And the links..

By: Ilya Lipovsky (lipovsky.delete@this.cs.bu.edu), February 21, 2008 11:07 am
Room: Moderated Discussions
JasonB (no@spam.com) on 2/20/08 wrote:
---------------------------
>Ilya Lipovsky (lipovsky@cs.bu.edu) on 2/20/08 wrote:
>---------------------------
>>Personally, I do not completely disagree with your very global view on what "science"
>>is. ...

>That's an interesting (but reasonable) way of looking at it.
>
>There are actually quite a few undecidable statements, with the continuum hypothesis and the axiom of choice being the two most famous ones. Wikipedia (I don't usually quote it this much, but these articles have actually been quite reasonable) lists a few more: http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Examples_of_undecidable_statements
>
>This is actually quite interesting, because the self-referential nature of the
>particular statements that are used to prove incompleteness (effectively, "This
>statement is false") don't, to my mind, rule out the possibility that all "normal"
>statements are decidable.

If I understand properly, "decidability" of a set refers to the fact that one can compute (i.e. decide) in a finite time whether individual elements belong.

I think you are trying to ask whether the set of "normal" statements (i.e. first-order logic statements that are logically valid (simply put, true)) is decidable. Indeed, that's the case, according to Gödel's Completeness theorem.

>The fact that there are entirely reasonable statements
>that turn out to be undecidable as well is non-obvious to me, although someone far
>smarter might realise that there is a connection between them all.
>
>>Nevertheless, I think even with all this philosophical stuff in mind, it's still
>>necessary to distinguish between science and math as being in very different realms.
>
>We normally use the term "empirical science" to describe what you have been calling
>"science"; maths and theoretical computer science are "formal sciences". Empiricists
>don't believe in anything except empirically-derived results, and you see them popping
>up from time to time complaining about string theory et al because an awful lot
>of work is put into something that they don't even consider "proper" science since
>we can't even predict what we would need to do to distinguish between string theory
>and the standard model. (Since we don't know which parameterisation of string
>theory matches our universe, we don't know what energies are required to produce
>the kinds of particles that would confirm its accuracy; the LHC might produce something
>that supports string theory (or supersymmetry at least), but then again it might
>produce nothing and the conclusion would be "Well, we just need more energy".)
>
>>Therefore, "computer science" is informatics ;-).
>
>QED? :-)

Absolutely, thanks for the correction :-D! So yes then, I suppose I am more of an empiricist when it comes to distinguishing science from everything else.
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TopicPosted ByDate
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  And the links..Anders Jensen2008/02/14 04:25 AM
    Disappointing..Linus Torvalds2008/02/14 10:17 AM
      Disappointing..Mark Roulo2008/02/14 11:03 AM
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        Disappointing..Linus Torvalds2008/02/15 05:01 PM
          Disappointing..anon2008/02/15 08:54 PM
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              The limits of single CPU speed are here.Howard Chu2008/03/17 01:47 AM
                The limits of single CPU speed are here.slacker2008/03/17 10:04 AM
    And the links..Howard Chu2008/02/14 12:58 PM
      I take some of that backHoward Chu2008/02/14 01:55 PM
      And the links..Jesper Frimann2008/02/14 02:02 PM
      And the links..Ilya Lipovsky2008/02/15 02:24 PM
        And the links..iz2008/02/17 10:55 AM
          And the links..JasonB2008/02/17 07:09 PM
            And the links..Ilya Lipovsky2008/02/18 01:54 PM
              And the links..JasonB2008/02/18 10:34 PM
                And the links..Thiago Kurovski2008/02/19 07:01 PM
                  And the links..iz2008/02/20 10:36 AM
                And the links..Ilya Lipovsky2008/02/20 03:37 PM
                  And the links..JasonB2008/02/20 06:28 PM
        And the links..JasonB2008/02/17 06:47 PM
          And the links..Ilya Lipovsky2008/02/18 02:27 PM
            And the links..JasonB2008/02/18 10:00 PM
              And the links..JasonB2008/02/19 03:14 AM
              And the links..Ilya Lipovsky2008/02/20 04:29 PM
                And the links..JasonB2008/02/20 06:14 PM
                  And the links..Ilya Lipovsky2008/02/21 11:07 AM
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                        rubyinline, etc.JasonB2008/03/02 05:26 PM
                rubyinline, etc.JasonB2008/03/02 06:01 PM
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                    rubyinline, etc.JasonB2008/03/03 03:57 PM
                      rubyinline, etc.Dean Kent2008/03/03 08:10 PM
                        rubyinline, etc.Michael S2008/03/04 01:53 AM
                          rubyinline, etc.Dean Kent2008/03/04 07:51 AM
                            rubyinline, etc.Michael S2008/03/04 08:29 AM
                              rubyinline, etc.Dean Kent2008/03/04 08:53 AM
                                rubyinline, etc.Michael S2008/03/04 11:20 AM
                                  rubyinline, etc.Dean Kent2008/03/04 02:13 PM
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                      efficient HLL'sPatrik Hägglund2008/03/05 01:23 AM
                        efficient HLL'sMichael S2008/03/05 02:45 AM
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                              efficient HLL'sWilco2008/03/06 02:27 PM
                    efficient HLL'sanon2008/03/05 08:20 AM
      And the links..Groo2008/02/17 04:28 PM
        And the links..Vincent Diepeveen2008/02/18 02:33 AM
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