RE: SUO: Re: Parse Of Things Remembered
Dear John,
Thank you for the explanation. See some further comments/questions below.
>
> Matthew West wrote:
>
> >As one of those mystified by "triadic irreducibility" please see some
> >comments below.
>
> The basic point that Peirce and Whitehead were making is that
> certain triadic relations, especially those that occur in
> perception, signs, and anything that has representation or
> intentionality bound up in it requires (explicitly or
> implicitly) three arguments. The notions of context and
> situation are particularly dependent on triadic relations.
>
> Peirce is the one who developed that idea in the greatest
> detail, but many others, including Whitehead made similar
> observations. To add a bit of variety to the quotations,
> I'll cite the following discussion by Whitehead:
>
> http://paradigm.soci.brocku.ca/~lward/Whitehead/White1_07.html
>
> This is Chapter 7 on the nature of objects from Whitehead's
> book _The Concept of Nature_. I recommend the whole chapter
> (or the whole book, for that matter) as a good introduction to
> Whitehead's process philosophy. For the issue of relations,
> I suggest that you look at pages 150 ff, starting with the
> following paragraph:
>
> The difficulties which cluster around the relation of
> situation arise from the obstinate refusal of philosophers
> to take seriously the ultimate fact of multiple relations.
> By a multiple relation I mean a relation which in any
> concrete instance of its occurrence necessarily involves
> more than two relata. For example, when John likes Thomas
> there are only two relata, John and Thomas. But when John
> gives that book to Thomas there are three relata, John,
> that book, and Thomas.
>
> To find this paragraph, click on the above URL, which starts
> at page 143 of the book. Then use the "find" option in your
> browser to search for the word "cluster".
MW: Thanks. But from what I see below this is more a matter of
viewpoint than substance. I'll take a look at it anyway. I tend
to be long on experience and short on reading.
>
> JS:
>
> >> 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).
>
> Indeed, it is important to recognize the event of giving as
> a distinct entity, but Peirce (and I) would claim that verbs
> represent entities just as clearly as nouns. The transformation
> that Pat used in this example is the same one that I use for
> translating English sentences to conceptual graphs. I use the
> same kind of "concept nodes" for verbs as for nouns, and all
> concepts map to variables in KIF or predicate calculus. But
> the point that Peirce, Whitehead, and I would make is that
> this transformation does not "reduce" the triadic relation to
> dyads because the full meaning of "giving" still resides in the
> single monad named "giving", which is assigned a variable e,
> which is then linked to exactly the same relata (or arguments)
> as the verb give.
MW: This then is the nub of it. I see the individual relations between
the activity and the participants in the activity, whilst you see the
pattern of all the roles in the activity. If this is what it boils down
to I don't have a problem.
>
> >> 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.
>
> I agree that this is not what Pat suggested. For many kinds
> relations, however, such a translation might be very useful,
> but the point is that no such decomposition for "give" can
> capture the full meaning.
MW: Yes. The examples I can think of where this does work is where
say x already stands for the activity, and y and z are participants
in the activity. However, in this case part3(y,z) would probably be
meaningless.
>
> >> 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.
>
> I agree with you. But Peirce and I would say that there is
> no "new" object here, but merely a recognition that "give" is
> an entity that deserves to have its own variable, such as e.
MW: It was still missing in the starting point.
> That entity e has exactly the same number of links to the
> other entities in the sentence as the verb give.
MW: Precisely.
>
> >> 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.
>
> No. The point that Peirce was making is that many relations
> (including basic relations that deal with representation,
> perception, intention, situation, and context) inevitably
> involve triads that cannot be decomposed into dyads. But
> Peirce also showed that tetrads and higher relations can be
> decomposed into triads.
MW: OK. In that case please show me how a measurement can be
reduced to triads. A Measurement is an activity that:
has a subject (the thing measured)
an observer (doing the measuring)
an instrument (e.g. thermometer)
a measure (what about the thing is being measured, e.g. temperature)
a result (the value e.g. 20)
a Unit of Measure (e.g. Celsius)
the time when the measurement was taken.
>
> John Sowa
>
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
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