Re: Is the meaning of order intrinsic ?

From: "Emery, Pat" <pemery@grci.com>

> To put things in an order is to arrange them in a sequence.

Yes of course.  A sequence is an order; and order is a sequence.  I don't
know how to distinguish the two.  I think for our purposes we can consider
those words synonyms.

>A sequence is a
> function.  I think all that you need for an intrinsic or non-intrinsic
> definition of order is to be able to define a function.

I don't know what you mean by "intrinsic definition".  To me something that
is intrinsic cannot be defined, or rather does not need to be defined.  In
model theoretic semantics they don't define Truth.  I suppose Tarski tried,
but I for one was not satisfied that he said anything.

I don't see how you can use the mechanism of a function to define sequence
either.  If I say f(a, b) =/= f(b, a) then I suppose I have defined that
(a,b) is an ordered pair in relationship to the function f.  But if sequence
was not already prior to the mechanism of our system the expression f(a, b)
would not even be distinguishable from the expression f(b,a) .. so such a
definition chases its own tail ... doesn't it?

On the other hand I can define a unordered pair using the intrinsic
mechinism of order which I am conjectureing is in all systems.  If f(a, b) =
f(b,a), then the pair (a,b) is unordered in relationship to the function f.

Seth Russell

Received on Thursday, 24 May 2001 14:54:17 UTC