Stephen writes > Consider the Cantor hierarchy and the way that "nameability" seems to > become more and more difficult as we climb higher and higher.

## Advertising

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