Inquiry Blog http://inquiryintoinquiry.com/2015/12/08/relations-their-relatives-16/ http://inquiryintoinquiry.com/2015/12/10/relations-their-relatives-17/ http://inquiryintoinquiry.com/2015/12/12/relations-their-relatives-18/
Peirce List JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/17890 GF:http://permalink.gmane.org/gmane.science.philosophy.peirce/17894 JBD:http://permalink.gmane.org/gmane.science.philosophy.peirce/17902 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/17907 HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/17911 GF:http://permalink.gmane.org/gmane.science.philosophy.peirce/17916 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/17955 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/17956 HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/17958 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/17991 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/18002 HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/18003 HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/18007 Helmut, List, I would not want the dyadic case to detain us too long, as often happens when we frame a simple example for the purpose of illustration and then fail to rise beyond it. I raised the example of biblical brothers simply as a way of illustrating the distinction between a relation proper, like that symbolized by the formula “x is y's brother” and any of its elementary relations, like the ordered pair (Cain, Abel). There are, however, a few more points that could be illustrated within the scope of this simple example. Recall that we had a universe of discourse X consisting of biblical figures and a 2-place relation B forming a subset of the cartesian product X x X such that (x, y) is in B if and only if x is a brother of y. The “biblical brother relation” B would contain a large number of elementary dyadic relations, or ordered pairs (x, y), for example: (Abel, Cain), (Isaac, Ishmael), (Esau, Jacob), (Benjamin, Joseph), … (Cain, Abel), (Ishmael, Isaac), (Jacob, Esau), (Joseph, Benjamin), … Because B is a symmetric relation, each unordered pair {x, y} makes its appearance as two ordered pairs, (x, y) and (y, x). The extension of the elder brother relation E would have the pairs: (Cain, Abel), (Ishmael, Isaac), (Esau, Jacob), (Joseph, Benjamin), … Peirce regarded a set of tuples as an “aggregate” or “logical sum” and would have written the above subset of B in the following way: B = Abel:Cain +, Isaac:Ishmael +, Esau:Jacob +, Benjamin:Joseph +, … +, Cain:Abel +, Ishmael:Isaac +, Jacob:Esau +, Joseph:Benjamin +, … So what does all this -- the distinction between relations in general and elementary relations plus the analysis of relations in general as sets or sums of elementary relations -- imply for the case of triadic relations in general and sign relations in particular? It means that non-trivial examples of triadic relations are aggregates, logical sums, or sets of many elementary triadic relations or triples. As a result, the classification of single triples and their components gets us only so far in the classification of triadic relations proper, and except in very special cases not very far at all. Regards, Jon On 12/12/2015 4:32 AM, Helmut Raulien wrote:
Supplement: I suspect, that my below consideration is non-Peircean, as far as I know, because I ony know examples by Peirce, that are about relatives, that is terms, i.e. language. Language, of course, can only be inter-subjective. An intra-subjective consideration as below may be weird or incalculable, but I guess, it can be interesting: In the mentioned (Alice loves Bob) case, it shows a difference between language and reality: Language suggests, that "loves" in "Alice loves Bob" denotes a relation between Alice and Bob. But a closer look shows, that in fact it is about a relation inside Alices mind (Bob might be a movie star, whom Alice only has seen on a TV screen). Jon, List, Thank you. I am happy, that I now am more or less clear about the difference eg. between relation and relative term, and general and elementary. I find it complicated to apply the mathematical relation concept to realworld situations. There seem to be relations (and relative terms) of the mind, and others of the material-energetic world. Eg. if there is a wall made of bricks, one can tell the relations each brick has towards another brick, and so define the topology of the wall with relations from relative terms like "is above of", "is north of", and so on. But if Alice loves Bob, then this is a relation in Alices mind (a subset of a product of the set of all aspects in Alices mind with itself). And "Alice and Bob love each other" perhaps is a relation between the relations in Alices mind, and those in Bobs mind. But which are these aspects of the mind? Not very easy, all this, I mean, at least at this intra-subjective level. Maybe it leads astray to some sort of obsolete reductionism, I dont know. Best, Helmut
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