements of L as having some
property in common, even if it's only their membership
in L. When we turn to devising some sort of formalism
for working with relations in general, whether it's an
algebra, logical calculus, or graph-theoretic notation,
it's in the nature of the task to “unify the manifold”,
to represent a many as a one, to express a set of many
tuples by means of a single sign. That can be a great
convenience, producing formalisms of significant power,
but failing to discern the many in the one can lead to
no end of confusion.

It's late ...
more later ...

Jon

On 4/13/2017 8:08 PM, Jon Awbrey wrote:
>
> Helmut, List,
>
> Yes, I think that something in that vicinity might be
> what's causing people so much trouble with this topic.
>
> Let me just review a few things ...
>
> One thing I always say at these junctures is that people really ought
> to take Peirce's advice and study his logic of relative terms and its
> relation to what most math and computer sci folks these days would call
> the mathematical theory of relations. Personally I find his 1870 Logic
> of Relatives very instructive, partly because he gives such concrete and
> simple examples of every abstract abstrusity and (2) because he maintains
> a healthy balance between the extensional and intensional views of things,
> drawing on both our empiricist and rationalist ways of thinking. Thereby
> hangs another problem people often have with understanding Peirce's logic
> and semiotics. We have what might be called diverse “cognitive styles” or
> “intellectual inclinations” that range or swing between the above two poles.
> I doubt if there's anything like pure types in the human arena, but thinkers
> do tend to lean in one direction or the other, at least, at any given moment.
> As a rule, though, we are almost always operating at two different levels of
> abstraction, whether we are aware of it or not, and our task is to get better
> at doing that, through increased awareness of how thought works. There is the
> level of intension, or rational concepts, and there is the level of extension,
> or empirical cases.
>
> Well, the striking of the grandfather clock tells me
> it's time for Big Bang Theory, so I'll have to break ...
>
> Regards,
>
> Jon
>
> On 4/13/2017 3:45 PM, Helmut Raulien wrote:
>> Jon [A. Schmidt], List,
>>
>> You wrote:
>>
>> “To be honest, given that the Sign relation
>> is genuinely /triadic/, I have never fully
>> understood why Peirce initially classified
>> Signs on the basis of one correlate and two
>> /dyadic /relations. Perhaps others on the
>> List can shed some light on that.”
>>
>> I have a guess about that: I remember from a thread
>> with Jon Awbrey about relation reduction something
>> like the following:
>>
>> A triadic relation is called irreducible, because
>> it cannot compositionally be reduced to three dyadic
>> relations. Compositional reduction is the real kind
>> of reduction. But there is another kind of reduction,
>> called projective (or projectional?) reduction, which
>> is a kind of consolation prize for people, who want to
>> reduce. It is possible for some triadic relations.
>>
>> Now a triadic relation, say, (S,O,I) might be
>> reduced projectionally to (S,O), (O,I), (I,S).
>>
>> My guess is now, that Peirce uses another kind
>> of projectional reduction: (S,S), (S,O), (S,I).
>>
>> It is only a guess, because I am not a mathematician.
>> But at least I would say, that mathematically a relation
>> with itself is possible, so the representamen relation
>> can be called relation too, instead of correl

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

[Jon Awbrey]

Helmut, List ...

Given that sign relations are special cases of triadic relations,
we can get significant insight into the structures of both cases
by examining a few simple examples of triadic relations, without
getting distracted by all the extra features that come into play
with sign relations.

When I'm talking about a k-place relation L I will always be
thinking about a set of k-tuples.  Each k-tuple has the form:

(x_1, x_2, ..., x_(k-1), x_k),

or, as Peirce often wrote them:

x_1 : x_2, ..., x_(k-1) : x_k.

Of course, L could be a set of 1 k-tuple,
but that would be counted a trivial case.

That sums up the extensional view of k-place relations.

Using a single letter like “L” to refer to that set of
k-tuples is already the genesis of an intensional view,
since we now think of the elements of L as having some
property in common, even if it's only their membership
in L.  When we turn to devising some sort of formalism
for working with relations in general, whether it's an
algebra, logical calculus, or graph-theoretic notation,
it's in the nature of the task to “unify the manifold”,
to represent a many as a one, to express a set of many
tuples by means of a single sign.  That can be a great
convenience, producing formalisms of significant power,
but failing to discern the many in the one can lead to
no end of confusion.

