On Thursday, December 20, 2018 at 12:46:06 PM UTC, Bruno Marchal wrote: > > > On 19 Dec 2018, at 16:52, [email protected] <javascript:> 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]> wrote: > > On Tue, Dec 18, 2018 at 5:42 PM <[email protected]> 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. >
*An "axiom" is any statement one assumes to be true. AG* I know only Carnap and Bunge to have attempted axiomatic (in the stricter) > logician sense for physics. > *Absent a Theory of Everything, there is no possible axiomatic structure "for physics". AG * They failed, > *It was a project doomed to failure because there is no such thing as a general theory of physics for which it could be applied. AG * > 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. > *Not merely "spirit", but concrete results. Einstein was able to derive the Lorentz transformation from his two postulates or axioms; namely, the Principle of Relativity and the invariance of the SoL for inertial frames, and in the process rendered Lorentz's ether theory irrelevant. AG* But like Euclid, he remains “intuitive” for the math part. > *Not merely intuitive, but concrete math results! See above. AG * *Same situation prevails for QM as far as axioms are concerned, but here there's nothing intuitive! For wave mechanics, there are about 4 or 5 postulates or axioms pulled out of a hat, from which the consequences follow. For Feynman's Path Integral model, there are 3 postulates, which have already been posted. AG* 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. > *Nothing intuitive about one of our best physics theory, QM, AG * > > 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]. > 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. > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To u > > ... -- 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.
