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?
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9Possible duplicates: http://physics.stackexchange.com/q/14939/2451 , http://physics.stackexchange.com/q/156909/2451 and links therein. – Qmechanic Feb 02 '16 at 17:30
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- 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.
– ACuriousMind Feb 02 '16 at 17:46 -
1no need of something so complicated. Likely some of the speculative theories will never be falsifiable because the lack of observations – Feb 02 '16 at 17:47
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1Goedel'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. – CuriousOne Feb 02 '16 at 22:58
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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.
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2Besides that, having more things "unproven" is good for science, since that is what science is for. – Asher Feb 02 '16 at 17:28