On Monday, December 3, 2018 at 2:42:26 PM UTC, Bruno Marchal wrote: > > > On 2 Dec 2018, at 15:00, [email protected] <javascript:> wrote: > > > > On Sunday, December 2, 2018 at 12:11:50 PM UTC, Bruno Marchal wrote: >> >> >> On 30 Nov 2018, at 12:13, [email protected] wrote: >> >> >> >> On Friday, November 30, 2018 at 12:34:13 AM UTC, Brent wrote: >>> >>> What can be inferred always depends on what you take as premises. If >>> you start from the Hilbert space formulation of QM or an equivalent >>> formulation* and you premise that there is a probability interpretation >>> of a state*, then Gleason's theorem tells you that the Born rule >>> provides the unique probability values. >>> >>> Brent >>> >> >> >> *So to get Born's Rule, Bruno would have to assume a huge amount IN >> ADDITION TO ARITHMETIC. I don't buy it. AG * >> >> >> On the contrary, mechanism assumes less than any other theory. And >> Mechanism is roughly the idea that the brain does not invoke magical things. >> >> The theory of everything, with mechanism assumed at the metalevel, assume >> only S K, S≠K, and the axioms >> >> 1) If x = y and x = z, then y = z >> 2) If x = y then xz = yz >> 3) If x = y then zx = zy >> 4) Kxy = x >> 5) Sxyz = xz(yz) >> >> I doubt that you will find an easier theory. >> (Exercice: prove that x = x) >> >> Bruno >> > > *But you haven't replied to my objection. In addition to logic and the > axioms of arithmetic, you must ALSO assume such a thing as probability > exists to even approach QM. What you have above won't cut it, IMO. AG * > > > > I do not assume any probabilities in the ontology. I justify them through > the phenomenology. Here I was just making clear that I assume only the 5 > rules and axioms above. There is three inference rules: > > 1) If x = y and x = z, then y = z > 2) If x = y then xz = yz > 3) If x = y then zx = zy > > And two axioms: > > 4) Kxy = x > 5) Sxyz = xz(yz) >
*Are the variables restricted to natural numbers, that is, the positive integers? What are these axioms, explicitly? And No, I don't believe there's enough here to infer de Broglie matter waves, or the quantum interference pattern for, say, the double slit. AG* > Nothing else is assumed, except mechanism and as much as needed > mathematics at the meta level, like in all theories. > > I don’t expect you to believe this immediately. I just present the result, > hoping you will study the proof. > > Bruno > > > > > >> >> >> >> >> >>> On 11/29/2018 10:23 AM, [email protected] wrote: >>> >>> *Regardless of rules of arithmetic and mathematical logic, I simply >>> don't believe that something like Born's Rule can be inferred without >>> actually observing a quantum interference pattern. AG* >>> >>> >>> >> -- >> 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 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. > 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 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.
