1. B

    Gödel's 2nd theorem ends in paradox

    Godel's 2nd theorem ends in paradox http://gamahucherpress.yellowgum.com/wp-content/uploads/GODEL5.pdf Godel's 2nd theorem is about "If an axiomatic system can be proven to be consistent and complete from within itself, then it is inconsistent.” But we have a paradox Gödel...
  2. H

    Godel's undecidability

    Hi, first point: This topic is about logic but I have found no category in this forum concerning eg logic, set theory atc, so I decided to place it in the category Applied Math. I have one quick remark (question): Is it so that Eucleid's fifth postulate (about parallels) is the "first"...
  3. H

    Is kendall rank coefficient compatible with Kurt Godel's completeness theorem?

    Hello everyone. In Logic, Predicate Calculus, "Kurt Gödel's completeness theorem" states that A formula is provable in the L (logical system) if and only if it is valid in the S (semantics). In Probability and Statistics, "Maurice Kendall's Kendall rank correlation coefficient"...
  4. L

    Godel incompleteness in set theory ZFC

    I am trying to understand what Godel incompleteness means in terms of ZFC. Let A be a set whose members satisfy predicate p. I suppose we can understand the predicate p as an axiom or a set of axioms that entail A - is that correct? If A is subject to Godel first incompleteness theorem...
  5. B

    Tough questions for those who believe Godel's Theorems

    Godel's Theorems are built on the premise that the following sentence is grammatical: G is not provable. That's not a grammatical statement. You can only assert G is not provable if you know what G stands for. Why isn't the following true? G is provable. Godel's followers cannot give a...
  6. M

    0^0 and Godel's incompleteness theorem

    I was studying on the binomial theorem and it seems that it requires that 0^0 is 1 On the other hand, the notion that 0^0 is indeterminate is also widespread. I would prefer if all mathematicians agreed on a concrete value for 0^0. Otherwise it seems like a shoddy concept ("we assign it such...
  7. D

    Godel's incompleteness theorems

    I don't really understand Godel's two incompleteness theorems. Could someon please explain them in simpler terms? Thanks.
  8. M

    Gödel's Theorems

    Hey guys, I'm reading Godel, Escher, Bach right now and it's sparked my interest in Godel's incompleteness theorems. The book encompasses so many ideas so sorry if this isn't in the right forum but it seems like it could go in about any topic. Anyway, my question is what class might one...
  9. M

    Godel, Escher, Bach

    Hey everyone, Recently I stumbled upon a book called "Godel, Escher, Bach" and I thought it looked and sounded extremely interesting. I looked it up on youtube to see if there were any reviews but i came across these MIT lectures with the title of the book as the title of the videos. I...
  10. K

    Godel's Incompletness Theorem

    Before we have a look at Godel's Theorem, Lets revisit few basic concepts First of all if G= A+B (i.e G= A or B) Then ~G = ~A . ~B(i.e negation of G = negation of A and negation of B) . This is De Moivre's theorem. Case1: Now let us consider a statement G which is either true or false . For...
  11. H

    Gödel's Completeness Theorem

    I'm currently reading this book called Set Theory and the Continuum Hypothesis, written by Paul Cohen, which is a model-theoretic investigation of the topics. I'm trying to rediscover the proof of Gödel's Completeness theorem for myself, but I'm kind of stuck on certain details of the proof...
  12. J

    Cool documentary on Cantor, Boltzmann, Gödel, and Turing

    Free on the Google tube. It's called Dangerous Knowledge and was done by the BBC. http://video.google.com/videosearch?q=dangerous+knowledge&hl=en&sitesearch=#