> On 19 Dec 2018, at 16:52, [email protected] wrote: > > > > On Wednesday, December 19, 2018 at 12:01:07 PM UTC, Bruno Marchal wrote: > >> On 18 Dec 2018, at 07:57, Bruce Kellett <[email protected] <javascript:>> >> wrote: >> >> On Tue, Dec 18, 2018 at 5:42 PM <[email protected] <javascript:>> wrote: >> On Tuesday, December 18, 2018 at 5:31:06 AM UTC, Bruce wrote: >> >> But we are talking about definitions of objects, not axioms of a theory. We >> know that any axiomatic theory will necessarily be incomplete -- there will >> be formulae in the theory that are neither theorems nor the negation of >> theorems. >> >> Based on the examples I previously offered, that QM and SR are axiomatic >> theories, can we conclude they're incomplete? AG >> >> Such theories of physics are not axiomatic theories. The things you referred >> to are broad principles, not axioms. > > That is right. Most theories in math and physics are not axiomatic. > > Concerning physics, nonsense! There's no difference between "the general > principles" defining quantum mechanics and SR, and the "axioms" defining > these theories. In SR, the genius of Einstein in 1905 was to put the theory > on an axiomatic basis which rendered Lorentz's ether theory irrelevant. AG
I guess you are using the term “axiomatic” in a more general sense that most logicians use that term. I know only Carnap and Bunge to have attempted axiomatic (in the stricter) logician sense for physics. They failed, but I think this should be pursued, as it will help for the type of consideration we have here, but that is a difficult task. Einstein was using the spirit of axiomatic thinking in SR, OK. But like Euclid, he remains “intuitive” for the math part. Minkowski axiomatic is more like the use in logic, but then it is no more physics. The difficulty to axiomatic physics is … the nature of what we man by “universe”, or by a physical reality, or even a physical experimental device. We work with our intuitive model of this, for good practical reasons. Bruno > > The same for mathematical logic: where formal axiomatic are the subject > matter, but all proofs are given informally (with the notable exception of > principle mathematica). > > Now, if we formalise a bit of quantum mechanics, we get quickly a theory rich > enough to define universal machine or numbers, so QM, when seen formally, is > incomplete for arithmetic. That does not mean that it is incomplete for > physics, a notion which is also not very well defined. For SR? It will > depends largely how we formalise it. > > Bruno > > > >> >> Bruce >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected] <javascript:>. >> To post to this group, send email to [email protected] >> <javascript:>. >> Visit this group at https://groups.google.com/group/everything-list >> <https://groups.google.com/group/everything-list>. >> For more options, visit https://groups.google.com/d/optout >> <https://groups.google.com/d/optout>. > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
