On 15 Sep 2017, at 01:55, Brent Meeker wrote:
On 9/14/2017 5:01 AM, Bruno Marchal wrote:
On 14 Sep 2017, at 13:22, ronaldheld wrote:
This should cause some discussion. Maybe belongs in the "is math
real" thread, but that one is large??
Ronald
What is your opinion?
The author believes that PI does not existed 100,000 years ago.
It looks like he believes that 100,000 existed 100,000 years ago,
making hard for me to understand why PI would not exist,
and in which sense, as PI is not a function of time.
That's just snark. There's nothing to indicate he thinks 100,000
existed 100,000yrs ago.
Fair enough.
Then the author seems to believe in a primary physical universe,
and does not seem aware that this is an assumption too, and indeed
arguably much stronger than assuming arithmetic.
He doesn't say anything about "primary" physical universe.
Which is part of the problem. That is why I said "it looks like ...",
but all its exemples and quotes (Galilee, Wigner) are typically
Aristotelian, and he mention the Aristotelian (anti-platonic) criteria
of truth (seeing and knocking on the table!).
Then his conclusion: PI does not exist, which alludes to the fact that
he has admitted that the table exists. In a discussion on what exists,
this, without precision does not need the qualitficative "primary". It
is just that in the Aristotelian Era people use matter for primitive
matter, and existence for physical existence.
Every time someone "assumes" a physical universe, you claim they are
assuming a "primary" physical universe.
"Assuming" leads almost to "primary", by default. "primary means
"assumed" in the fundamental theory (up to some equivalence relation).
This doesn not follow at all. First, he isn't assuming a physical
universe - he's observing it.
By asking if PI exists, he assumes (unclearly, OK) that he is
observing something real, or "really real".
Of course, we never observe if something is primary, and our immediate
perception just told us something about ourself. It is a consciousness
state.
He is arguing that assuming arithmetic, and the rest of mathematics,
is the stronger assumption.
Stronger than what? It is here that he is vague, and he forces the
reader to at least temporarily, take the physical existence for
granted. But "physical existence" if primary is either completely
unclear (what is primary matter?) or invoke physical *laws*, which
always are described as number relations. They are measurable numbers,
but they assume arithmetic, at the least. If you assume classical
mechanics and billiard balls, you get the Turing universality
equivalent (with respecto the computable) with very elementary
arithmetic (Robinson theory).
The main problem is that the author does not put its assumption on
the table, and take for granted that existence is physical existence.
Observation is the antithesis of "taking for granted".
Right. But in metaphysics, like when discussing on PI existence, we
cannot take for granted that what we observe is real. Just by taking
the Dream Argument into account. He seems to be doing exactly that.
You too, sometimes. But that is only an Aristotelian habits, and it
beg the question when discussing on what exists.
The indexical form of computationalism that I study has the advantage
to be utterly clear on this, once we fix the starting universal
machinery to start with. Like
K exists
S exists
if x exists and y exists, then (x y) exists.
And the "meta-induction" principles, made explicit for the Gödel-
Löbian "observer/dreamer", which says that nothing exists but what you
can get from the axioms above.
So, what exists is clear: it is K, S, (K K), (K S), ... ((K (S K))
K), etc.
The minimal Turing universal belief is then for all x y ((K x) y) = x,
and for all x, y, z, (((S x) y) z) = ((x z)(y z)).
In the first order logical specification of that theory, + the
induction principle: P(K) & P(S) & for all x [P(x) & P(y) ->. P((x y))]
That gives Löbian combinators, they obey to G and G*. It can be shown
that all self-referentially correct classical combinators, or number,
or (Turing) machine, are Löbian.
Classical means they believe that classical logic is secure on the
finite and computably enumerable things. It is not full blown
classicalism like with set theoretical realism, or any "precise"
mathematicalism.
That does not make sense with mechanism (probably), but to be
franc, I am not sure this makes sense even without mechanism. He
confuses also mathematical theory and mathematical reality, it seems.
What do *you* think? What would be your primary assumption?
My feeling is that it is a waste of time to guess what exists or
not before saying what we are willing to assume as primitively
true, or what is the metaphysical background accepted.
That's because you're a theologian at heart and want to start with a
god.
In the fundamental studies we always start from a god, i.e. a Reality
which explains the things simply and coherently.
It is God in the sense: explains everything, and (incompleteness) we
cannot prove (public rational justification) that there is a reality.
The god of computationalism is simple, in fact, if computationalism is
true, then it is a secret that the universal machine is God.
Oops.
The fact is that G1* proves p <-> Bp <-> Bp & p <-> Bp & Dt <-> Bp &
Dt & p.
But G1 proves none of those equivalences, and indeed, gives a
different views of what God knows to be one thing.
The universal machine put some mess in the arithmetical Heaven, and
its soul is teared apart by its eight (4 + 4*infinity actually) points
of view possible.
The "God" of the Machines/Combinators/Numbers is more like a universal
dreamer which lost itself in a labyrinth of dreams, yet mathematical
structured, and which might be able to awaken, or to become lucid, to
recognize itself, to say "hello" to itself, but also to lost itself
again, and again. And like all gods with a quasi-name, the "God" of
computationalism hides another God. The (arithmetical) Truth is *big*
and complex, even the gods pay taxes, (in some sense)...
Note that no One can know that computationalism is true (that is why I
insist on the conditional, and why I mention that the Yes-Doctor
requires an act of faith).
Bruno
What, you ask, was the beginning of it all?
And it is this ...
Existence that multiplied itself
For sheer delight of being
And plunged into numberless trillions of forms
So that it might
Find
Itself
Innumerably (Shri Aurobindo)
Brent
Bruno
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