Hi, Bruno and my warm thanks for your friendly explanations. I need time to
chew into them and find out how we indeed can think beyond the capabilities
of our knowledge - our mind. This pertains to the great minds (Church to
Marchal as well). All I read in my first glance was 'thoughts in human
terms' done by existing human minds and suppositions about 'other' minds
that may think more. I have to get to terms with the idea that a 'humanly'
identified theory (may include Babage whom I appreciate a lot) can extend
into items (I evade: 'topics') never heard of so far and into relations of
such. To terms that the world as we think of today (that includes the recent
- advanced - views as well) is a primitive, limited model of some poorly
undestood information we received so far and formulated into our
conventional sciences, even advanced worldviews.
Human logic is just that: "human". 2+2 = 4 is how the human mind can accept
math. In terms of the 'unlimited', our quantities, even numbers (pardon me
for the attack) are humanly formed entities and the substrates in the
endless totality (everything?) may not justify them once we take a
differently centered view. Who can pretend to know (including computations)
what may be going on in differently composed universes, what forces (if any)
and changes (if any) may occur and what conclusions may be drawn - without
knowing - in unknown substrates? IF there ARE substrates at all????? - (not
only in our simplifying translation?)
Topics may not be in an unlinmited interconnectedness of them all, unless WE
assign our interest and it's known relations into restrictions into
So please, give me some time to let my mind 'sink into' your positional
writing - and MAYBE to re-evaluate my ideas.
PS. A silly question: would it have been possible to establish conputation
before the 'new' knowledge of the "zero" was acquired? If the answer is NO,
let me imagine that 'other' (like the zero-like importance) novelties will
come up later on and change ways how we all think. J
On Fri, Mar 18, 2011 at 11:12 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:
> Hi John,
> In computer science there is something interesting which can be seen as a
> critics or as a vindication of what you are saying. That thing is the Church
> thesis, also called Church-Turing thesis, (CT) and which has been proposed
> independently by Babbage (I have evidence for that), Emil Post (the first if
> we forget Babbage), Kleene, Turing, Markov, but not by Church (actually).
> The thesis has many versions. One version is that ALL computable functions
> can be defined in term of lambda expressions, or in term of Turing machines,
> or in term of Markov algorithm, or in term of Post production system, etc.
> All those versions are provably equivalent.
> Such a thesis *seems* to be in opposition with your idea that complete
> knowledge is impossible. But it is not.
> The contrary happens. Indeed the thesis concerns only completeness with
> respect to computability, and then, as I have already explain on this list,
> it entails the incompleteness of any effective knowability concerning just
> the world of what machines can do. Church thesis makes it impossible to find
> *any* complete theory about the behavior of machines. I explain this in the
> first footnote of the Plotinus' paper. I can explain if someone ask more. It
> is proved by a typical use of the (Cantor) diagonalization procedure.
> It vindicates what you say, really. We can sum up this by
> Completeness with respect of computability provably entails a strong form
> of incompleteness for our means of knowability and provability about
> machines' possible behavior.
> This can be proved rigorously in few lines. It is stronger and easier than
> Gödel's incompleteness, and it entails Gödel's incompleteness once we can
> show that the propositions on the computable function can be translated into
> arithmetical propositions (the lengthy tedious part of Gödel's proof).
> Not only Church thesis makes it possible to think about 'everything', but
> it makes us able to prove our (machine's) limitation about the knowledge
> about that everything. In any case, this makes us modest, because either CT
> is wrong and we are incomplete for computability, or CT is true and we are
> incomplete about our knowledge about computability, machines, and numbers.
> On 16 Mar 2011, at 17:10, John Mikes wrote:
> In my opinion an oxymoron.
>> We cannot even 'think' of it without a complete knowledge of everything,
>> the entire wholeness, call it 'totality' underlying such 'theory'.
>> "All possible" anything, (algorithms, descriptions, assumptions, whatever)
>> - encompass only those 'possibilities' we can think of
>> in the volume of our acquired knowledge (of yesterday). Even (our?)
>> 'impossibilities' are impossible within such framework.
>> We cannot step out from our circle of knowledge into the unlimited unknown
>> world. Any comp we can identify (or even just 'speak' about) is within our
>> world of known items and their relations. Includable into our ongoing
>> Compare such framework of yesterday with a similar assumption of 1000, or
>> 3000 years ago and the inductive development will be
>> There is no way we could include the presently (still?) unknown (but maybe
>> tomorrow learnable) details of the world (including maybe new logical ways,
>> math, phenomenological domains, etc.) into our today's worldview of "all
>> possible". [Forget about sci-fi]
>> Maybe even the ways of composing 'our' items (topics, factors, relations
>> and even 'numbers') is a restricted limitational view in the 'model'
>> representing the present level of our development - of which conventional
>> sciences form a part.
>> Comparing e.g. the caveman-views with Greek mythology and with modern
>> 'scientific' futurism (like some on this list) supports this opinion. So I
>> would be cautious to use the qualifier 'COMPLETE'.
>> John Mikes
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