> Nam Nguyen wrote:
>> Jesse F. Hughes wrote:
>>> MoeBlee <jazzm...@hotmail.com> writes:
>>>> On Jun 16, 8:32 pm, Nam Nguyen <namducngu...@shaw.ca> wrote:

>>>>> Basically my claim is:

>>>>> Given a formal system T, the set of T's theorems can *not* contain more
>>>>> non-logical symbols than that of T's axiom-set.
>> MoeBlee wrote:
>>>> If the system uses logical axioms, then I don't see how the above
>>>> could be incorrect.
>> Ok. But hoe does this relate to my claim above which is *general*?
>> What did he try to say here: a refute, or a support to my claim?

>>> It could be incorrect, depending on the exact specification of the
>>> logical axioms and rules of inference, right?  In the most trivial
>>> case, we may treat all of the usual axioms as zero-ary inference
>>> rules.

>>> But I assume that Nam meant "T's *non-logical* axiom-set" in any
>>> case.  Perhaps he can clarify what he meant to say?
>> My claim says exactly what we saw above there. T's axiom-set is the
>> set of T's axioms, nothing more nothing less. Because FOL= is assumed,
>> this axiom-set will be non-empty (since x=x is in it). Would this axiom-
>> set have any non-logical symbol? My claim doesn't say; but nonetheless
>> it's still the set of axiom of T! Likewise, the set of T's theorems
>> is just that: the set of T's theorems!

>> So my claim is a very simple meta statement that's either true or false
>> but there's nothing mysterious or hard to understand what it says.

>> But it's ok to me that you asked for clarification. And I've clarified
>> it.

> I haven't been following this thread closely, just dipping into it
> from time to time, but it appears to me, that (with the the exception
> of one small point, treated below) with this post you have established
> your point beyond contention, as irreducibly and trivially true.

> Congratulations to you, and to Moeblee also, for putting his finger
> on the significant point, that the axiom set necessarily includes
> the set of logical axioms.

> The only remaining quibble is the point Jesse Helms raises.  FOL
> can be treated as an axiomless system, consisting only of a set
> of rules for transforming one string into another.  You state
> above that for FOL= there is at least one axiom, x = x.

> I am insufficiently interested in FOL= to know whether it can
> also be treated as an axiomless system.