Re: Skolem Again

On 4 Oct 2005 12:42:02 -0700, William of Ockham
<d3uckner@xxxxxxxxxxxxxx> said:
> P1. L-S tells us that orthographically identical theories may have
> different models.

It tells us no such thing.

> By "orthographically identical", I mean that the textbooks used to
> teach the theory, and which list the principal theorems of the theory,
> are word for word the same.

Then they are *exactly the same theory* -- in which case they have
*exactly the same models*. Models don't glom selectively onto a
combination of theory+textbook.

> P2. Theories that are learned in an identical way cannot have
> different meanings.
> P3. But theories with different models have different meanings.

> P1 is a consequence of a mathematical truth.

No, it isn't, it is a consequence of your failure to understand the L­S
theorem. What the (downward) L-S theorem tells us that if a given
theory -- one particular theory -- has any infinite models at all, it
has a countable model. Your talk of "orthographicall identitical
theories" is sheer confusion. Any insights you have here are completely
obscured by the fact that you are arguing in ignorance. It is really
unbecoming for someone as smart as you to be arguing in the classic mold
of a crackpot.

> I assume P2 is obvious (and no one here has disagreed with it). Here
> is the argument for P3.

Problem is, P1 is false.

.