Re: Skolem Again



> Chris Menzel wrote:

> > Well, P2 is scarcely grammatical, but let's focus on P3.
>
William of Ockham wrote:
> What is ungrammatical about "The same theory must have the same
> meaning"? Absolutely standard English.

You are SO COMPLETELY full of ***.
SAME is BINARY. Same AS WHAT?? You have said "the same theory"
withOUT an ANTECEDENT! I repeat, same AS what??

> Meaning, for those who prefer
> it expressed that way, if x is a theory and y is a theory,

But you didn't MENTION the possibility of both x AND Y being
theories. You just said "the same theory". That IS ungrammatical.

> and x=y,
> then x has the same meaning as y.

In STANDARD English, that would be "EQUAL theories have equal
meanings",
or "identical theories have identical meanings". Theories and meanings
PLURAL. DESPITE the fact that "true" equality would imply that there
is only one theory and only one meaning. The point is that in real
life
you DON'T get 1: You get TWO different PRESENTATIONS of things that
turn out to be SUFFICIENTLY SIMILAR in character that you HYPOTHESIZE
some underlying single thing as having produced them. That is of
course
precisely why YOU were originally tempted to talk about
"orthographically
indentical theories". Lots of things that happen in "standard English"
DON'T stand up well to serious consistent analysis.
That's another reason why most of US resort
as often as we do to FORMAL languages. That is even more true when
the things being discussed are abstract; abstractions behave
differently
from concrete things in some ways.

> In any case, as you now recognise, the disagreement is bound to be
> about P3.
>
> > From the fact
> > that a given interpretation of a theory makes all of its axioms true it
> > does not follow that it can properly be considered the theory's meaning.
>
> But if grasp of meaning is grasp of truth-conditions, this is terribly
> difficult to avoid.

Don't be ridiculous. EVERY model or interpretation is FURTHER
away from the meaning of the theory THAN THE THEORY ITSELF is!
THe theory itself should not even be thought of as having a meaning
anyway! Look in a dictionary! What do you see, there, as being
blessed
with meanings?? YOu DON'T see THEORIES! YOu see INDIVIDUAL WORDS!
At best one could assign meanings to whole sentences, based on the
meanings of the words. But NOBODY assigns meanings to anything
infinitely
big like a whole theory! Sentences are about as big a thing as you
would
ever NEED to assign a meaning to. The FORMAL theory BY DEFINITION
consists ONLY of the sentences that are PROVABLE, that are theorEMS.
That is WHY it is CALLED a theoRY! The axioms can meaningfully be said
to assign meanings to THOSE sentences. NO MODEL WHATSOEVER is relevant
to these sentences because ALL these sentences (and their denials) have
THE SAME truth-value in ALL models! There is no disagreement among
the-multiple-models-of-the-1-theory about the truth-value of any of
these
sentences. So the theory can reasonably, and model-INdependently, be
said to assign a meaning to them, much as the dictionary does to words.
MODELS NEVER assign meaning TO ANYthing! All models can do IS ROB
sentences of clear meaning BY DISAGREEING WITH EACH OTHER as to whether
the sentence is even true or false!

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