What’s Your World View?

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• Postmodernist! I am 94% post-modern. I always suspected I might be, but now that an internet quiz has confirmed it I feel much better.

  Is there anyone who actually believes that "Science can solve all problems and answer all questions, eventually"? That seems to be several miles more implausible than the rest of the statements, no matter how much I love science.

• Um. I took the quiz yesterday and did not record my results, but I was most Materialist, and then Postmodernist not too far behind. I am pretty sure that science can EVENTUALLY solve all problems and answer all questions. I do not feel that any one person will ever bear witness to all of it. But I think that any question individually could be answered at one time by science.

• Okay, I guess the intent probably was "there is no question which science can't eventually answer" which is much weaker than being able to solve all problems or answer every possible question. Still, I don't buy it. Unless you accept "we can never know that" as a valid answer to "why does the universe exist?"

• Even I, science boy, will have to state something that may seem completely the oppostie of what you might expect:

  There will always be some questions that science will never be able to answer.

  Why? Because of Kurt Gödel's Incompleteness Theorem.

  Here's one of the more formal ways to state the theorem:

  Let T be a formal theory for which the Gödel numbering (a numbers system in which all formauls and proofs in T each assigned a natural number to uniquely identify them) and diagonal lemma can be carried through, and all axioms - and hence theorems - of which are true. Then T is incomplete, i.e. there are sentences in the language of the theory- as exemplified by the Gödel sentence G for T - which can neither be proved, nor refuted in the theory.

  Whoa. Major math-geekery here. What ol' egghead was trying to say is that each and every branch of mathematics has some axioms that could never be proven within that branch of math itself. You have to go outside that system into a larger branch of mathematics, which in turn would have its own set of axioms that couldn't be proven within that branch of mathematics, unless you then went outside that system, which would put you in yet a larger branch of mathematics...and so on.

  The practical gist of what G�del says is nicely written by Carl Boyer with Isaac Asimov in A History of Mathematics:

  G�del showed that within a rigidly logical system such as Russell and Whitehead had developed for arithmetic, propositions can be formulated that are undecidable or undemonstrable within the axioms of the system. That is, within the system, there exist certain clear-cut statements that can neither be proved or disproved. Hence one cannot, using the usual methods, be certain that the axioms of arithmetic will not lead to contradictions ... It appears to foredoom hope of mathematical certitude through use of the obvious methods. Perhaps doomed also, as a result, is the ideal of science - to devise a set of axioms from which all phenomena of the external world can be deduced.

  In other words, scientific proof of the limits of science. Hence my answer.

  For a whimsical look at Gödel's Theorem, read Douglas Hofstadter's classic book, Gödel, Escher, Bach: An Eternal Goldern Braid.

  Because Gödel's Theorem is often condensed to "there are some things that are true but can't be proved", it is often cited as proof of the existence of God. That's a stretch; at best, the Theorem can be used as an inspiration for an argument for the existence of God.

  That's not to say that Gödel didn't come up for an argument for the existence of God. Gödel was an admirer of Leibniz (one of the people to blame for calculus), who believed in the possibility of "rational theology" and cam eup with an ontological argument for the existence of God. Gödel himself also conceived his own argument for the existence of God, which is covered in detail here.

• By the bye, there's more on Gödel's Incompleteness Theorem here.

• Haven't you learned yet that you're not supposed to prove me wrong in public?

• I didn't prove you wrong, sweetie: I prefer to think of it as scientifcally proving you mostly right.

• Scored the exact same as Accordion Guy for Culturally Creative (81%) but the rest is quite different.

• Lola needs to do the test again. She didn't really like to hear that she is materialist.

• Lola took the test again and was fundamentalist. She found the religion questions a little vague. They assume that people belong to a religion.