On 21 Oct 2014, at 17:14, John Clark wrote:
On Tue, Oct 21, 2014 at 8:45 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
>> people proposing a Super Turing Machines are much more vague.
> I was not proposing any Super Turing machines. I was alluding that
the simple algorithm consisting to run a machine and wait if it
stops or not
is enough toi compute the Halting oracle
Wait? How long should I wait?
Well, it depends which programs you want to know if it stops or not.
The disonaur program stopped. In case it is that one. But for the
search of a proof of Goldbach in ZF, you might have to wait a bit long
more.
You can bound the running time of the programs with the Busy Beaver
function (BB).
The answer to your question is : no more than BB(k) seconds where k is
the number of bit used to describe the program you ask if it stops or
not. I assume a machine doing computational step in one second.
If it's still going after a million years should I give up and
conclude it will never stop, how about a billion, it it's still
going after a hundred thousand million billion trillion years how do
I know it won't stop in the next 3 seconds?
You can bound it by the BB functions, of course, you cannot compute
it, but it means that in the limit, you do compute the function. In
that sense, time acts as a halting machine oracle. I never pretend
that this is feasible, but there is a sense that a universe might do
that, or a portion of that.
>>> I don't not assume set theory, infinities, etc.
>> So you don't assume the real numbers exist?
> Indeed.
Interesting.
>> If so then not everything that mathematics is capable of
describing exists, and the same is true of another language, English.
> Computationalism implies the "arithmetical Platonia" is quite
enough. You can put the "real numbers" in the machine's
epistemology. You don't need ontological real numbers.
In nearly every post you say I'm confused, but this time I really
am. Do you think real numbers exist or do you not?
What I think is of no concern to you.
I work in a theory (computationalism + an infinitesimal use of Occam
Razor, and the classical theory of knowledge).
In that theory, the real numbers do not exist, as what exists is only
0, s(0), s(s(0)), etc.
But the real numbers still exists at the machine epistemological
level. Some can even be "physical", and some are only in the mind of
the machine, notably as useful tool for reasoning about machines and
their behavior, a bit like the use of analysis on problem in (natural)
number theory.
>>> you need to unstuck your mind in step 3
>> First you need to fix the first 3 steps.
> You have already agreed with step 0, 1, 2.
Have I? I haven't looked at it in years,
You seem to use a lot of energy to not understand.
if you put a gun to my head I could no longer even tell you what
steps 0, 1, or 2 were or if it was in step 3 that I decided that
the entire thing was worthless or if it was in some other step, and
nothing you have said more recently makes me think it deserves a
second look.
>Your refutation of step 3 confused the first person view [blah blah]
Yeah yeah I've heard it all before a thousand times: you're the
first human being in the history of the world to realize that there
is a difference between the first person and the third person,
You said that. The point is that if you accept the definition given,
then the FPI is a triviality to prove, and then you can move on step
4. That's all.
Bruno
and the distinction still confuses the particular first person who
is writing this sentence.
John K Clark
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