Re: Is the meaning of order intrinsic ?

From: "Bill Andersen" <andersen@ontologyworks.com>

> Hi all.  I'm new to the list and usually I like to read for a while before
> writing but ... I just can't help myself!  Please forgive me.

Apology not accepted ... you should have written sooner!

> > Actually I think it is quite easy to define the truth-value 'Truth'.
It's
> > simply an attitude adopted by an agent towards a particular statement.
Look
> > ma, no metaphysics :)
>
> You don't have a metaphysics?  Then what are "attitude", "agent", and
> "statement"?

Hmmmm ... nested cutely under your well framed question seems to me to be
the assumption that to have a metaphysics, is to have an ontology.  Well
Fine :))   Where is it that I go, to start my ontology ?

> If a planet explodes on the other side of the universe where there are no
> "agents" is it in fact "seth-russel-true" that there is one less planet
than
> before the time of the explosion?

Interesting question ... very uninteresting place you have imagined where
there are no agents .... but no! .... it is in fact
urn:robustai.net/attitudes/SethRussell#NonSense that there is one less
planet there then before (what time of the explosion?).

> Ok ... I'm an "agent" and I have the "seth-russel-true" "attitude" toward
> the following "statement" (which we will call S):

Then you are a liar, because you are not Seth Russell.

>  [1]  "S is false"

But since you asked, Seth Russell has calculate the attitude
urn:robustai.net/attitudes/SethRussell#NonSense toward statement [1].

>Seems your theory of "truth" needs some work.

How so?

> > Yeah this is pretty much the way numbers are defined with set theory.
But
> > I still have a trouble with using this technique of defining a sequence.
My
> > thesis is that 'ordering' is a first principal, is prior, is axiomatic
(at
> > least to humans and the systems they tend to construct).
>
> Look out - words like "prior [to mathematics]" are getting awfully close
to
> metaphysics!

I'm sure your right.  I've been struggling with arriving at a good ontology
to use to express this term "prior, axiomatic, innate, a first principal,
atomic".  Any suggestions are certainly very welcome.   If 'Thing' be the
name of the top class of our ontology, then a subclass of that might be
named 'Pattern' with 'Sequence' being an obvious name of a subClass thereof.
Yet any Thing isA Concept, least it not exist in our ontology, and a concept
seems to me to be just a Pattern and we are not allowed to loop. ... so go
figure ....

> > It seems to me
> > that to disprove this thesis you would need to be able to define an
order
> > without using anything that presupposes that order already.  Your
syntactic
> > string (sequence of characters) above of course contains that
> > presupposition.
>
> You are confused.

I'm beginning to think that is a truism; sience it seems
urn:robustai.net/attitudes/SethRussell#True in any case i examine :(

>The sequence of characters is irrelevant.  It is meant to
> encode a representation of a set, which is not presupposed to have any
such
> ordering.

You seem here to inform me of the state of affairs that I had affirmed
already at [#here1].  Was that merely an oversight on your part, or had you
wished to imply some additional information here ?

>It is the properties of that set, interpreted via the axioms of
> set theory (particularly equality), that make the representation conform
to
> our intuitions about orderings.

I fail to see how any symmetric relationship (namely equality) could ever
establish a sequence.

>Note this makes no metaphysical appeal to
> the notion of an order whatsoever -- it simply is one way (as Pat pointed
> out, I think, there are many) to represent the notion of order.

And do you have any refutation to my rather clumsy attempt [2] to deny that
Pat and his predecessors whom I take to have hung out with Guiseppe Peano,
have successfully represented order in a to-our-ontology valid method ?

[2] http://robustai.net/mentography/order.gif

> If you want to talk about metaphysical order, then you will have to invoke
> an appropriate theory of states-of-affairs, which has nothing to do with
> what Pat talked about.

I didn't know that I would have been wanting to talk of a thing that could
have been called 'metaphysical order'.   All I wanted to do was to represent
a sequence without calling upon a medium that already presupposed sequence.
Or, iow, I would like to know how I could describe a sequence to an alien
agent that had no experience with either space or time.

[#here1]
> > But let's forgive that trespass for a moment, because I
> > know what this string means and have interpreted it in a graph [1] quite
> > apart from the ASCII string you used.
>
> What topological properties does your graph have?

Ahhh ... now there's the rub .... discussing that is why i asked my dumb
questions originally.   I claim that a labeled directed graph has intrinsic
topological properties that need no explaining.  Pat, and now you, seem not
to be able to see them.  I keep wondering whether this is Pat's (and now
your) obtuscience or simply my stupidity.

>Sounds like it "contains a presupposition".

And what presupposition would that be ???????

>So you want to use the axioms of graph theory instead of
> set theory, go ahead.  You win a cookie.

Ahhh ... a delicious cookie indeed ... when can i take the first bite ?

I must admit that I have enjoyed answering your letter .... thanks for the
dialogue ...

Seth

Received on Saturday, 26 May 2001 12:28:22 UTC