> On 3 Oct 2019, at 12:12, Alan Grayson <agrayson2...@gmail.com> wrote:
> 
> 
> 
> On Thursday, October 3, 2019 at 3:39:26 AM UTC-6, Bruno Marchal wrote:
> 
>> On 1 Oct 2019, at 20:29, John Clark <johnk...@gmail.com <javascript:>> wrote:
>> 
>> How Many Universes Are There? <https://www.youtube.com/watch?v=XglOw2_lozc>
>> 
> 
> 
> 0.
> 
> Bruno
> 
> You've turned Tegmark upside down,

That looks intersting, but I don’t know. Maybe you can elaborate. I published 
my material well before Tegmark, and start from a very different problem (the 
mind-body problem). 
When Tegmark send me his Mathematical Hypothesis paper, I suggest him to use 
the Mechanist hypothesis explicitly to clarify possible ambiguities. What is 
common is the Mathematicalism, but Tegmark still miss the psychologicalism, or 
the theologicalism needed to get physics from arithmetic (and arithmetical 
self-reference).



> on his head. But the same core fallacy remains. AG 

Which one?

I say 0 universe since my birth, not because it would be incompatible with 
Mechanism (which it is), but because I have never seen any evidence for an 
ontologically real universe. I have no doubt that long and deep histories 
exists, but this requires only assumption in arithmetic.

Keep in mind that I give a theory (indeed a very simple one: Kxy = x, and Sxyz 
= xz(yz). All the rest are definitions and theorem (made in that theory).

Well just to be sure, you need some inference rule, so the entire theory is:

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

AXIOMS

4) Kxy = x
5) Sxyz = xz(yz)

(See the combinators thread for an explicit proof that this is Turing 
universal). 

To be sure, I can use much more complicated theory, like the complete first 
order predicate calculus + the axioms:

1) 0 ≠ s(x)
2) x ≠ y -> s(x) ≠ s(y)
3) x ≠ 0 -> Ey(x = s(y)) 
4) x+0 = x
5) x+s(y) = s(x+y)
6) x*0=0
7) x*s(y)=(x*y)+x

… which as the same time is the one taught informally in high school.

Bruno


> 
> 
> 
> 
>> John K Clark
>> 
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