Re: what follows from denying an axiom

On Thu, 22 Jan 2009 16:49:56 -0800 (PST), george <greeneg@xxxxxxxxxxxxx>
said:
On Jan 22, 2:58 pm, Chris Menzel <cmen...@xxxxxxxxxxxxxxxxxxxx>
wrote:
you frequently stick your foot in your mouth.

Flaunting ignorance is an efficient way of getting it corrected,
in a context where that is what people care about. Unfortunately,
people here (me included) usually care more about defending their
egos.

Case in point here.

Yes, indeed, it is.

What I *said* was:

I DO NOT give a ***!
THIS is about what *I* am saying!

Well, yes, about what you said I said:

Second-order languages have a generalized model theory (from
Henkin) that is essentially first-order.

To which you responded:

The Henkin semantics IS NOT SECOND-ORDER ANYTHING

despite the fact that, not only had I not said it Henkin's semantics was
second-order, I had explicitly stated that it is first-order.

You do understand English well enough to see that that does not say that
Henkin's semantics itself is second-order, right?

This issue IS NOT what *I* do or don't understand!

It is certainly AN issue in a discussion if your misunderstandings are
leading you to make false or confused claims.

The ISSUE is what YOU do or don't understand!

It is an issue if indeed I am making false or confused claims because I
am misunderstanding something.

Unfortunately, your goal here is not really increasing anyone's
understanding.

Sure it is; yours, at least.

It is just proving that you didn't make a mistake.

That's just silly. I'm happy to acknowledge mistakes when I make them,
I just haven't made any in this instance. You, by contrast, are simply
overflowing with them. Your biggest confusion is to try to find an
error in my utterly innocuous and uncontroversial claim above. A second
error is your apparent belief that it is improper to refer to languages
with predicate quantifiers as second-order languages when in fact this
practice is almost universal (and easily justified). An error of more
recent vintage, based upon a technical confusion about the range of
second-order quantifiers in general interpretations, is that Henkin's
semantics is not a proper generalization (in the mathematical sense) of
standard second-order semantics.

MY point was that if you ALREADY KNEW that the Henkin semantics was
not second-order, THEN YOU SHOULD NEVER have claimed that it provided
"a generalized model theory for second-order languages". THAT IS JUST
BULL***.

No, in fact it is a common way of describing Henkin's semantics -- vide
the Enderton reference of the post to which you are replying. What is
odd is the fact that you find this description the least bit
problematic.

What it DOES provide is a TRUNCATED FIRST-order model theory for
second-order languages.

Huh? Replace your odd adjective "truncated" with "essentially" and you
have almost exactly *my* characterization of Henkin's semantics!
Notably, like mine, your characterization depends on the fact that
"second-order language" can be defined completely syntactically.

Or, if model theory is inherently in first- order ZFC or something
like it, it is that first-order THING's LAME attempt to SOMEhow make
itself relevant to some second-order consideration.

I can make no sense whatever of this claim.

PRECISELY BECAUSE it is basically equivalent to something first-order,
THE HENKIN SEMANTICS IS NOT WORTHY OF THE SLIGHTEST consideration OR
MENTION in the context of this conversation.

To the contrary, it is quite relevant to my original point, which was
that the use of a second-order language no more guarantees fixity of
meaning than the use of a first-order language, as both are susceptible
to nonstandard interpretations. In fact, you did make a couple of
interesting philosophical responses to this, one concerning the semantic
simplicity of "all" in comparison to "number" and another comparing the
kinds of "ontological contamination" one might have in the first- and
second-order cases due to the possibility of nonstandard
interpretations. I think you were pursuing some genuine philosophical
insights there. It's too bad you decided instead simply to
self-destruct over silly points of usage. I was beginning to think that
a discussion with you might actually be worthwhile.

.