It's late ...
more later ...

Jon

On 4/13/2017 8:08 PM, Jon Awbrey wrote:


Helmut, List,

Yes, I think that something in that vicinity might be
what's causing people so much trouble with this topic.

Let me just review a few things ...

One thing I always say at these junctures is that people really ought
to take Peirce's advice and study his logic of relative terms and its
relation to what most math and computer sci folks these days would call
the mathematical theory of relations.  Personally I find his 1870 Logic
of Relatives very instructive, partly because he gives such concrete and
simple examples of every abstract abstrusity and (2) because he maintains
a healthy balance between the extensional and intensional views of things,
drawing on both our empiricist and rationalist ways of thinking.  Thereby
hangs another problem people often have with understanding Peirce's logic
and semiotics.  We have what might be called diverse “cognitive styles” or
“intellectual inclinations” that range or swing between the above two poles.
I doubt if there's anything like pure types in the human arena, but thinkers
do tend to lean in one direction or the other, at least, at any given moment.
As a rule, though, we are almost always operating at two different levels of
abstraction, whether we are aware of it or not, and our task is to get better
at doing that, through increased awareness of how thought works.  There is the
level of intension, or rational concepts, and there is the level of extension,
or empirical cases.

Well, the striking of the grandfather clock tells me
it's time for Big Bang Theory, so I'll have to break ...

Regards,

Jon

On 4/13/2017 3:45 PM, Helmut Raulien wrote:

Jon [A. Schmidt], List,

You wrote:

“To be honest, given that the Sign relation
is genuinely /triadic/, I have never fully
understood why Peirce initially classified
Signs on the basis of one correlate and two
/dyadic /relations.  Perhaps others on the
List can shed some light on that.”

I have a guess about that: I remember from a thread
with Jon Awbrey about relation reduction something
like the following:

A triadic relation is called irreducible, because
it cannot compositionally be reduced to three dyadic
relations.  Compositional reduction is the real kind
of reduction.  But there is another kind of reduction,
called projective (or projectional?) reduction, which
is a kind of consolation prize for people, who want to
reduce.  It is possible for some triadic relations.

Now a triadic relation, say, (S,O,I) might be
reduced projectionally to (S,O), (O,I), (I,S).

My guess is now, that Peirce uses another kind
of projectional reduction:  (S,S), (S,O), (S,I).

It is only a guess, because I am not a mathematician.
But at least I would say, that mathematically a relation
with itself is possible, so the representamen relation
can be called relation too, instead of correlate.

Best,
Helmut




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http://www.cspeirce.com/peirce-l/peirce-l.htm .

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

[Jon Awbrey]

Thread:
JAS:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00080.html
JA:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00088.html
HR:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00200.html
JAS:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00202.html
JAS:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00203.html
GR:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00204.html
HR:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00205.html
HR:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00210.html

Helmut, List,

Yes, I think that something in that vicinity might be
what's causing people so much trouble with this topic.

Let me just review a few things ...

One thing I always say at these junctures is that people really ought
to take Peirce's advice and study his logic of relative terms and its
relation to what most math and computer sci folks these days would call
the mathematical theory of relations.  Personally I find his 1870 Logic
of Relatives very instructive, partly because he gives such concrete and
simple examples of every abstract abstrusity and (2) because he maintains
a healthy balance between the extensional and intensional views of things,
drawing on both our empiricist and rationalist ways of thinking.  Thereby
hangs another problem people often have with understanding Peirce's logic
and semiotics.  We have what might be called diverse “cognitive styles” or
“intellectual inclinations” that range or swing between the above two poles.
I doubt if there's anything like pure types in the human arena, but thinkers
do tend to lean in one direction or the other, at least, at any given moment.
As a rule, though, we are almost always operating at two different levels of
abstraction, whether we are aware of it or not, and our task is to get better
at doing that, through increased awareness of how thought works.  There is the
level of intension, or rational concepts, and there is the level of extension,
or empirical cases.

