> On 27 Feb 2018, at 11:42, Telmo Menezes <te...@telmomenezes.com> wrote:
>
>> Depends on what you mean by "proof", we sentence people to prison based on
>> proof of their crime. Not all proof is mathematical. And mathematical
>> proof is only relative to the axioms.
>
> I think that this is one of those cases where the term is overloaded.
> I would argue that, for most people, proof has a strong connotation of
> "case closed". Mathematical proof is the only domain where this is
> actually true.
In real life mathematics, you are right, at least for Arithmetic, except that
even here some ultra-finitists would disagree.
In real life mathematics, the proof are informal, and usually convincing. They
correspond, in the theology of the machine, to
[]p & p
And they do not correspond to the formal proof []p, despite from a 3p view, on
assumed correct (simple) machine, we can see they are the same, but the
(simpler than us) machine cannot see it.
Only computability is “really” absolute. Provability means only rational
justification from my primitive belief.
Now, at the meta level, we all agree on the axioms of arithmetic, and so for
arithmetic, what you say is true … but remains not provable by us. Our
conviction remains based on our consciousness, and we have to project our
rationality on the other to proceed. We do that since we are child, so it is
difficult to realise that we make an act of faith there, but it is there, and
with mechanism, needs to be there.
That is really the kind of things which are so counter-intuitive that the use
of the machine self-reference logic (machine’s theology (G*) or/and machine’s
science (G)) is obligatory.
> Everywhere else it is relative: it means sufficient
> evidence for some course of action to be taken.
All axioms, to be accepted, even in pure mathematics, requires some faith. This
is not related to the fact that the axioms are not provable from less, but it
is related with the fact that adopting the axioms means we believe they are
consistent, yet we cannot even assume that consistency without either becoming
inconsistent, or changing completely the theory into a much more powerful
theory, on which this remark will reapply again and again.
> I suspect that judges
> and lawyers like the term because it makes everyone sleep better at
> night. I never see contemporary scientists using the term, only
> science journalists. Again, this makes sense: the general public likes
> to feel that science is settling matters. I think it is anti-pedagogic
> to talk about scientific theories being "proven", because it conveys
> the wrong idea about what science is and what science does. For a
> serious scientist, nothing is ever settled and no cases are closed.
OK. (And for a metamathematician or mathematical logician, this is true even
for x + 0 = x, at the object level, but not at the informal level well all
science is done, and that is why it concerns metaphysics or philosophy of
mind/theology, not engineering, physics, or mathematics).
> There are strong hypothesis at a given time, there are effective
> models for certain domains, and one does the best one can with them.
> The lack of this "case closed" attitude is precisely what makes
> science such a magnificent endeavour, and why it shines so bright
> above the certainties of the religious fundamentalists and the
> ideologues.
Absolutely.
The problem is that very often, materialists confuse physics and metaphysics.
They interpret religiously physics, which is not a problem neither in physics,
nor in metaphysics, if done consciously. When done unconsciously, the whole
computationalist mind-body problem will dissolve into pure pseudo-religion, and
that did happen already in Aristotle, and much more with its institutionalised
religion. They will criticise the whole metaphysics and religion, and separate
this from science, because they have chosen their religion and metaphysics, but
without awareness of the fact, taking it fir being science, which it is not
(and that is the key thing that Plato did understood, but Aristotle did not (or
evacuate it by the usual mockery and insult technic, applied to Plato, in his
metaphysics).
Bruno
>
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