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JoshuaZ comments on Local truth - Less Wrong Discussion

13 Post author: NancyLebovitz 20 December 2013 05:04PM

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Tags: epistomology high_pressure chemistry science

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Comment author: JoshuaZ 22 December 2013 05:09:43PM 1 point [-]

There are no interesting consistent and complete axiom systems (recently discussed here by probabilistic approches).

This depends pretty heavily on what you mean by interesting, since it requires something like being able to model Peano Arithmetic or at least Robinson arithmetic. But first order reals or first order C are "interesting" systems (in the sense that we study them and there are open problems that can be phrased in terms of them) and are consistent and complete.

Comment author: Gunnar_Zarncke 22 December 2013 09:32:12PM 0 points [-]

First order reals [...] are "interesting" systems (in the sense that we study them and there are open problems that can be phrased in terms of them) and are consistent and complete.

I wasn't aware of that. Can you give some link?

Comment author: JoshuaZ 22 December 2013 10:18:22PM 2 points [-]

See here.

Comment author: Gunnar_Zarncke 22 December 2013 10:55:04PM 0 points [-]

Thanks.

I know quantifier elimination from CS and it makes for some useful practical algorithms but it seems not to be very powerful.

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