[PEIRCE-L] Aw: Re: Elementary Relatives or Individual Relatives

Tue, 08 Dec 2015 08:44:31 -0800

 
Jon, list,
thank you, Jon. Your example is less complicated than mine was. So the elementary relation does not determine the general relation or general relative term. So, both, elementary and general relation do not have a token-type- connection with each other, I think. So it is confusing to me, that both are called "relation". In mathematics, I think, an actual subset of a cartesian product is a relation. This seems like secondness to me. The term "smaller than" is a relative term, I guess. This seems like firstness or thirdness to me, depending on whether it is the reason for (ground of, quality of) an actual subset, or the interpretation of this actual subset.
Best,
Helmut
 08. Dezember 2015 um 02:08 Uhr
"Jon Awbrey" <[email protected]> wrote:
 
 
Helmut, 
 
I think a few people are making this harder than it needs to be.
 
Let's put aside potential subtleties about elementary vs. individual vs. infinitesimal relatives and simply use “elementary relative” to cover them all at a first approximation. One of the advantages of this usage is that it allows us to exploit a very close analogy with the way “elementary transformations” function in linear algebra, affording a bridge to practical applications of semiotics.
 
Let's make a concrete example. Say we have a universe of discourse X = biblical characters.
 
Linguistic phrases like “brother of___” or “x is y's brother” and many others can be used to indicate a dyadic relation B forming a subset of X x X such that (x, y) is in B if a only if x is a brother of y.
 
I will use Peirce's notation x:y for the ordered pair (x, y). Among other things it's easier to type on the phone. 
 
In the universe X of biblical characters, Abel : Cain is an elementary relation in the brotherhood relation B.
 
But Abel : Cain also belongs to the relation E indicated by “elder brother of" and again to the relation V indicated by “victim of”.  So the elementary relation by itself does not determine the general relation or general relative term that we may chose to consider it under.
 
This means that classifying relations is a task at a categorically higher level than classifying elementary relations.
 
In the special case of triadic sign relations, almost all the literature so far has tackled only the case of elementary sign relations.
 
Regards,
 
Jon On Dec 3, 2015, at 5:52 PM, Helmut Raulien <[email protected]> wrote:
 
Hi Jon, All,
I dont want to interrupt the discussion about terms, but I have a question that is about the mathematical relation- but I think this consideration might be expanded to semantics and semiotics. In mathematics, I have read somewhere, a relation is a subset of a cartesian product. Now I think, that there is a difference between the actual subset, and the reason for it, as well as the result of it. So I think, there are three different things: relation reason, actual relation (subset), and relation result. I wonder, whether this is a matter in mathematics. It seems triadic somehow. Example: Three equal sets A=B=C={1,2,3}. The relation reason is:"a unequal b unequal c unequal a", in other words: "No equal elements in a tuple". The actual relation is then: {(123)(132)(213)(231)(312)(321)}. Now this actual relation could have had another relation reason too: "a+b+c=a*b*c", in words: "The elements added is equal as the elements multiplied with each other". So, for relation result you have the relation reason, plus this second thing, the "might-have-been-too-reason". Of course this is a coincidence, but by fetching a bit far, one might say, that it is a crude example for how prejudices or myths come into being. Now, am I right with guessing, that the actual relation (the subset) is the elementary relation, and eg. "no equal elements" is a proper relation?
Helmut
 
 03. Dezember 2015 um 21:00 Uhr
"Jon Awbrey" <[email protected]>
 
Thread:
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/17890
GF:http://permalink.gmane.org/gmane.science.philosophy.peirce/17894

A budget of readings for present and future reference:

Survey of Relation Theory
http://inquiryintoinquiry.com/2015/11/30/survey-of-relation-theory-%E2%80%A2-2/

First, we need to be clear about the difference between objects and signs:

Relations are formal objects of discussion and thought while
Relative Terms are signs we use to denote/describe relations.
(The shorthand term "relative" is short for "relative term".

The default meaning for "relative term" is "general relative term",
that is, a term whose denotation extends over many objects.

The default meaning for "relation" is "general relation",
that is, a formal object that is a set of many elements.

Next, we need to be clear about the distinction between
relatives (= general relatives) and elementary relatives.

Note. There is a distinction in Peirce's usage between
elementary relatives and individual relatives, but if we
factor in what he says about the Doctrine of Individuals
and recognize that we are dealing with abstract forms
then it becomes a "distinction without a difference".
So I will tend to use the terms interchangeably.

Here is one place where Peirce exhibits his appreciation
for the critical difference between relatives in general
and elementary or individual relatives.

