Benji York wrote: > Jean-Marc Orliaguet wrote: > >> Benji York wrote: >> >>> Can you give an example of one of these pieces of knowledge? >> >> >> "John gives a book to Mary" > > >> If you store the relations "John drops the book" and "Mary picks the >> book" how will you know if the book belongs to Mary and belonged to John >> before it was given to her? You could add "the book belongs to John" >> "the book belongs to Mary", add some date information, add the fact that >> the action is a gift (reification), ... all the pieces still have to be >> put together. This will need to be interpreted in a language (or a query >> language that does unions, intersections, ..) that knows how to put the >> pieces together. The model is very verbose is not explicit at all. > > > I assume you mean "no combination of dyadic predicates using only > John, the book, and Mary as subjects and objects". If so, I agree. > > We're drifting fatally off topic here, but: Just as there are some > statements that cannot be expressed as dyadic predicates, are there > also those which cannot be expressed as triadic predicates? > > "John gives a book to Mary in exchange for 5 euros" > > If you store the relations "John gives a book to Mary" and "Mary gives > 5 euros to John" how will you know that the 5 euros were payment for > the book?
Now we'll really off-topic, but well: Actually there is a theorem (called the "reduction thesis", hinted by Peirce 100 years ago, and proved first in 1988) that says that even though no combination of dyadic relations can be used to build a genuine triadic relation, any relation of adicity > 3 can be built by combining triadic relations. Here is a quote that I found (CP. 6 is Collected Papers of C.S Peirce vol6): CP 6.323. A tetradic, pentadic, etc. relationship is of no higher nature than a triadic relationship; in the sense that it consists of triadic relationships and is constituted of them. But a triadic relationship is of an essentially higher nature than a dyadic relationship, in the sense that while it involves three dyadic relationships, it is not constituted by them. If A gives B to C, he, A, acts upon B, and acts upon C; and B acts upon C. Perhaps, for example, he lays down B, whereupon C takes B up, and is benefited by A. But these three acts might take place without that essentially intellectual operation of transferring the legal right of possession, which axiomatically cannot be brought about by any pure dyadic relationships whatsoever. Here is the example that you took, analysed into 6 triadic relations: --- START QUOTE --- Peirce: CP 7.537 There are no more Kainopythagorean categories than these three. For the first category is nonrelative experience, the second is experience of a dyadic relation, and the third is experience of a triadic relation. It is impossible to analyze a triadic relation, or fact about three objects, into dyadic relations; for the very idea of a compound supposes two parts, at least, and a whole, or three objects, at least, in all. On the other hand, every tetradic relation, or fact about four objects can be analyzed into a compound of triadic relations. This can be shown by an example. Suppose a seller, S, sells a thing, T, to a buyer, B, for a sum of money, M. This sale is a tetradic relation. But if we define precisely what it consists in, we shall find it to be a compound of six triadic relations, as follows: Peirce: CP 7.537 1st, S is the subject of a certain receipt of money, R, in return for the performance of a certain act As; Peirce: CP 7.537 2nd, This performance of the act As effects a certain delivery, D, according to a certain contract, or agreement, C; Peirce: CP 7.537 3rd, B is the subject of a certain acquisition of good, G, in return for the performance of a certain act, Ab; Peirce: CP 7.537 4th, This performance of the act Ab effects a certain payment, P, according to the aforesaid contract C; Peirce: CP 7.537 5th, The delivery, D, renders T the object of the acquisition of good G; Peirce: CP 7.537 6th, The payment, P, renders M the object of the receipt of money, R. Or we may define a sale as the execution of contract of sale. The contract of sale has two clauses. The first clause provides for a giving and a receiving. The giving is by the seller of the commodity; the receiving is by the buyer of the same commodity. The second clause provides for a giving and a receiving. The giving is by the buyer of the price; the receiving is by the seller of the same price. The execution is of the first clause and of the second, etc. But I do not think this latter definition as good as the other, since it introduces several unnecessary elements and also covertly brings in four pentadic relations, such as the relation of the buyer to the first and second clauses of the contract and to the separate executions of them. --- END QUOTE --- /JM _______________________________________________ Zope3-dev mailing list Zope3email@example.com Unsub: http://mail.zope.org/mailman/options/zope3-dev/archive%40mail-archive.com