On 20 Aug 2017 17:23, "Bruno Marchal" <marc...@ulb.ac.be> wrote:
On 20 Aug 2017, at 17:24, David Nyman wrote:
On 20 Aug 2017 2:46 p.m., "Bruno Marchal" <marc...@ulb.ac.be> wrote:
On 19 Aug 2017, at 01:21, David Nyman wrote:
On 18 August 2017 at 18:13, Bruno Marchal <marc...@ulb.ac.be> wrote:
>
> On 18 Aug 2017, at 15:39, David Nyman wrote:
>
> He points at a mug and says that 'representations' (meaning numbers)
> aren't to be confused with things themselves.
>
>
>
> He confuses a number and a possible representation of a number.
>
> LIke many people confuse the (usual, standard) arithmetical reality with a
> theory of the arithmetical reality. Yet after Gödel we know that no
> theories at all can represent or encompass the whole of the arithmetical
> reality.
>
> It is not much different that confusing a telescope and a star, or a
> microscope and a bacteria, or a finger and a moon, or a number and a
> numeral ("chiffre" in french).
> But in math, it is quite frequent. In logic, such distinction are very
> important. In Gödel's proof, we need to distinguish a mathematical being,
> like the number s(0), the representation of the number s(0), which is the
> sequence of the symbol "s", "(", "0", ")" (and that is not a number, but a
> word), and the representation of the representation of a number, which,
> when we represent things in arithmetic will be something like
> 2^3 * 3^4 * 5^5 *7^6, which will be some s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(
> ....(0)...). (very long!).
>
>
> But what is the 'thing itself' at which he points?
>
>
> A mug. I guess.
>
Just so.
The question will be "what is a mug in itself". A materialist would say
that it is a structured collection of atoms, but a mechanist has to say
something like "a common pattern pointed at by some normal (in Gauss sense)
machine sharing some long (deep) histories. Something like that.
Yeah, something like that. I enjoyed Frenkel's talk actually. I like his
enthusiasm for mathematics. It's funny though he doesn't seem to appreciate
his implicit assumptions, or indeed that he is in fact expressing a
particular metaphysical position. Is math real? I mean, really real?
Trouble is, people assume that the answer is obvious, whether they think
it's yes or no.
We need only to agree on what we agree.
It's taken me years to appreciate this fully. The funny thing is that when
you say this to people they often object that this is the case only in
mathematics or logic, not in the 'real' world. But actually we can never
avoid the fact that we are always reasoning in terms of the assumptions of
some theory or other, whether it's explicit or not (usually not). So we
need to agree on what we agree, indeed.
The beauty of the Church's thesis, is that it entails by "theoremata" the
existence of the emulation of all computations in elementary arithmetic.
We can indeed agree to agree on that.
(Just that fact, and computationalism, should make us doubt that we can
take a primary physical reality for granted: it is the dream argument with
a vengeance).
Indeed.
The question is not "is math real", but do you believe that 2+0= 2, and a
bit of logic.
Difficult to disagree with.
I do not claim that the whole of philosophy or theology can become science,
but I do claim that if we assume mechanism, then by Church's thesis,
philosophy and theology becomes a science, even in the usual empiricist
sense.
About time too.
There is something funny here. The theology of the machine is
ultra-non-empiricist, as the mystical machine claims that the whole truth
(including physics) is "in your head and nowhere else". ("you" = any
universal machine). But that is what makes the machine theology testable,
by comparing the physics in the head of any (sound) universal machine with
what we actually observed.
Easier said than done though.
Math is real? Which math? I doubt that sincere people doubt arithmetic, and
I have never heard of parents who would have taken their kids out of a
school for the reason that hey have been taught that 2+2=4; neither in the
Western nor Eastern worlds.
Possibly in Airstrip One.
Now, for limit and real numbers it is much less obvious. here intutionist
and classical philosophy diverge. With Mechanism, it is better to
considered analysis (and eventually physics) as universal machine mind
tools. Gödel's incompleteness justifies partially why the machine needs to
invent infinities to better figure out themselves. Before Gödel, most
mathematician, like Hilbert, were hoping that with the finite and the
symbolic we could justify the consistency of the use of the infinities, but
after Gödel we know that even with the infinities we cannot circumscribe
and justify the consistency of the finite and the symbolic. The root of the
undecidability is the Turing-universality. With the conceptual discovery of
the universal machine, we got the tools to understand that we have no idea
what they are. Nor what they are capable of doing. A universal machine can
defeat all effective theory about itself, and it knows already that its
soul (first person) is not a machine.
So, to be clear: is *arithmetic* real? I think so. Fundamentally (up to the
Turing equivalence).
Good.
Is analysis real, yes, but only as a a phenomenological simplification of
the digital, which has still its laws.
But here we have no Church thesis, and no real notion of "standard model".
Should we teach infinitesimals whose consistency follows some work in non
standard model of arithmetic? Should we use intuitionist analysis? with or
without the intuitionist Church's thesis (not really related to the
classical).
On RA, there is unanimity (among humans today).
On PA there is unanimity minus one (Nelson)
On Analysis, or set theories, there is no unanimity, but a clear classical
"mainstream", and a lot of different, but easily related options reflecting
taste and personal opinions.
I doubt less that 24 is composite than any assumption in physics,
metaphysics, theology or whatever applied sciences.
That 24 is composite is among the 3p notions which are the closest to the
non communicable 1p certainty of consciousness here and now (the only non
doubtable thing).
Truth is certainly undoubtable.
David
Bruno
David
Bruno
David
>
> Bruno
>
>
>
>
>
>
> https://futurism.com/the-most-important-question-underlying-
> artificial-general-intelligence-research-is-math-real/
>
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