Helmut, List, Maybe I can clear up a few confusions about the relational standpoint by resorting to a simpler case of a triadic relation, one I'm guessing we all learned about early in our schooling, namely, the one involved in the operation of subtraction, x - y = z. When I was in school we learned a set of quaint terms for the numbers x, y, z in the relation and I wasn't sure they still taught such things so I checked the web and found a page that described the terms just as I remembered them:
☞ http://www.mathsisfun.com/numbers/subtraction.html The number x is called the "minuend", the number y is called the "subtrahend", the number z is called the "difference". So we come to the questions: Are minuends an own class? Are subtrahends an own class? Are differences an own class? To answer these questions we need to observe the distinction between relational roles and absolute essences (or ontological substances). If our notion of number is general to include negative numbers then any number can appear in any one of the three places, so minuend, subtrahend, and difference are relational roles and not absolute essences or ontological substances. We can tell this because it follows from the definition of the subtraction operation. When it comes time to ask the same questions of objects, signs, and interpretant signs then any sort of definitive answer can only come from the definition of a sign relation we've chosen as the one that best befits our intended subject matter. Regards, Jon On 6/18/2015 6:17 PM, Helmut Raulien wrote:
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" <[email protected]> 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
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