Hi Lee,
I see that you have not yet experienced the wonders of non-well founded
set theory! Let me point you to the first paper that I read that started me
down this road:
http://www.cs.brown.edu/people/pw/papers/math1.ps
I hope you can view Postscript files. Let me know if otherwise.
Stephen
----- Original Message -----
From: "Lee Corbin" <lcorbin.domain.name.hidden>
To: <everything-list.domain.name.hidden>
Sent: Saturday, May 21, 2005 2:32 PM
Subject: RE: WHY DOES ANYTHING EXIST (typos corrected)
> 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 - 15:37:13 PDT