RE: SUO: Re: Parse Of Things Remembered
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".
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.
>> 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.
>> 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.
That entity e has exactly the same number of links to the
other entities in the sentence as the verb give.
>> 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.
John Sowa