Well, the striking of the grandfather clock tells me
it's time for Big Bang Theory, so I'll have to break ...

Regards,

Jon

On 4/13/2017 3:45 PM, Helmut Raulien wrote:
> Jon [A. Schmidt], List,
>
> You wrote:
>
> “To be honest, given that the Sign relation
> is genuinely /triadic/, I have never fully
> understood why Peirce initially classified
> Signs on the basis of one correlate and two
> /dyadic /relations.  Perhaps others on the
> List can shed some light on that.”
>
> I have a guess about that: I remember from a thread
> with Jon Awbrey about relation reduction something
> like the following:
>
> A triadic relation is called irreducible, because
> it cannot compositionally be reduced to three dyadic
> relations.  Compositional reduction is the real kind
> of reduction.  But there is another kind of reduction,
> called projective (or projectional?) reduction, which
> is a kind of consolation prize for people, who want to
> reduce.  It is possible for some triadic relations.
>
> Now a triadic relation, say, (S,O,I) might be
> reduced projectionally to (S,O), (O,I), (I,S).
>
> My guess is now, that Peirce uses another kind
> of projectional reduction:  (S,S), (S,O), (S,I).
>
> It is only a guess, because I am not a mathematician.
> But at least I would say, that mathematically a relation
> with itself is possible, so the representamen relation
> can be called relation too, instead of correlate.
>
> Best,
> Helmut

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

[kirstima]

Jon,

Whilst I agree with your points on what must be taken seriously, there 
remains serious problems with understanding understanding.


Your approach comes from information theoretical viewpoint. Which relies 
on bits. Not so human understanding.


All information theories rely on a certain kind of view of human mind. 
Which has been prevalent hundreds of years, during all modernity.


I am not sying that what you write goes wrong or anything like that. I 
admire your meticulous logical consistency.


What I am saying is that its aplicability seem to me limited. Just like 
Euclidean geometry is still as valid as ever, but the view on its 
applicability has changed.


If the limits are taken as a serious problem to ponder, I'm all fore 
your work.


Regards,

Kirsti
Information may be tranmitted from machine to machine, but human minds 
do not take in information like a mail package.





Jon Awbrey kirjoitti 12.4.2017 16:46:

Kirsti, List ...

I put a slightly clearer version of my last post on my blog:

https://inquiryintoinquiry.com/2017/04/10/icon-index-symbol-%e2%80%a2-3/

I posted in under the Icon Index Symbol rubric
as those two questions ran together in my mind.

I appended a few resources on sign relations,
triadic realtions, semiotic information, and
Peirce's logic of information that may be of
use to inquiring minds.

Regards,

Jon



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

[Jon Awbrey]

Clark, List ...

It's the sort of thing everyone knew when I first started working
with (what were then called) “very large data bases” (VLDBs) back
in the late 70s.  I think there's a genealogy that goes straight
from Ted Codd to Arthur Burks to Peirce.  Seems like I recall
John Sowa wrote more on this somewhere.

Random Bit Off The Internet:

http://amturing.acm.org/award_winners/codd_1000892.cfm

Regards,

Jon

On 4/12/2017 12:33 PM, Clark Goble wrote:



On Apr 12, 2017, at 9:30 AM, Jon Awbrey  wrote:

I'm guessing an engineer would have some acquaintance with
relational databases, which have after all a history going
back to Peirce, and I would recommend keeping that example
in mind for thinking about k-adic relations in general.


I didn’t know that. Was the computer science that developed relational 
databases engaging with Peirce explicitly? Any good place to get a primer on 
that history?



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

[Jon Awbrey]

Jon,

I'm guessing an engineer would have some acquaintance with
relational databases, which have after all a history going
back to Peirce, and I would recommend keeping that example
in mind for thinking about k-adic relations in general.

