Re: SUO: RE: Ontology, Epistemology, Semiotics
Hi Cathy, thanks for following up. IThis discussion is quite useful,
nevertheless below are a few more expressions of puzzlement.
Best,
Pierre
> On Sat, 13 Sep 2003, Pierre Grenon wrote:
>
> > > > However it seems that this is true also in hogher arity claims: John is
> > between
> > > > Mary and Rosamonde according to Wilbert. It does not seem reducible to
any
> > > > combination of ternary claims by the standards of the analysis of
ternary
> > > > claims themselves.
> > >
> > > (isBetween BETWEENNESS_RELATION001 John)
> > > (delimitsBetweenness BETWEENNESS_RELATION001 Mary)
> > > (delimitsBetweenness BETWEENNESS_RELATION001 Rosamonde)
> > > (avowedBy BETWEENNESS_RELATION001 Wilbert)
> > >
> > > And then break that up into 2 triads as I showed in earlier messages....
> > >
> > > Sorry, that's the last one, I promise. :-)
> >
> > Hey Cathy, you won#t get away so easily with this. :)
> >
> > I can't find the time now, though I promise I#ll think more about this and
try
> > to see how you propose to break these following the earlier example. I
guess
> > the previous example didn't completely enlight me. It still isn't clear to
me
> > what#s this thridness which is preserved when you break down further. From
what
> > I can tell, it's the number three in a somewhat arbitrary fashion. (Seems
that
> > you can always pick up your three things and say 'see there are three of
> > them'.) In the earlier example, it's even less clear to me as equality as
> > precisely the effect of removing the putative distinction... So I guess I'm
> > still as confused as to where or what thirdness is and how it is not a
trivial
> > claim which has no particular fundamental or practical significantion (but
for
> > the Peirced ones?)
>
> Fair enough.
>
> The thirdness is just about the arity of the relations involved. BUT there
> is a complication because in a representation like the one I gave above,
> not all the logically relevant relations are explicitly stated in the form
> of predicates. There is a masked identity relation linking the tokens of
> BETWEENNESS_RELATION001, which is represented not via a predicate but
> iconically via the fact that the character-strings in each case are the
> same (which we interpret as an identity relation without realizing it,
> having been trained to do so).
So if understand you well. The claim about this veiled identity relation is
that it relates the two occurrences of the strings 'BETWEENNESS_RELATION001'. I
presuem there is another relation which holds between one of the occurrences in
your text and the occurrence of this string in the previous sentence. One
clarification question would be: is it the same relation which holds?
I think I sort of see now the point and what mood semiologists are in, but
honestly I am not sure I see - let's see how to put it in a non offensive way -
either the signification of these cogitations or their value - or put it
another way, to whom it may have some value besides semiologists.
> This is why Peirce preferred his graphical notation over such algebraic
> notations - it is more perspicuous because it gets all the logically
> relevant relations out on the table and represents them in the same way,
> instead of the mish-mash above. Thus (in answer to an earlier message of
> Rich's) this is not a mere matter of representational ease.
>
> John Sowa has been making this point for the past few days but I wanted to
> say it in my own way as well :-)
I appreciate your efforts for rationalizing this and making it a little less
esoteric.
> > As for the solution here, I find it quite ingenious. I wouldn't have
expected
> > that you took token relations into consideration. (Am I correct that this
is a
> > token? it seems to fail otherweise.) I'm not sure what to think about this
> > actually. At any rate, this is a quite courageous move. (Is that some
Peirce
> > orthodoxy by the way or is it your craft?) It seems to me that there is an
> > obvious issue of infinite regress lurking there however.
>
> Yes it's a token. And it's not my idea but Peirce's (nicely explicated by
> Robert Burch, who is at Texas A&M, in the 90s).
Thanks for the reference.
> As you can see, the key is the ability to 'perform 'hypostatic
> abstraction' on any relation to make it itself into a relatum. The way
> Pierluigi put things, in terms of a continually extensible
> 'triangulation', was actually a very good explication of this (thanks,
> Pierluigi). But in order for such triangulation to work, the identity
> relation must be transitive, and transitivity is an essentially triadic
> relation. (Thus the irreducibility of thirdness)
Again, I'm not sure what's the significance and value of these reflexions are,
say speaking as an ontologist. It is also odd to think of transitivy as a
relation in a rigorous way. It seems to me to be a property of certain
relations. It involves three terms, at any rate three signs (is that what you
mean?), for each of the relata. Maybe I sort of see what kind of things you are
looking at, maybe not. It remains for isnatnce that the fact that signs are
signs and would they be different that wouldn't make the objects they may be
taken to signifiy (or whatever the Peirce jargon is) different, would it? So I
don't quite clearly see how issues of numerical identity about signs and so on
are so crucial for ontology.
> Here we have a glimpse of why Peirce thought scholastic realism was so
> important
This is getting hardcore. Vision is blurred but I'll try to open my eyes wider
if that can help. ;)
> -- not in metaphysics, but in logic. Quine, although explicitly
> disavowing metaphysical nominalism in a number of places (e.g. claiming to
> have an ontological commitment to classes), was nominalist in spriit in
> many ways in his logic, IMO, not least of which was his extensionalism.
>
> Cheers,
> Cathy.
>
> --------------------------------------------------------------------------
> Cathy Legg, Phd Cycorp, Inc.
> Ontologist 3721 Executive Center Dr., ste 100
> www.cyc.com Austin, TX 78731-1615
>
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>
>
>
--
Pierre Grenon, IFOMIS Uni Leipzig
http://people.ifomis.uni-leipzig.de/pierre.grenon/
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