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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