Bruno Marchal wrote:
> ...
> OK, you and Quentin have already solve this, I will not comment. Just a
> little summary in two points:
>
> 1) The deep reason why we can hope (pray, bet on, ...) in the universal
> dovetailer is just Church thesis which is possible thanks to the fact
> the set of programmable partial(*) functions is enumerable and close
> for the diagonalization procedure (unlike the case of the total
> programmable function which gives a non recursively (mechanically)
> enumerable subset of the partial functions.
> 2) But so, to execute all programs, we have to *dovetail* so that we
> will not been stuck in some infinite computations.
>
>
> (*) I include the total functions in the partial functions. A total
> function is a particular case of a function which is defined only on a
> subset of N, but here the subset is N itself. I will say a function is
> *strictly* partial when it is not total.
> I will try to make a summary of the main definitions and theorems.
>
> Bruno
> http://iridia.ulb.ac.be/~marchal/
OK. I think I understand what you are saying, on a surface level. Of
course a surface level will never be able to expose any contradictions.
I'm just riding this wave as long as I can before deciding to get off.
It seems that there are very deep concepts here. We are standing on
the shoulders of computability giants. I think it would take a Godel
or a Church or Turing to find any problem with your whole argument, if
there is any. My feeling is that any "problem" is actually just lack
of deep enough insight, either on the part of the attempting-refuter of
the argument, or on your part, or both.
By the way, I am also cognizant that what you are covering here
actually is pretty standard stuff and actually has been pored over by
the giants of computability. So like I said, I'm riding the wave.
On a certain level, it bothers me that Church's Thesis is said to not
have any proof. But maybe it is sort of like Newton's gravity. It is
just a descriptive statement about what can be observed. And yet... we
still don't really understand gravity. Here we are at the level where
all there is is falsifiability. And, by the same diagonalization
argument, you'd have to be God to falsify this "stuff".
Tom
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Received on Thu Jun 15 2006 - 07:54:10 PDT