FOM: certainty

[F. Xavier Noria]

On Wed, 6 Jan 1999 11:11:02 Arnon Avron wrote:

| On Wed, 23 Dec 1998 0:52:36 +0100 Xavier Noria wrote:
|
| > We agree what is right about naturals and what not. All our N's have an
| > associative addition, and prime and composite numbers and questions to
| > know the answer, but I think that _truth_ have nothing to do with it.
| > 
| > Our N's satisfy that 2 + 2 is equal to 4, but, to my mind, this is our
| > _agreement_ about our abstraction. Saying "2 + 2 = 4 is true" sounds
| > quite different to me.

[snip]

| Unfortunately, I dont feel that I have the right to say what is right
| about *your* N's. How can I know?

I think you cannot know it on your own. We should need to share some
information at least, and I emphasize this is only my opinion.

| since you (and Vladimir Sazonov) have several N's, you have at least one
| which is different from my own poor, lonely N (this only follows, I admit,
| from what is right about *my* logic. You may of course have several other
| logics!). So how can we agree about your N's with which I will never
| possibly have any acquaintance?

Probably, if `several N's' means something like `non-isomorphic models
of a given feasible set of axioms', we'll agree.

Th(N) is the set of first-order formulas valid in what?

Does your N satisfy GC?

-- Xavier