RE: SUO: Re: Parse Of Things Remembered
Dear John,
As one of those mystified by "triadic irreducibility" please see some
comments below.
> 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".
MW: Well I disagree. What it is really doing is recognising an object
that was hidden by the initial incomplete analysis, i.e. the giving
activity in which the other objects are participants (except the time
which gives the temporal location of the activity).
>
> 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).
MW: Doing this would be just silly, but it isn't what Pat has suggested.
>
> 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).
MW: Yes, but the new argument represents a real object. My experience
is that most of the time when there is a triadic or higher relation
there is a hidden object - often an activity (or process or event if
you prefer) and sometimes another relation.
>
> 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".
MW: Well if we follow that line of argument there is only one enormous
relation of all objects.
>
> John
>
Regards
Matthew
===============================================================
Matthew West http://www.matthew-west.org.uk/
Principal Consultant Shell Visiting Professor
Operations & Asset Management The Keyworth Institute
Shell Services International The University of Leeds
http://www.shellservices.com/ http://www.keyworth.leeds.ac.uk/
H3229, Shell Centre, London, SE1 7NA, UK.
Tel: +44 207 934 4490 Fax: 7929 Mobile: +44 7796 336538
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