most of Russell's *paradoxi* were just versions of "Uncle Bertie is lying, again," with the temporal reference left out; the Village Barber e.g. is easily resolved in plain language (barbers don't usually cut their own hairs; they go to another village for that). if you want to know about his more fullsome and "productive" lies as an alleged Peace Activist, you can look it up on the LaRouche website.
the books you cite are to heterogenous; Singh and Aczel are pretty awful, striving to be somewhat mathless; Kline, I haven't read as much of as Klein, who's not For Dummies; Rucker's 4D stuff is just a joke, continuing the British Psychical Research crap, Abbot Abbot Squeezed Flatlandmania superfluousness (modern, even more deathless exercises of this "school" are from Ian Stewart, Dewdney etc. -- don't have to read the whole thing); Penrose and Hofstadter are good, as little as I've read of them (NB: Penrose's "tribar" is just a God-am Mobius strip); Smullyan's book on reverse-engineering chess is great, if I ever read it, set as a Homes novel -- I doubt if you could find any author that is more "expository."
there is nothing difficult about Godel's proof, and there are many expositions of it. I mean, how can you know any thing -- if you can, you can know this. some tines, the solution to a "math problem" is just "more mathematics" (*mathemata*, the *study* of music, geometry, astronomy, arithemtic).
> mathematics. For example, books by Hofstadter, Penrose, Rucker, > Smullyan, Kline, Singh, Aczel, and maybe others. She is troubled that a
> formal, you still have to deal with the informal notion of proof: does > Godel's proof compel us to believe that Godel's theorem is actually
> of what we are saying. Hence, an utterance such as "I am lying" (i.e. > the Liar paradox) must be analyzed as if it contained its implicit
> Our skeptic notes that consistency is the concern of the liar. Those
uh-oh, here cometh the Last Digit of Pi -- dude *cited* Sokal, heh-heh -- not the digit in the Director's Cut of "Contact".... there is no sufficient reason for you or me to comprhened Wiles' proof, which you can take to be alleged til such time as you might do that; there are probably two-many (at least) proofs of Fermat's "last" theorem, wich appears to be a very early result of his & indicative of his method, perhaps the first use of it, which might even have subsumed "infinite descent" in some sense ... that is, you may as well think about his theorem with other math, or geometry, or what ever, with the possible exception of "probability," since that can never prove any thing (after all, per your example, their are an infinity of 50th powers).... in other words, Well it looks like Fermat could have proved it, and this British guy in a closet has been reported to have in a Famous Math Journal out of New Jersey; maybe there are elementary proofs in between or around them.... NB: Fermat made not even one mistake, that I know of, including his conjecture about the Fermat numbers, but it took a hundred years, aside from F"L"T, to show thatso, what was his mehtod?
> > Not really. There are lots of people with essentially the same > > skeptical arguments who come into these newsgroups. > > The word for someone who claims modern mathematics derives from Jewish > mysticism (or Neoplatonism, or Gnosticism, or Advaita Vedanta, or > Freemasonry) is not "skeptic".
thus: how simple of a reference do you want, relating to "really, really tall office-buildings that are hit by a plane filled with fuel for a transontinental flight, bigger than a flock of V2s?..." just guessing, about the V2 equivalence.... do you want it to be in only Self-consistent Muslim Physics?... the important thing, of course, is that they were offices for the "earned income" folks, hte folks who are bringing you the Protocol of the Elders of Kyoto (sik), whether or not you agree with the tactics, or even on who had used them on us.
> Yeah, and while you're at it why don't you gravitation experts explain > how the WTC buildings can spontaneously gravitationally collapse into
thus: note the key phrase, which I hasn't noticed til a day after I posted it, that they actually did have an amendment to *extend* the God-am preclearance rules -- how much further, I know not -- although it may have been illegal to pass it.
>Of the four amendments defeated in the House, three had the support of a >majority of the chamber's 231 Republicans. Only the suggestion that the >Voting Rights Act be extended to cover other jurisdictions was defeated by >majorities of both Republicans and Democrats.
thus: compression is only & always deployed around tension.