Re:Jim Willgoose JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15624 JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15636 JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15639 JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15641 JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15657 JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15664
Jim, List, Arranging the individual relatives -- for various reasons, I prefer the term "elementary relatives" and will eventually switch to that -- in k-dimensional arrays is merely a matter of convenience and need not concern us too much at our present level of abstraction. The important thing is the representation of k-adic relatives and relations in extensional form via sets of k-tuples like A:B, A:B:C, ... (in Peirce's usual notation) or (A, B), (A, B, C), ... (as might be more common today). In a form like "lover of ---" the word "lover" is a place-holder for the rèlate and the blank is a place-holder for the correlate. So the number of blanks is the adicity of the relation minus one. We can always express the same relation through the auxiliary of a copula, as "--- is a lover of ---". Regards, Jon On 2/12/2015 8:19 PM, Jim Willgoose wrote:
Thanks Jon. I put integers to each of the nine dual relatives in the first three columns and rows. (in Bold print) I then rotated the block left 90 degrees three times. Crease the diagonals <357> <753>, tack down the 4 corners <3333>, and pull the apex <7777> straight up into a pyramid. Voila! This method seemed more efficient conceptually than the previous. 3 6 9 1 2 3 2 5 8 4 5 6 1 4 7 7 8 9 9 8 7 7 4 1 6 5 4 8 5 2 3 2 1 9 6 3 I had a further question about some word examples. Peirce seems to roll the relate into the relative term such that the number of places is short one. For instance, "buyer of a ----- for-----from------" appears to count the number of correlates only. I bring this up since the relate symbol ":" usually has a letter attached on the left side. Small issue though. In any case, matrices seem to be a way, if not the predominant way to introduce abstract algebra. I appreciate your keepng this thread alive . Jim W
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