# Re: Objects and Relations

From: Keith H Duggar <duggar_at_alum.mit.edu>
Date: 15 Feb 2007 21:30:42 -0800

David BL wrote:
> JOG wrote:
> > Yes exactly, if you so wished. Or a surrogate could
> > represent its path over time, whatever gets the job
> > done.
>
> So you're saying a surrogate id can represent an
> "untrackable attribute", standing for the complete world
> line of a particle through space and time, without
> actually acknowledging that the particle exists!

As I pointed out before, 'exists' is a semantic vacuum. Your final phrase is equivalent to "without actually acknowledging that the particle is ... !" The '...' is empty, meaningless filler just as "exists". Until that void is replaced with facts, it remains meaningless.

> How do you explain the surrogate id in the relation
>
> Position(*id,*t,x,y,z)
>
> used to record the world lines of multiple particles that
> are otherwise indistinguishable?

You are so close; so very close to an epiphany. If they are otherwise indistinguishable then don't distinguish them! Not knowing the context I can't say for sure but it seems either (t x y z) or (t x y z count) would be more appropriate for configuration and ((t x y z) (t x y z)) for transitions.

> > > I am struggling with your assertion that relations
> > > only are about roles and values, not entities.
>
> > A relation is a subset of the cross-product of n
> > domains. Those domains do not contain 'entities' they
> > contain values. I hope that clarifies it.
>
> Far from it. Let me explain my pov, by describing what
> various terms mean to me. Perhaps you may see something I
> have wrong. If that is the case I would appreciate
> something more specific and useful than merely "nonsense"
> (as Bob would typically say).
>
> The word "exists" appears a lot in mathematics. For
> example consider
>
> P = there exists nonzero integers x,y,z
> such that x^2 + y^2 = z^2

That is a specific, well defined use of the word "exists" (quantification) attached to a predicate (x^2 + y^2 = z^2). And the predicate is crucial. In contradistinction, informal use of "exists" (certainly as you have used it attached to "entity") map to meaningless statements such as:

P = there exists x y z ...

that amount to nothing until ... is filled in.

> Generally speaking mathematicians don't waste time arguing