RE: Is the meaning of order intrinsic ?

From: Seth Russell [mailto:seth@robustai.net]

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

>>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.

You asked, "Is the meaning of order intrinisc?"  By "intrinsic definition" I
mean the mechanism that you would need to define or have for the "meaning of
order to be intrinsic".

>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?

For example take a look at:
http://www.shu.edu/html/teaching/math/reals/infinity/defs/ordering.html or
http://burks.brighton.ac.uk/burks/foldoc/9/116.htm

But as I previously stated, "I think there may be an intrinsic order and a
non-intrinsic order." ...  "The system needs to preserve the positional
order( if the system has a
concpet of an ordered list )."  Beyond this explicitly the user should be
able to define what it means to them for a list to be in a paticular order.
For this the language will
need a way for the user to define a function.  

>Seth Russell

Pat Emery