Thread: JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/16523 HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/16550 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/16551 HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/16572 HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/16573 HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/16595
Re: Relation Reduction : Examples of Projectively Reducible Relations http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction#Examples_of_projectively_reducible_relations Helmut, List, I constructed the "Ann and Bob" example back when I was enrolled in a Systems Engineering program and had to explain how sign relations would naturally come up in building intelligent systems possessed of a capacity for inquiry. My adviser asked me for a simple, concrete, but not wholly trivial example of a sign relation and after cudgeling my wits for a while this is what fell out. Up till then I had never much considered finite examples before since the cases that arise in logic always have formal languages with infinite numbers of elements in their syntactic domains if not also in their object domains. Now, the first thing that we need to get clear about is that there are two sign relations being described in this example: L_A is the sign relation that captures how Ann interprets the signs in S = I = {"Ann", "Bob", "I", "you") to denote objects in O = {Ann, Bob}. L_B is the sign relation that captures how Bob interprets the signs in S = I = {"Ann", "Bob", "I", "you") to denote objects in O = {Ann, Bob}. Each of the sign relations, L_A and L_B, contains 8 triples of the form (o, s, i) where o is an object in the object domain O, s is a sign in the sign domain S, and i is an interpretant sign in the interpretant domain I. These triples would be called "elementary" or "individual" sign relations, as distinguished from the "general" sign relations that generally contain many sign relational triples. It's a little harder to carry out this discussion in plain text, without the proper formatting required to distinguish different uses of various letters, especially "I" and "i", but if this much is clear we can move on to discuss the two types of reducibility and irreducibility that arise in semiotics. But I will have to break for dinner first ... Jon On 7/1/2015 3:45 PM, Helmut Raulien wrote:
Jon, List, I am referring to the second link of yours: "Relation reduction", the second example with A (Ann), B (Bob) u (you), i (I), resp. the representations of them, representation indicated by quotation marks, eg. "A" instead of A. My question is: Isnt it about a set of possible relations, instead of about one relation? To say, that the set of possible triadic relations is reducible to three sets of possible dyadic relations, that does not have to mean, that one triadic relation is reducible to three special dyadic relations, does it? Best, Helmut *Von:* "Jon Awbrey" <[email protected]> Helmut, List, The facts about relational reducibility are relatively easy to understand and I included links to relevant discussions in my initial posting on relation theory: • Survey of Relation Theory ( http://inquiryintoinquiry.com/2015/05/16/survey-of-relation-theory-%E2%80%A2-1/ ) The following article discusses relational reducibility and irreducibility in general terms and gives concrete examples of reducible and irreducible triadic relations of the sort we find in mathematics and semiotics, illustrating the two types of reducibility that usually come up in discussions of the sort that most concern us here: • Relation Reduction ( http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction ) These examples were introduced in the other articles on triadic relations and sign relations and I believe that one could learn a lot from their careful consideration: • Triadic Relations ( http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation ) • Sign Relations ( http://intersci.ss.uci.edu/wiki/index.php/Sign_relation ) 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 [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
