Cf: Relations & Their Relatives • Discussion 1 https://inquiryintoinquiry.com/2015/02/27/relations-their-relatives-discussion-1/
Re: Peirce List https://web.archive.org/web/20150619134001/http://comments.gmane.org/gmane.science.philosophy.peirce/15704 ::: Helmut Raulien https://web.archive.org/web/20150619133003/http://permalink.gmane.org/gmane.science.philosophy.peirce/15719 The “divisor of” relation signified by x|y is a dyadic relation on the set of positive integers M and thus may be understood as a subset of the cartesian product M × M. It is an example of a “partial order”, while the “less than or equal to” relation signified by x ≤ y is an example of a “total order” relation. The mathematics of relations can be applied most felicitously to semiotics but there we must bump the “adicity” or “arity” up 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 discussion, S is the set of “signs”, and I is the set of “interpretant signs” involved in the same discussion. One thing we need to understand is the sign relation L ⊆ O × S × I relevant to a given level of discussion may be rather more abstract than what we would call a “sign process” proper, that is, a structure extended through a dimension of time. Indeed, many of the most powerful sign relations generate sign processes through iteration or recursion or similar operations. In that event, the most penetrating analysis of the sign process or semiosis in view is achieved through grasping the generative sign relation at its core. Regards, Jon
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