Re: Skolem Again

On 5 Oct 2005 12:29:41 -0700, William of Ockham
<d3uckner@xxxxxxxxxxxxxx> said:
> Chris Menzel wrote:
>> 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.
>
> Then rewrite the premisses so we agree P1 is true. Thus
>
> P1 One and the same theory may have different models
> P2. The same theory must have the same meaning
> P3. But the meaning of a theory depends on which model we take it to
> have
>
> These together yield a contradiction. Which of the premisses is false?

Well, P2 is scarcely grammatical, but let's focus on 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.
Some of its objects may, for example, have properties that we clearly
do not intend. Hence, the model can't be what we mean by our axioms.

.

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