On 04 Dec 2014, at 22:05, John Mikes wrote:
Bruno: one of your tiny little aberrations:
how did "existence" changed in your argument into "physical
existence"?
I am studying the digital version of the antic Mechanism idea, already
explained to the king Milinda (plausibly the greek king called
"Menandre" in french) some millenaries ago, but reinstated by
Descartes, notably.
In the theory, I have given an argument (UDA) which leads to a scheme
of theories of everything: all theories in which we can defined a
Turing universal system. It will define the same physics.
I have chose arithmetic and combinators as simple concrete example.
So what exist "really"? You have the choice between numbers 0, 1, 2,
3, ... (or combinators K, S, KK, KS, ...) and nothing else, except
that we postulate also the addition and multiplication laws (resp
application and abstraction, which does not introduce any new number,
but is needed to define the universal system, here universal numbers,
which will dream and select the anything else).
My usual parody of Kronecker sum up well what happens: God cretaed the
natural numbers, all the rest are dreams by the (universal number).
So something ontologically exists if it is equal to some
s(s(s(s(s(s(0)))))).
Then you have the epistemological existence, and this will include
physical existence. Something physically exist if it is observable,
and by UDA we know that this means having some probability one in a
repeatable way from some first (plural) person points of view.
Mathematically this is capture by the physical or material modalities.
precisely the one given by the []p & p (and []p & <>t, and []p & <>t &
p) with p sigma_1 (that is a proposition of arithmetic having the
shape "it exists n such that P(n) with P decidable).
Keep in mind the math of the points of view
p ontological existence level
[]p science level, the level of beliefs, ideas, sometimes called
the doxastic level.
[]p & p knowledge level
[]p & <>t Observable level, first person plural, the physical, proper
[]p & <>t & p The observable and perceptible level
They all differ (obey different logic), and with p sigma_1 they all
defined quantum modal logic, and so provide structure akin to Hilbert
Space (very abstract one), with symmetries (making the experience/
experiment repeatable) and reflexivity.
That leads to a way to distinguish the pure mathematical existence Ex
(... x .... ) from the different form of existence:
we have a notion of scientific existence (as ideas): [] Ex [] (...
x ....), physical existence (the same, but with the modal box
redefined as being the modal operator corresponding to the nuance above.
But here, we were in the physical context, and so we were talking only
about physical existence.
Bruno
I argued that there is no such difference, since nobody can identify
the term "physical" in unquestionable format. Just like the
"Godcreated Earth".
JM
On Wed, Dec 3, 2014 at 5:01 AM, Bruno Marchal <[email protected]>
wrote:
On 02 Dec 2014, at 22:42, LizR wrote:
On 2 December 2014 at 22:56, Bruno Marchal <[email protected]> wrote:
On 02 Dec 2014, at 01:18, LizR wrote:
Unicorns exist, but they are more commonly called rhinos.
Hmmm... OK. With a large definition of unicorn. I mean those are
very large unicorns!
The point is that may have been the origin of the legend -
traveller's tales that got distorted. Plus the narwhal horn as
mentioned by John.
Of course unicorns may exist, in that evolution may have produced
something that looks like a unicorn on a planet somewhere. They
aren't that unlikely (unless you include the stuff about virgins
and so on).
In "our universe"? I don't know. Perhaps if life itself is not that
rare, and I have no clues on this. I have evidence that life is
frequent, and that life is not frequent. They compensate each other.
Yes, that's why I only said they "may" exist. Given that it seems a
reasonable adaptation that could easily occur (unlike say cows able
to jump over the moon or fire-breathing dragons....probably). So if
life is common enough in the universe, evolution could have
produced something fairly unicornish somewhere.
Although in the arithmetical reality, there are infinities of
dreams, including sharable first person plural coherent long one,
in which unicorn (with again some large definition) can exist.
OK, although I don't know how that works I am prepared to believe
you (like Harry Potter universes in the MWI)
Of course, with my definition of unicorn, as *fictitious* objects,
belonging only to fairy tales, they don't exist, even in arithmetic.
So something that only looked like a unicorn wouldn't count...? :-)
That's the point, and you did illustrate it well when mentioning the
rhinos. Nobody would pretend that now we know that unicorn exists,
because of the rhinos, unless (s)he is in a context where unicorn is
taken literally as meaning "one corn". Unicorn, like Sherlock
Holmes, are terms normally denoting fictive object/notion, unlike
PI, sqrt(2), or the Higgs bosons which exist in some form (algorithm
for making prediction, for example).
That the idea of unicorns comes from the rhino is an interesting
idea, but it would not make the unicorn *of the fairy tale* into
physical existence. They do exist, but only in fairy tales (which is
different of not existing at all or not conceivable, etc).
Bruno
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