Re: On Formal IS-A definition

On May 10, 12:07 am, paul c <toledobythe..._at_oohay.ac> wrote:
> David BL wrote:
> > On May 9, 11:38 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>
> >> My set of three variables and a dog fully complies with ZFC.
>
> > Here is a quote from (http://en.wikipedia.org/wiki/Zermelo
> > %E2%80%93Fraenkel_set_theory)
>
> > "ZFC has a single primitive ontological notion, that of a hereditary
> > well-founded set, and a single ontological assumption, namely that all
> > individuals in the universe of discourse are such sets. Thus, ZFC is a
> > set theory without urelements (elements of sets which are not
> > themselves sets)."
> > ...
>
> So? I would like to know what problem arises if a db's attribute values
> stand for singleton sets instead of 'urelements'.

What do singleton sets have to do with this?

I'll say it three times now: It can be convenient to use urelements. Algebraic systems don't bother formalising the elements of sets like the natural numbers as particular sets. This is convenient because for example there are many alternative "encodings" of the natural numbers using hereditary sets with a defined successor function that obeys the Peano axioms. Here is one "encoding":

0 = {}
1 = {{}}
2 = {{},{{}}}
3 = {{},{{}},{{},{{}}}}

In this case the successor function satisfies S(n+1) = n union {n}. It can be proven for example that S is an injection (which is one of the Peano axioms).

An alternative "encoding" is:

0 = {}
1 = {{}}
2 = {{{}}}
3 = {{{{}}}}

Mathematicians like to focus on the essence of things, hence the importance of morphisms, and indeed this led to category theory where they play a central role. Mathematicians say *the* natural numbers because they are unique up to isomorphism. This is the only reason to downplay the foundations of set theory where every object in the universe of discourse is a particular set.

That doesn't mean a mathematical set can contain dogs or variables. That's just ridiculous.

> How can that possibly
> change a dbms' results? How can it prevent Rosie from having properties
> in common with some variable or other? Would Codd care or just call
> this technocracy at its silliest?

I assume you you mean technobabble not techocracy. Furthermore I assume you mean obscurity through gratuitous technical terminology (rather that good technical prose that appears like technobabble to the nontechnical).

Are you suggesting axiomatic set theory is technobabble?

I think you've got it arse about. Technobabble often involves confusing/mixing pure mathematical abstractions with the informal. Indeed mention of a mathematical set containing a dog is a sure sign of technobabble.

I cannot speak for Codd but I imagine he would simply say that databases record values, such as string values like "rosie". I think he would agree that a database cannot store a dog. Received on Mon May 10 2010 - 05:24:39 CEST