Inquiry Blog • 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/
Peirce List JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15704 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15705 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15708 JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/15716 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15718 HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/15719 Helmut, List, Right, the "divisor of" relation signified by "x|y" is a dyadic relation on the set of positive integers M, so it can be understood as a subset of the cartesian product M×M. It is an example of a "partial order", whereas the "less that or equal to" relation signified by "x ≤ y" is an example of a total order relation. And yes, the mathematics of relations can be applied most felicitously to semiotics, but here we must bump up the adicity or arity to three. We take any sign relation L to be subset of a cartesian product O×S×I, where O is the set of objects under consideration in a given discourse, S is the set of signs, and I is the set of interpretant signs involved in the same discourse. One thing we need to understand here is that the sign relation L ⊆ O×S×I relevant to a given level of discussion can be rather more abstract than what we would call a "sign process" proper, that is, a structure extended through a dimension of time. Many of the most powerful sign relations are those that generate sign processes through iteration or recursion or other operations of that sort. When this happens, the most penetrating analysis of the sign process or semiosis in view will come through grasping the core sign relation that generates it. Regards, Jon On 2/18/2015 5:51 PM, Helmut Raulien wrote:
Jon, Jerry, List, I think, what you wrote is interesting: That a (mathematical) relation is a subset of the set of possible tuples (cartesian product) that are made from the elements of two sets, a tuple being a pair of one element from set A and one element from set B. Set B can also again be set A, then it is the relation upon A. The subset can be chosen arbitrarily, then the reason for the relation is the free will of the mathematician at work. Or it may be something like "smaller than", then it is the set of tuples in which the first element (from set A) is smaller than the second (taken from B). In this case the relation has a natural reason, but it still takes a person to see, that one element is smaller than the other. And this person also has to define A and B. Why am I writing this? I was thinking of how can this mathematics be applied to semiotics. Semiotics is metaphysics, that is universal theory of nature. So I was thinking: In which way can nature, reality, be separated into two sets? My answer is: These two sets are the set of events, and the set of entities. This is the most fundamental natural distinction of reality into two sets, that does not need an observer concept, because this distinction has existed yet in preorganic nature. It is natural. Relation now is in the first place a relation between an event and an entity. It must be a symmetrical relation, because in preorganic nature there was no mathematician to define which is set A and which is set B. Now there are two ways to continue: Either compare these considerations with Peirce, and ask: Has the triad "Event, entity, relation" something to do with "1ness, 2ness, 3ness", or with "representamen, object, interpretant"? Or the second way of approach is, to develop a semiotics and a systems theory based on the triad "event, entity, relation", not caring about Peirce first, but waiting to see later, whether there will be parallelities. I think this is a good idea. I want to follow it, but maybe somebody else smarter than me can do that faster and more efficient. Best, Helmut
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