According to Gödel's incompleteness theorem, no matter how many statements you prove, you will always have a set of statements not proved. Does this imply that some time in the future, scientific development will come to a halt due to our inability to discover/invent anything new?

  • 9
    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/14939/2451 , physics.stackexchange.com/q/156909/2451 and links therein. $\endgroup$
    – Qmechanic
    Feb 2 '16 at 17:30
  • 1
    $\begingroup$ 1. Any meaningful sense in which this question could be asked is a duplicate of the linked questions. 2. Your statement of the incompleteness theorem is non-sensical - it says every axiomatic system is either inconsistent or has true statements which cannot be proven, while you're just saying that there are unproved statements. $\endgroup$
    – ACuriousMind
    Feb 2 '16 at 17:46
  • 1
    $\begingroup$ no need of something so complicated. Likely some of the speculative theories will never be falsifiable because the lack of observations $\endgroup$
    – user46925
    Feb 2 '16 at 17:47
  • 1
    $\begingroup$ Goedel's theorem is only relevant for statements about infinite sets, to begin with. Any statement about finite sets is trivially testable by enumerating its results over the entire set. There are no infinite sets in physics, so that alone removes any possible application. $\endgroup$
    – CuriousOne
    Feb 2 '16 at 22:58

No. In mathematics we prove conjectures, theorems, etc. In science we do not prove a hypothesis. We run experiments to either support or refute the hypothesis, but as time goes on and new evidence becomes available conclusions can swing direction. Proof is an exercise pursued by mathematicians.

  • 2
    $\begingroup$ Besides that, having more things "unproven" is good for science, since that is what science is for. $\endgroup$
    – Asher
    Feb 2 '16 at 17:28

Not the answer you're looking for? Browse other questions tagged or ask your own question.