Re: Resiliency To New Data Requirements

Bob Badour wrote:
> Keith H Duggar wrote:
> > Bob Badour wrote:
> > > Marshall wrote :
> > > > Neo wrote :
> > > > > That task has been to find the most general method
> > > > > of representing things.
> > > >
> > > > Answering that question is easy. The most general
> > > > method of representing things is to use bits.
> > >
> > > There is a more general method, which is to use
> > > sets. See formalism as a foundation of mathematics.
> > >
> > > {} is the canonical set with zero elements and represents zero or false
> > > {{}} is the canonical set with one element and represents one or true
> > > {{},{{}}} is the canonical set with two elements etc.
> >
> > I would have said the "most general way of representing
> > things" is a sequence of symbols from an alphabet. Of
> > which {}, {{}}, {{}{{}}}, along with the characters I'm
> > using now to represent English, predicate logic, etc are
> > all examples. If you limit the alphabet to only two
> > symbols 0 and 1 then you have binary sequences.

>

(since similar discussions frequently crop up in sci.logic a cross-post might get some interesting input.)

My suggestions for the most general uses only a single concept: language. Yours uses three concepts: set, element, and zero. :-)

Seriously, giving a concept a name (set for example) doesn't make it more or less singular. Determining the singularity of concepts is notoriously difficult. Surely you are aware that the set concept is often argued and many attempts are regularly made to provide a correct and complete definition.

The "element" language you used seems to indicate a concept of "set" as a collection of elements with the collection regarded as a whole or in Cantor's words "Any collection into a whole M of definite and separate objects m of our intuition or our thought."

Thus, there are in fact two concepts in this concept of set: element and aggregate. The concept of aggregate or wholeness being necessary to distinguish {{}}, {{},{}}, etc from {} for example. Furthermore, you can't get very far without at the additional concept of the empty set (or the concept of zero, nothing, etc) or ur-elements or some other atoms.

So you chose element, collection, and zero, while I chose 0, 1, and sequence. Which seem equally simple, no? No, I admit to also seeing sets as somehow "more simple". Partly because the concept of collection seems more simple than sequence obviously because collection lacks order. Though as natural as order is to humans perhaps the sequence concept does not add much if any "conceptual" complexity.

Alas, the question was of "generality" not simplicity. And I've never seen set theory represented without the use of sequences of symbols ;-) (Loaded statement of course.)

• Keith -- Fraud 6