[Zope3-dev] Re: Zope3-dev Digest, Vol 25, Issue 37

[Jean-Marc Orliaguet]

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