SUO: Re: Numbrance Of Times Perished
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Pat Hayes wrote:
>
> [Jon Awbrey wrote:]
> >
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> >
> > Pat Hayes wrote:
> > >
> > > [John Sowa wrote:]
> > > >
> > > > Pat,
> > > >
> > > > We went round and round on this issue before,
> > > > so I don't want to repeat the experience.
> > >
> > > I didnt go round and round on this issue.
> > > I wrote a review of Burch's thesis which
> > > I believe settled the matter conclusively.
> > > (J. Man-Machine Studies, 1995)
> > >
> >...
> > >
> > > 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))
> >
> > What this translation says is just this:
> >
> > | t in R iff there is an e in R such that e = t.
> >
> > I think that the total lack of any analysis in this ought to be evident
>
> 1. That isn't what it in fact says (even in the case n=1, it says
> "if there is an e in R such that first(e,t)"), but in any case ...
Let's recall what has been established:
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Subj: SUO: Re: Irreducible Try-It-And-See
Date: Wed, 21 Mar 2001 21:06:57 -0500
From: Jon Awbrey <jawbrey@oakland.edu>
To: Stand Up Ontology <standard-upper-ontology@ieee.org>
CC: pat hayes <phayes@ai.uwf.edu>,
West, Matthew MR SSI-GREA-UK <Matthew.R.West@is.shell.com>,
Josiah Lee Auspitz <lee@textwise.com>, sowa@bestweb.net
Speaking of truth-functional connectives,
Pat Hayes premissed:
If you insist that it is a function on truthvalues
and therefore a ternary relation, then I will concede
that such things are needed. However, I will then assert
even more strongly the utter banality and unimportance of
this result. As far as I know, nobody, not even Scheffer,
has ever asserted that one can do without binary connectives.
Jon Awbrey concluded:
Substituting identicals into what I hope is your transparent context:
Therefore nobody is saying that one can do without triadic relations.
The End.
http://suo.ieee.org/email/msg04176.html
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I then made some remarks about the informational identity
among "axiomatic", "banal", "commonplace", "evident",
"obvious", "plain", "trivial", "truistic",
or words to that lack of effect.
So our anatomy of n-arity has already articulated
the triadic structure of the ligaments and sinews
in the covering skin and connective tissue of the
beast, and we are now cutting down to the bone of
the n-tuples themselves, to see whether they also
manifest a constitution that is adamantly triadic.
The way that I read what you say: For any n, what
you call "e" and what you call "<t1, ..., tn>" are
one and the same thing. Again, what you call "R"
on the left and what you call "R" on the right are
the same name for the same thing, too. I had been
granting you the benefit of the doubt, and reading
"Definiendum --> Definiens" to be the intended aim
of the arrow -->, but now it appears that you mean
implication; can that possibly be what you intend?
So I am still wondering what you mean by this:
| R(t1, ..., tn)
| --->
| (exists e)(R(e) & first(e, t1) & second(e, t2) & ... & nth(e, tn))
I did not imagine that you meant any sort of recursive "transliteration".
Yet there is, to write it strictly, this "R(<t1, ..., tn>)" on the left,
while again there is this "R(e)" on the right, a pseudonym for the same,
so I must wonder what is supposed to be the use of this "transliteration",
if more than to scrawl some letters across the page?
> 2. It doesnt puport to be any kind of ANALYSIS, only a transliteration.
> The existence of the transliteration establishes the claim made: that
> anything that can be said, can be said using at most binary relations.
I do not see that. The arity of R is the same on both sides, is it not?
> It is a very simple point, and like most simple points,
> it seems silly to exercise lots of energy denying it,
> when its truth is as plain as the nose on your face.
I shall check the glass you hold as you pass,
but no, being simple does not render it true,
for fictions are usually simpler than truths,
indeed, it is one of the diagnostic symptoms.
Jon Awbrey
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