Supplement: On the other hand, even if interpretants are not an own class (or is the word "domain"?), their representations in a mind may well be, and certainly are. So- triadicity is rescued for me, I now think.
Dear Jon, Peircers,
I am wondering whether, mathematically spoken, there really are 3-adic relations in semiotics. An interpretant is a 2-adic relation (between representamen and object). But are interpretants an own class? Or are they a common class with representamens (syntactic domain)- or are some of them so, while others (the final interpretants) re-enter into the domain of objects? And: to regard the three sets objects, representamens, interpretants, doesnt this regarding (action of a mind) mean that they are represented? And doesnt representation by a mind mean, that these representations are all objects, other than the represented? So: Is the triadic relation between representamen, object and interpretant possibly a relation between three objects? In this case, it is not triadic: It is a 2-adic relation between the set of objects, and the same set of objects- at least reducible to this, I suspect. On the other hand one might say: The objects of a mind are divided into three classes: Representations of representamens, objects, and interpretants. Three classes mean 3-adicity. But then there is the problem again that I have mentioned: Are interpretants an own class?
Best,
Helmut
Von: "Jon Awbrey" <jawb...@att.net>
Post : Survey of Relation Theory • 1
http://inquiryintoinquiry.com/2015/05/16/survey-of-relation-theory-%e2%80%a2-1/
Peircers,
A couple of off-list exchanges prompts me to post this Survey
of previous contributions and discussions on relation theory.
In this Survey of previous blog and wiki posts on Relation Theory, relations are viewed
from the perspective of combinatorics, in other words, as a topic in discrete mathematics,
with special attention to finite structures and concrete set-theoretic constructions, many
of which arise quite naturally in applications. This approach to relation theory, or the
theory of relations, is distinguished from, though closely related to, its study from the
perspectives of abstract algebra on the one hand and formal logic on the other.
Elements
========
* Relation Theory
( http://intersci.ss.uci.edu/wiki/index.php/Relation_theory )
Relational Concepts
===================
* Relation Construction
( http://intersci.ss.uci.edu/wiki/index.php/Relation_construction )
* Relation Composition
( http://intersci.ss.uci.edu/wiki/index.php/Relation_composition )
* Relation Reduction
( http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction )
* Relative Term
( http://intersci.ss.uci.edu/wiki/index.php/Relative_term )
* Sign Relation
( http://intersci.ss.uci.edu/wiki/index.php/Sign_relation )
* Triadic Relation
( http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation )
* Logic of Relatives
( http://intersci.ss.uci.edu/wiki/index.php/Logic_of_relatives )
* Hypostatic Abstraction
( http://intersci.ss.uci.edu/wiki/index.php/Hypostatic_abstraction )
* Continuous Predicate
( http://intersci.ss.uci.edu/wiki/index.php/Continuous_predicate )
Blog Dialogs
============
* Relations & Their Relatives
( http://inquiryintoinquiry.com/2015/02/17/relations-their-relatives-1/ )
{ http://inquiryintoinquiry.com/2015/02/17/relations-their-relatives-2/ )
( http://inquiryintoinquiry.com/2015/02/18/relations-their-relatives-3/ )
( http://inquiryintoinquiry.com/2015/02/27/relations-their-relatives-4/ )
( http://inquiryintoinquiry.com/2015/03/04/relations-their-relatives-5/ )
{ http://inquiryintoinquiry.com/2015/03/05/relations-their-relatives-6/ )
( http://inquiryintoinquiry.com/2015/03/19/relations-their-relatives-7/ )
( http://inquiryintoinquiry.com/2015/03/22/relations-their-relatives-8/ )
Resources
=========
* Peirce's 1870 Logic Of Relatives
( http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives )
Regards,
Jon
--
academia: http://independent.academia.edu/JonAwbrey
my word press blog: http://inquiryintoinquiry.com/
inquiry list: http://stderr.org/pipermail/inquiry/
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey
facebook page: https://www.facebook.com/JonnyCache
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
http://inquiryintoinquiry.com/2015/05/16/survey-of-relation-theory-%e2%80%a2-1/
Peircers,
A couple of off-list exchanges prompts me to post this Survey
of previous contributions and discussions on relation theory.
In this Survey of previous blog and wiki posts on Relation Theory, relations are viewed
from the perspective of combinatorics, in other words, as a topic in discrete mathematics,
with special attention to finite structures and concrete set-theoretic constructions, many
of which arise quite naturally in applications. This approach to relation theory, or the
theory of relations, is distinguished from, though closely related to, its study from the
perspectives of abstract algebra on the one hand and formal logic on the other.
Elements
========
* Relation Theory
( http://intersci.ss.uci.edu/wiki/index.php/Relation_theory )
Relational Concepts
===================
* Relation Construction
( http://intersci.ss.uci.edu/wiki/index.php/Relation_construction )
* Relation Composition
( http://intersci.ss.uci.edu/wiki/index.php/Relation_composition )
* Relation Reduction
( http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction )
* Relative Term
( http://intersci.ss.uci.edu/wiki/index.php/Relative_term )
* Sign Relation
( http://intersci.ss.uci.edu/wiki/index.php/Sign_relation )
* Triadic Relation
( http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation )
* Logic of Relatives
( http://intersci.ss.uci.edu/wiki/index.php/Logic_of_relatives )
* Hypostatic Abstraction
( http://intersci.ss.uci.edu/wiki/index.php/Hypostatic_abstraction )
* Continuous Predicate
( http://intersci.ss.uci.edu/wiki/index.php/Continuous_predicate )
Blog Dialogs
============
* Relations & Their Relatives
( http://inquiryintoinquiry.com/2015/02/17/relations-their-relatives-1/ )
{ http://inquiryintoinquiry.com/2015/02/17/relations-their-relatives-2/ )
( http://inquiryintoinquiry.com/2015/02/18/relations-their-relatives-3/ )
( http://inquiryintoinquiry.com/2015/02/27/relations-their-relatives-4/ )
( http://inquiryintoinquiry.com/2015/03/04/relations-their-relatives-5/ )
{ http://inquiryintoinquiry.com/2015/03/05/relations-their-relatives-6/ )
( http://inquiryintoinquiry.com/2015/03/19/relations-their-relatives-7/ )
( http://inquiryintoinquiry.com/2015/03/22/relations-their-relatives-8/ )
Resources
=========
* Peirce's 1870 Logic Of Relatives
( http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives )
Regards,
Jon
--
academia: http://independent.academia.edu/JonAwbrey
my word press blog: http://inquiryintoinquiry.com/
inquiry list: http://stderr.org/pipermail/inquiry/
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey
facebook page: https://www.facebook.com/JonnyCache
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
