-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of meekerdb
Sent: Wednesday, January 07, 2015 12:12 PM
To: [email protected]
Subject: Re: Why is there something rather than nothing? From quantum theory to
dialectics?
On 1/7/2015 3:22 AM, Bruno Marchal wrote:
>
> On 06 Jan 2015, at 20:21, meekerdb wrote:
>
>> On 1/6/2015 1:48 AM, Bruno Marchal wrote:
>>>
>>> On 03 Jan 2015, at 06:05, 'Roger' via Everything List wrote:
>>>
>>>> Even if the word "exists" has no use because everything exists, it
>>>> seems important to know why everything exists.
>>>
>>>
>>>
>>>
>>> But everything does not exist. At the best, you can say everything
>>> consistent or possible exist.
>>>
>>> Anyway, as I said, the notion of nothing and everything, which are
>>> conceptually equivalent, needs a notion of thing. That notion of
>>> thing will need some thing to be accepte
>>>
>>> It is often ambiguous in this thread if people talk about every
>>> physical things, every mathematical things, every epistemological things,
>>> every theological things, ...
>>>
>>> So, we cannot start from nothing.
>>>
>>> We light try the empty theory: no axioms at all. But then its
>>> semantics will be all models, and will needs some set theory (not
>>> nothing!) to define the models. The semantics of the empty theory is a
>>> theory of everything, but in a sort of trivial way.
>>>
>>> Computationalism makes this clear, I think. We need to assume 0 (we
>>> can't prove its existence from logic alone, we need also to assume
>>> logic, if only to reason about the things we talk about, even when they do
>>> not exist).
>>
>> What does it mean to "assume 0". Is it to assume a collection of
>> things
>
> No. If we assume a collection, we would do set theory, or something.
> We might assume some intended collection at the metalevel, but if we
> build a formal theory (a machine), we will not assume a collection at the
> base level.
>
>
>
>> such that every element has a unique successor (per some ordering
>> relation) and there is one element that is not the successor of any other
>> element, which we call zero?
>> That seems to assume things too.
>
> Assuming zero means here that we add a symbol ("0") in the language
> alphabet, and we assume some logical formula. The non logical symbol
> that we have introduced are "0, s, + and *", and we assume some formula like:
>
> ~(0 = s(x)), for any x (the x are always supposed to denote the
> object of our universe, here the intended standard natural numbers)
> also:
>
> 0 + x = x
> 0 * x = 0
>
> We don't assume anything else (about zero).
So 0 is just a mark on paper, a symbol that is not a symbol "of" anything such
as the empty set.
I get the feeling that '0' has a lot more meaning for Bruno than merely being a
vertically oriented oval drawn on a paper (or computer screen), that it is a
symbolic notational reference to a rather profound concept, which eluded the
world for much of its recorded history. It wasn't until the fifth century A.D.
in India that mathematicians fully conceived of it giving it conceptual
existence, though it was used earlier as a kind of decimal place holder as far
back as 300BC or thereabouts -- in Babylon. It was the Italian mathematician
Fibonacci who introduced the concept back into the church darkened intellectual
deserts of Europe in 1200 AD. Placeholder type zero's -- to differentiate an
empty number column seems to have been adopted in ancient Sumer. It is only
however much later that the concept of zero was really understood.
Read somewhere that the concept of zero was independently arrived at by three
different cultures -- as far as we currently know that is -- including the
Olmecs (the mother culture of meso-America) from whom the Mayans later adopted
it -- A Mexican anthropologist friend of mine told me this while I was living
down there in the Veracruz cloud forests some years ago. Most accounts,
attribute the meso-American discovery of the concept of zero to the Mayans, but
he insisted that the Mayans had picked it up from the much earlier Olmec mother
civilization.
-Chris
>
>
>
>
>>
>>> Then once we have the numbers, the addition and multiplication
>>> axioms, we have a Turing universal system and all its relative
>>> manifestations, i.e. all computations or all true sigma_1 sentences,
>>> and the physical reality is an illusion coming from the internal statistics
>>> on the computations.
>>
>> But in your UDA the fact that the computer executing the UD is Turing
>> universal seems irrelevant.
>
> The UD is a universal machine, programmed to generate and execute all
> programs. A computer is by definition a Universal machine.
How is a "program" defined? Isn't it just a deterministic sequence of states?
>
>
>
>
>> It simply executes all possible sequences of states - it doesn't
>> necessarily compute anything in the Turing sense.
>
> It does not generate all possible sequences of states. It genuinely
> execute each programs, on each input in the Turing sense. It just do
> it litlle pieces by little pieces, but the computations are genuine
> computations. You might look at the code. I am not sure why you say
> that it generates all sequence of states. You confuse perhaps with the
> library of Babel.
>
>
>> In fact those threads that compute something halt and will become of
>> measure zero as the UD proceeds.
>
> Intuitively, but the incompleteness breaks the intuition, and the
> measure is determined by the logic of self-reference restricted to the
> Sigma_1 sentences (which represents both sates and finite halting
> computations).
>
> That works. We do get a quantization which behaves up to now as it
> should, if computationalism and quantum mechanics are correct.
What is the justification for restriction to Sigma_1 sentences?
Brent
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