Re: On Formal IS-A definition

On May 9, 9:29 am, David BL <davi..._at_iinet.net.au> 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)."
>
> and this (fromhttp://en.wikipedia.org/wiki/Hereditary_set)
>
> "In set theory, a hereditary set (or pure set) is a set all of whose
> elements are hereditary sets. That is, all elements of the set are
> themselves sets, as are all elements of the elements, and so on."
>
> I wonder whether Bob enjoys putting a leash on a set and taking it for
> a walk.

I wonder if you know what a variable is? Or more specifically I wonder if you can prove that a variable is not a set? Well, that is a rhetorical question really because I already know that a variable /is/ a set. Or rather, because the word "is" is vacuous most of the time, a variable can be represented by a set. Since you enjoy wikipedia so much (since when did wikipedia become an authoritative source?) try reading this (thoughtfully):

   http://en.wikipedia.org/wiki/Variable_(mathematics)

and see if you can figure out how it is that variables can be represented by sets. Hint, a variable is a /symbol/.

Once you've got that it should be easy to understand how one can have sets of variables.

Now honestly I would have thought, from what you've posted in the past, that you would already have known this. Taken from previous discussions we have the following:

   DBL knows that in formal semantics /variables/ are /interpreted/    DBL knows that an interpretation is formally a /relation/ mapping

      variables (and all other symbols) to elements of the /domain of
      interpretation/ also sometimes called a "universe"

ergo DBL /should have known/ that variables are sets.

KHD Received on Mon May 10 2010 - 07:34:00 CEST