On Sunday, December 2, 2018 at 12:11:50 PM UTC, Bruno Marchal wrote:
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> On 30 Nov 2018, at 12:13, agrays...@gmail.com <javascript:> wrote:
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> 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
>>
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> *So to get Born's Rule, Bruno would have to assume a huge amount IN 
> ADDITION TO ARITHMETIC. I don't buy it. AG *
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> On the contrary, mechanism assumes less than any other theory. And 
> Mechanism is roughly the idea that the brain does not invoke magical things.
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> 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 *

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>> On 11/29/2018 10:23 AM, agrays...@gmail.com wrote:
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>> *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*
>>
>>
>>
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