Re: Skolem Again

On 9 Oct 2005 08:51:15 -0700, William of Ockham
<d3uckner@xxxxxxxxxxxxxx> said:
> If I make a mistake, please tell me what's wrong.

ok, but I sorta thought that's what I and others have been doing.

>> It's about the implications of a technical result of which you
>> are ignorant.
>
> And which I am trying to understand, both by finding the'right'
> textbook, and from what you are saying. I apologise if anything I say
> comes off as 'spouting'.

By which I only meant "going on at length".

>> Most of your confusion arises from the fact that you are having
>> such trouble distinguishing truth from truth in a model.
>
> As I understand, "S is true in M" means that the state of affairs said
> to exist by S, is included in M.

But why do you insist on understanding it like that? "S is true in M"
has an *extremely* precise meaning in model theory, which is essential
to having a good grasp of the L-S theorem. There are no such things as
states of affairs in model theory *at all*.

> I don't know what 'true' means.

Well, in this context, true in the universe of sets, which is a species
of truth in a model (modulo some set/class issues that I'll ignore
here). The point, again, is that many of our theories are designed to
characterize as far as possible one specific model, or perhaps a class
of structurally similar models, and by "truth" we mean truth in *them*.

>> Do you mean, a given interpretation may result in "x is uncountable"
>> being true of some set of things of which it is 'really' false?
>
>> True *in some model* of some set of things of which it is "really"
>> false.
>
> It's the 'really' I am having trouble with. Why do you put scare
> quotes around?

I was simply following your lead. They add nothing.

.

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