Re: SUO: RE: Ontology, Epistemology, Semiotics
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).
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 :-)
> 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).
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)
Here we have a glimpse of why Peirce thought scholastic realism was so
important -- 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.
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Cathy Legg, Phd Cycorp, Inc.
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