On Tuesday, March 5, 2019 at 6:23:42 AM UTC-6, Bruno Marchal wrote:
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> On 5 Mar 2019, at 00:43, Brent Meeker <meek...@verizon.net <javascript:>> 
> wrote:
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> On 3/4/2019 3:54 AM, Bruno Marchal wrote:
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> On 3 Mar 2019, at 20:43, Brent Meeker <meek...@verizon.net <javascript:>> 
> wrote:
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> On 3/3/2019 4:52 AM, Philip Thrift wrote:
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>>
> Here's an example David Wallace presents (as an "outlandish" possibility): 
> Suppose in *pi *(which is computable, so has a *program* (a spigot one, 
> in fact) that produces its digits. Suppose somewhere in that stream of 
> digits is the Standard Model Equation
>
>     (say written in LaTeX/Math but rendered here)
>      
> https://www.sciencealert.com/images/Screen_Shot_2016-08-03_at_3.20.12_pm.png
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> So what could this mean? (He sort of leaves it hanging.)
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> Nothing.  Given a suitable mapping the SM Lagrangian can be found in any 
> sequence of symbols.  It's just a special case of the rock that computes 
> everything.
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> Even if rock would exist in some primitive sense, which I doubt, they do 
> not compute anything, except in a trivial sense the quantum state of the 
> rock. A rock is not even a definable digital object. 
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> It's an ostensively definable object...which is much better.
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> Ostension is dream-able. 
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> If someone want to convince me that a rock can compute everything, I will 
> ask them to write a complier of the combinators, say, in the rock. I will 
> ask an algorithm generating the phi_i associated to the rock.
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> There is no particular phi_i associated to the rock.  That's the point.  
> The rock goes thru various states so there exists a mapping from that 
> sequence of states to any computation with a similar number of states.
>
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> It is a mapping of states. It is like a bijection. You need something like 
> a morphism preserving the computability structure, which do not exist in 
> the rock. A computation is not just a sequence of states, it is a sequence 
> of states defined by the universal machine which brought those states. 
>
> There are bijections between N and Z, but only Z is a group, because those 
> bijections does not preserve the algebraic structure. Similarly, there is a 
> bijection between a computation and a movie of that computation, but it 
> does not preserve the causal/logical relation between the states, which is 
> a universal machine for the computation, and just a linear order for the 
> sequence, without structure, of the states.
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>   Of course one may object that the actual computation is in the 
> mapping...but that's because of our prejudice for increasing entropy.
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> OK.Now, a bijection between a physical computation and an arithmetical 
> computation do preserve the computability structure, that is why we can say 
> that the arithmetical reality/model implements genuinely the computations.
>
> Bruno
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>

The bijection

   material [physical] computation ↔ arithmetical computation 

is like (New Testament) Paul's thesis: There's earthly bodies and spiritual 
bodies.

"Not all flesh is the same: People have one kind of flesh, animals have 
another, birds another and fish another. There are also heavenly bodies and 
there are earthly bodies; but the splendor of the heavenly bodies is one 
kind, and the splendor of the earthly bodies is another. ... If there is a 
natural body, there is also a spiritual body."

Spiritual or heavenly fictionalism is like arithmetical fictionalism: 
spirits (like numbers) do not exist.

- pt




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