I wrote a number of introductions to relation theory,
triadic relations, and sign relations in that vein,
for example, here:

Relation Theory
http://intersci.ss.uci.edu/wiki/index.php/Relation_theory

Triadic Relations
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation

Sign Relations
http://intersci.ss.uci.edu/wiki/index.php/Sign_relation

Regards,

Jon

On 4/12/2017 10:14 AM, Jon Alan Schmidt wrote:
> List:
>
> I was finally able to borrow Aaron Bruce Wilson's new book,
> *Peirce's Empiricism:  Its Roots and Its Originality*, via
> interlibrary loan this week.  Previously I could only access
> the Google preview, but from that I could tell that the whole
> thing would be well worth reading.  He points out in chapter 2
> that a law of nature is a *relation*, which leads me to pose a
> new question — can a relation be a Sign?  Again, I am referring
> to the relation *itself*, not its representation in verbal,
> diagrammatic, or other form.
>
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Professional Engineer, Amateur Philosopher, Lutheran Layman
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>

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

[Jon Awbrey]

Kirsti, List ...

I put a slightly clearer version of my last post on my blog:

https://inquiryintoinquiry.com/2017/04/10/icon-index-symbol-%e2%80%a2-3/

I posted in under the Icon Index Symbol rubric
as those two questions ran together in my mind.

I appended a few resources on sign relations,
triadic realtions, semiotic information, and
Peirce's logic of information that may be of
use to inquiring minds.

Regards,

Jon

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

[Jon Awbrey]

Kirsti, List ...

I put a slightly clearer version of my last post on my blog:

https://inquiryintoinquiry.com/2017/04/10/icon-index-symbol-%e2%80%a2-3/

I posted it under the Icon Index Symbol rubric
as those two questions ran together in my mind.

I appended a few resources on sign relations,
triadic realtions, semiotic information, and
Peirce's logic of information that may be of
use to inquiring minds.

Regards,

Jon

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

[Jon Awbrey]

Kirsti,

Thanks for the notice.

Of course that setup is barely a beginning.

It is only the grounds out of which understanding must grow,
IF our understanding is to proceed on these two conditions:

MAT. We take the methods and tools that C.S. Peirce gave us seriously.
COR. We take the context of research in scientific inquiry seriously.

In practice, of course, we do not take the whole actual universe U
as our starting point, but begin by constructing concrete examples
of systems, say, a system defined by its state space X, and we try
to determine what sort of conditions X must satisfy in order for X
to possess any sort of representation at all of its own structure.

That is the sort of thing has been investigated a lot when it comes
to ordinary sorts of axiom systems and computational systems, where
people speak of the system having a “reflective property” but there
needs to be much more work done with reflection in semiotic systems.

Regards,

Jon

On 4/10/2017 9:25 AM, kirst...@saunalahti.fi wrote:

Jon A.

Seems valid to me. But it does not answer the quest for understanding. - If you 
see my point.

Kirsti

Jon Awbrey kirjoitti 7.4.2017 02:02:

Jon, List ...

I've mentioned the following possibility several times before, but
maybe not too recently.

A sign relation L is a subset of a cartesian product O×S×I, where O,
S, I are the object, sign, interpretant domains, respectively. In a
systems-theoretic framework we may think of these domains as dynamical
systems.

We often work with sign relations where S = I but it is entirely
possible to consider sign relations where all three domains are one
and the same. Indeed, we could have O=S=I=U, where the system U is the
entire universe. This would make the entire universe a sign of itself
to itself.

A very general way to understand a system-theoretic law is in terms of
a constraint — the fact that not everything that might happen
actually does. And that is nothing but a subset relation.

So the law embodying how the universe represents itself to itself
could be nothing other than a sign relation L ⊆ U×U×U.

Regards,

Jon

http://inquiryintoinquiry.com [3]

On Apr 6, 2017, at 3:36 PM, Jon Alan Schmidt
 wrote:


List:

With the discussions going on in a couple of threads about semeiosis
in the physico-chemical and biological realms, a question occurred
to me. What class of Sign is a law of nature? I am not referring to
how we _describe_ a law of nature in human language, an equation, or
other _representation_ of it; I am talking about the law of nature
_itself_, the real general that governs actual occurrences.

As a law, it presumably has to be a Legisign. What is its Dynamic
Object--the inexhaustible continuum of its _potential_
instantiations, perhaps? How should we characterize its S-O
relation? It is not conventional (Symbol), so is it an existential
connection (Index)? What is its Dynamic Interpretant--any given
_actual _instantiation, perhaps? How should we characterize its S-I
relation--Dicent, like a proposition, or Rheme, like a term?

