Re: SUO: Re: Parse Of Things Remembered
>Pat,
>
As Karl Marx once said, "Je ne suis pas Marxiste." ....
OK, fair enough. I think that the form of what you say often creates
more heat than the content. :-)
>Let's drop the term "reduction to dyad" along with the term
>"irreducible triadicity" because they sound more high-falutin'
>than they deserve to be.
Indeed.
>To be as mundane and explicit as possible, let me take the
>verb "give", which Peirce, Whitehead, and you have used as
>an example, as in "John gave the book to Mary." And let
>us try to rephrase that sentence as a conjunction of other
>English sentences, which involve no more than two of the three
>entities "John", "Mary", and "the book" in any one sentence.
>
>Question: Is it possible to for any such conjunction of
>sentences to capture the full meaning of the sentence
>"John gave the book to Mary"?
>
>For example: "John dropped the book. Mary picked it up."
>
>This doesn't capture the transfer of ownership involved
>in giving.
>
>Example 2: "John renounced ownership of the book. Mary
> claimed ownership of the book."
>
>This captures the change of ownership, but not John's
>intention of having Mary rather than anyone else assume
>ownership.
>
>Example 3: "John initiated an act of giving. The giving
> had a book as object. The giving had Mary as recipient."
>
>This example does capture the three-way relationship, but
>only by creating another entity "giving", which itself has
>the open slots in its definition -- formally speaking,
>any representation of "giving" must have "frame-like" or
>"lambda-calculus-like" representation, which contains
>three inner variables or slots. Then each of the three
>sentences instantiates one of those slots.
Well, that isnt QUITE right, since in my earlier message I
represented 'giving' by a simple name. But I'm being very formal and
persnickety here, I concede; the logical expression which might be
said to define the meaning of 'e' mentioned all three things, and it
couldn't have done that without mentioning all three.
OK, if THAT is the point, then of course I will agree with it
immediately: we will need to write axioms that mention more than two
things, or use more than two relation symbols, or whatever. But now I
am puzzled by the emphasis on threeness for a different reason, since
it seems to me for example that if we are to really capture the full
meaning of 'give' we will probably need to relate it to about 7 or
more other concepts (whether they are expressed formally as relations
or names or whatever). If we are at this rather loose level of
discussion, I don't see how one can insist that "threeness" is
particularly important. A giving involves two agents, a thing given,
an intention (maybe several), a time, a place (usually), probably a
reason, maybe an overarching larger event or circumstance (such as a
birthday), etc. . Most things have many connections to other things,
and (depending on how strictly one understands 'full meaning') their
full meaning cannot be stated without making reference to more than
three of them. So why do you stop at three?
(Let me say what my suspicion is, so you can refute it if I am wrong.
I think that when it comes to reducing n>3 to 3, y'all want to cite
Peirce's result as showing conclusively and mathematically that the
reduction can be done; but when it comes to going from 3 to 2, you
want to get all kind of sketchy, and argue that that last step is
just a dry formal result with no real meaning, and if you look behind
the mere mathematics you will still see trinities everywhere. My
problem is that if I stay mathematical and strict I can reduce it all
to 2, and if I follow your intuitive perspective I can't reduce it to
3.)
A related issue is the idea, which arises in various forms, that any
particular number of relations is somehow indicative of a particular
semantic content, as for example the idea that threeness is somehow a
litmus test for the presence of intentionality. Saying that Chicago
is between NY and Orlando crucially involves a trinary relation, but
it doenst seem to involve intentionality. Maybe I've been
misunderstanding your messages to Matthew, but you often seem to draw
this kind of a conclusion, which I find puzzling.
>The only point that Peirce, Whitehead, and I have been trying
>to make is that there are concepts in English, such as Give,
>which cannot be defined without using a frame, a lambda
>expression, or some such formal device that contains three
>distinct slots, variables, boxes, or whatever.
>
>Those are things that I called "mediators" in my toplevel
>ontology. Furthermore, those mediators keep appearing and
>reappearing whenever there is some kind of representation,
>perception, intention, or context involved.
So is *any* trinary concept a mediator? Eg how about 'between'?
Pat
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