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 7
http://inquiryintoinquiry.com/2015/02/28/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-7/

<QUOTE>

Chapter 3. The Logic of Relatives (cont.)
=========================================

§4. Classification of Relatives

225. Individual relatives are of one or other of the two forms

A : A
A : B

and simple relatives are negatives of one or other of these two forms.

226. The forms of general relatives are of infinite variety,
but the following may be particularly noticed. ...

</QUOTE>

It needs to be appreciated that classifying relations is vastly
more complex than classifying elementary or individual relations.

In particular, classifying sign relations is vastly more complex
than classifying elementary or individual sign relations, which
is just about all that the massive literature on sign taxonomy
has been able to touch, albeit confusedly, from Peirce's time
to ours.

Regards,

Jon

On 12/3/2015 11:31 AM, [email protected] wrote:
> Jon,
>
> This doesn't explain “the difference between relations proper and elementary relations” (which you said was
> "critically important to understand"), because the latter term is itself used in a specific "technical sense" by
> Peirce in the places you cite. It doesn't help to understand which “technical sense” of the word you have in mind.
>
> My guess is that what’s confusing some of us in understanding triadic relations is that some of them relate
> correlates which are themselves relations. (Perhaps correlates which are not relations are “individual relatives”?)
>
> Gary f.
>
>
>
>
>
> -----Original Message----- From: Jon Awbrey [mailto:[email protected]] Sent: 2-Dec-15 22:30
>
>
>
> Peircers,
>
>
>
> As I wrote before, I used the phrase "relations proper"
>
> merely to emphasize that I was talking about relations in the technical sense. Another common idiom to the same
> purpose would be "relations, strictly speaking".
>
>
>
> As for "elementary relatives", Peirce uses this term in the 1870 Logic of Relatives.
>
> See, for example, CP 3.121ff and a later remark at 3.602ff.
>
>
>
> See Also:
>
>
>
> ☞ <https://www.google.com/search?hl=en&as_q=Peirce&as_epq=Elementary+Relative>
> https://www.google.com/search?hl=en&as_q=Peirce&as_epq=Elementary+Relative
>
>
>
> And toward the end of this section:
>
>
>
> ☞ <http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction#Operational_Representation>
> http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction#Operational_Representation
>
>
>
> Regards,
>
>
>
> Jon
>
>
>
>> Gary, all,
>
>>
>
>> I used the phrase “relations proper” to emphasize that I was speaking
>
>> of relations in the strict sense of the word, not in any looser sense.
>
>> I have been reading Peirce for almost 50 years now and I can't always
>
>> recall where I read a particular usage. In the 1970s I spent a couple
>
>> of years poring through the microfilm edition of his Nachlass and read
>
>> a lot of still unpublished material that is not available to me now.
>
>> But there is no doubt from the very concrete notations and examples
>
>> that he used in his early notes and papers that he was talking about
>
>> the formal objects that are variously called elementary relations,
>
>> elements of relations, individual relations, or ordered tuples.
>
>>
>
>> I did, however, more recently discuss a number of selections from
>
>> Peirce's
>
>> 1880 Algebra of Logic that dealt with the logic of relatives, so I can
>
>> say for a certainly that he was calling these objects or the terms
>
>> that denote them by the name of “individual relatives”.
>
>>
>
> …
>
>>
>
>> On 11/27/2015 12:42 PM, <mailto:[email protected]> [email protected] wrote:
>
>>> Jon,
>
>>>
>
>>> If it’s critically important to understand the difference between
>
>>> “relations proper” and “elementary relations”, can you tell us what
>
>>> that difference is, or point us to an explanation? These are not
>
>>> terms that Peirce uses, so how can the rest of us tell whether we understand them or not? Being unfamiliar with
>>> those terms does not indicate lack of understanding of the important concepts they signify.
>
>>>
>
>>> Gary f.
>
>>>
>
>>> From: Jon Awbrey [ <mailto:[email protected]> mailto:[email protected]] Sent: 27-Nov-15 11:16
>
>>>
>
>>> Gary, all,
>
>>>
>
>>> It is critically important to understand the difference between
>
>>> relations proper and elementary relations, also known as tuples.
>
>>>
>
>>> It is clear from his first work on the logic of relative terms that
>
>>> Peirce understood this difference and its significance.
>
>>>
>
>>> Often in his later work he will speak of classifying relations when
>
>>> he is really classifying types of elementary relations or single tuples.
>
>>>
>
>>> The reason for this is fairly easy to understand. Relations proper
>
>>> are a vastly more complex domain to classify than types of tuples so
>
>>> one naturally reverts to the simpler setting as a way of getting a foothold on the complexity of the general
>>> case.
>
>>>
>
>>> But nothing but confusion will reign from propagating the categorical error.
>
>>>
>
>>> Regards,
>
>>>
>
>>> Jon
>
>
>


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