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt [1] - twitter.com/JonAlanSchmidt
[2]



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

[kirstima]

Jon A.

Seems valid to me. But it does not answer the quest for understanding. - 
If you see my point.


Kirsti

Jon Awbrey kirjoitti 7.4.2017 02:02:

Jon, List ...

I've mentioned the following possibility several times before, but
maybe not too recently.

A sign relation L is a subset of a cartesian product O×S×I, where O,
S, I are the object, sign, interpretant domains, respectively. In a
systems-theoretic framework we may think of these domains as dynamical
systems.

We often work with sign relations where S = I but it is entirely
possible to consider sign relations where all three domains are one
and the same. Indeed, we could have O=S=I=U, where the system U is the
entire universe. This would make the entire universe a sign of itself
to itself.

A very general way to understand a system-theoretic law is in terms of
a constraint — the fact that not everything that might happen
actually does. And that is nothing but a subset relation.

So the law embodying how the universe represents itself to itself
could be nothing other than a sign relation L ⊆ U×U×U.

Regards,

Jon

http://inquiryintoinquiry.com [3]

On Apr 6, 2017, at 3:36 PM, Jon Alan Schmidt
 wrote:


List:

With the discussions going on in a couple of threads about semeiosis
in the physico-chemical and biological realms, a question occurred
to me. What class of Sign is a law of nature? I am not referring to
how we _describe_ a law of nature in human language, an equation, or
other _representation_ of it; I am talking about the law of nature
_itself_, the real general that governs actual occurrences.

As a law, it presumably has to be a Legisign. What is its Dynamic
Object--the inexhaustible continuum of its _potential_
instantiations, perhaps? How should we characterize its S-O
relation? It is not conventional (Symbol), so is it an existential
connection (Index)? What is its Dynamic Interpretant--any given
_actual _instantiation, perhaps? How should we characterize its S-I
relation--Dicent, like a proposition, or Rheme, like a term?

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt [1] - twitter.com/JonAlanSchmidt
[2]



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

[Jon Awbrey]

Jon, List ...

I've mentioned the following possibility several times before, but maybe not 
too recently. 

A sign relation L is a subset of a cartesian product O×S×I, where O, S, I are 
the object, sign, interpretant domains, respectively.  In a systems-theoretic 
framework we may think of these domains as dynamical systems.

We often work with sign relations where S = I but it is entirely possible to 
consider sign relations where all three domains are one and the same. Indeed, 
we could have O=S=I=U, where the system U is the entire universe. This would 
make the entire universe a sign of itself to itself.

A very general way to understand a system-theoretic law is in terms of a 
constraint — the fact that not everything that might happen actually does.  And 
that is nothing but a subset relation. 

So the law embodying how the universe represents itself to itself could be 
nothing other than a sign relation L ⊆ U×U×U.

Regards,

Jon

http://inquiryintoinquiry.com

> On Apr 6, 2017, at 3:36 PM, Jon Alan Schmidt  wrote:
> 
> List:
> 
> With the discussions going on in a couple of threads about semeiosis in the 
> physico-chemical and biological realms, a question occurred to me.  What 
> class of Sign is a law of nature?  I am not referring to how we describe a 
> law of nature in human language, an equation, or other representation of it; 
> I am talking about the law of nature itself, the real general that governs 
> actual occurrences.
> 
> As a law, it presumably has to be a Legisign.  What is its Dynamic 
> Object--the inexhaustible continuum of its potential instantiations, perhaps? 
>  How should we characterize its S-O relation?  It is not conventional 
> (Symbol), so is it an existential connection (Index)?  What is its Dynamic 
> Interpretant--any given actual instantiation, perhaps?  How should we 
> characterize its S-I relation--Dicent, like a proposition, or Rheme, like a 
> term?
> 
> Regards,
> 
> Jon Alan Schmidt - Olathe, Kansas, USA
> Professional Engineer, Amateur Philosopher, Lutheran Layman
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

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