Stephen writes
> Consider the Cantor hierarchy and the way that "nameability" seems to
> become more and more difficult as we climb higher and higher.
Yeah, remember Rudy Rucker's joke in "Infinity and the Mind" where
he points out "It is interesting to note that the smaller large
cardinals have much grander names than the really big ones. Down
at the bottom you have the self-styled inaccessible and indescribable
cardinals loudly celebrating their size, while above, one of the
larger cardinals quietly remarks that it is "measurable"."
What has happened, I think, is that the seventh or eighth time that
your mind is completely blown, even having your mind *blown* gets
familiar---and even perhaps a bit dull. The Red Queen could also
have told Alice that every day before breakfast, she has her
whole world view turned upside-down and inside-out at least several
times.
> The reason why this question has no answer is because there is no point
> at which the question about "First Causes" can be posed such that an answer
> obtains that is provably True. This is the proof that Bruno's work shows us,
> taking Gödel's to its logical conclusion.
Come on, now. Nobody here, understands what Bruno's done, except
*maybe* Bruno. You draw the most sweeping conclusions from the smallest
things. Common sense tells one that questions about "First Causes"
don't have any answers of substance, but it's a stretch to say that
this comes from rumination about Gödel's theorem. Sounds just like
the people who derived moral relativism from Einstein's work.
> Additionally, the notion of a "first cause", in itself, is fraught with
> tacit assumptions. Consider the possibility that there is no such a thing as
> a "first cause" just as there is no such thing as a privileged frame of
> reference. We are assuming that there is a "foundation" that is manifested
> by the "axiom of regularity":
>
> http://www.answers.com/topic/axiom-of-regularity?method=5
>
> Every non-empty set S contains an element a which is disjoint from S.
>
> Exactly how can Existence obey this axiom without being inconsistent?
> Before we run away screaming in Horror at this thought, consider the
> implications of Norman's statement here:
You misunderstand what the axiom is saying. (I admit, I was
shocked and appalled at your rewording of it---but then it
turned out that *you* were not the criminal who reworded it
this way. It's actually in the link you provide!! (Thanks.))
Well, at least liability if not criminality, unless it's
immediately added that what this is saying is that we
demand that any S set have the property, in order to
qualify as being a real set, that it is not incestuous
with at least one of its elements: I mean, there is at
least one of its elements that it doesn't share an element
with.
For example, if S = {a,b,c}, say, then we cannot have
a = {b,c}, and b = {a}, and c = {a,b,c}, because then it's,
like, totally devoid of substance. Whereas if there was
some *honest* element d in S such that d = {a, S, c, f},
then while it is pretty wild to have S itself, along with
the other suspiciously incestuous elements like a and c
contributing to the potential delinquency, at least it has
f, which makes it free from total engagement in perverse
behavior.
*Regularity* was the nicest axiom that Zermelo found that
saved us from the very worst kind of circularity, I guess.
Lee
Received on Sat May 21 2005 - 14:36:11 PDT