Re: SUO: Re: Parse Of Things Remembered
Pat,
Peirce and Whitehead were both familiar with the point
you keep repeating endlessly:
>Had Peirce or Whitehead lived a little longer maybe they would have
>become aware of the fact that any n-ary relation can be defined in
>terms of binary relations, with the aid of the existential
>quantifier. The translation, as I know you know, John, is this:
>
>R(t1,...,tn) ---> (exists e)(R(e) & first(e, t1) & second(e, t2)
>&...& nth(e, tn))
>
>where 'first', 'second', etc., are some fixed set of binary
>relations. (In case grammar these correspond to cases such as
>'agent', 'subject' and so on, and the 'e' is something like an event
>or a situation, of type R, corresponding to the verb of the simple
>sentence, as in:
Now let me use your example to explain the point which both
CSP and ANW were trying to make, which and you keep missing:
>Gave(John, Book, Mary, yesterday)
> --->
>(exists e)(Giving(e) & agent(e, John) & subject(e, book) &
>recipient(e, Mary) & time(e, yesterday)) ).
This is the transformation that Ernst Schroeder used in his 1890
book for replacing triadic and higher relations with dyadics.
Both Peirce and Whitehead were very familiar with it, and they
both rejected it because it is *not* a decomposition into
dyads. It is merely a relabeling of the arguments 1, 2, 3, 4
with labels "agent", "subject", "recipient", and "time".
What CSP and ANW were trying to explain is that the verb
"give" and many other irreducible triads *cannot* be reduced
to conjunctions of dyads of the following form:
give(x,y,z) = part1(x,y) & part2(y,z) & part3(y,z).
In this decomposition, part1, part2, and part3 are pure dyads
that only relate two arguments at a time. In Schroeder's
decomposition, which you keep repeating, you have to introduce
a new argument e, which links the monad named "giving" to
each of the other arguments: agent(e, John), subject(e, book),
recipient(e, Mary), and time(e, yesterday).
Notice that you have *not* performed a reduction of a triad
(or tetrad in this case) to a conjunction of dyads because
your new argument e links "giving" to every one of the other
arguments. All the triadicity (or tetradicity) is still buried
in the monad named "giving".
John