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
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
<QUOTE>
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).
</QUOTE>
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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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
<QUOTE>
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).
</QUOTE>
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
--
inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
facebook page: https://www.facebook.com/JonnyCache
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