Re: On Formal IS-A definition

On May 10, 8:06 am, Keith H Duggar <dug..._at_alum.mit.edu> wrote:
> Mathematically there is no "modification" or "mutation" nor
> any such anthropomorphic passage of time sense. A variable is a
> symbol. That symbol might have a binding. That binding is also a
> relation whose key is the variable symbol and in the case of an
> imperative interpretation if the variable is "mutable" also the
> "time" or "program counter" or similar is part of the key. For
> example the variable X might have the following binding relation
>
>    S T V
>    X 0 0
>    X 1 0
>    X 2 5
>    X 3 5
>    ...
>
> where S is the variable symbol, T is the "time", and V is the
> bound value. But note that nothing "changes" at T=2 from this meta
> perspective of math where "time" is just yet-another dimension.

Thank you for the clarification.

>
> > Wrong.  You can't modify a homomorphism just like you can't modify a
> > number or a set.  Homomorphisms are values and are therefore
> > immutable.  You have invented a homomorphism variable to hold a
> > homomorphism value.  What you claimed were variables were just values
> > intended to act as inputs to a homomorphism function.
>
> Except his error is irrelevant. Variables are symbols and are
> representable by sets. Their bindings (regardless of extent ie
> dependence on "time") can be represented by relations which are
> sets just as their interpretations are relations which are sets.

Regardless of how I try to define a set of variables, it seems I can only define a set of values and interpret it variably. I find Bob's reference to Clinton more significant now than at first. I suspect that asserting what a variable, a set, or anything else 'is' defers the interpretation and representation of the concept.

Should we write our posts in E-prime to represent our interpretations more clearly? Received on Mon May 10 2010 - 11:21:08 CEST