On 6/8/2020 4:36 AM, Bruno Marchal wrote:
On 7 Jun 2020, at 23:03, 'Brent Meeker' via Everything List
<[email protected]> wrote:
On 6/7/2020 5:08 AM, Bruno Marchal wrote:
The UDA *proves* that the fundamental reality = arithmetic.
All proofs are relative to their premises. You just assume arithmetic is real.
To assume arithmetic is real is ambiguous, if not non sensical.
A proposition cannot be ambiguous or nonsensical and also proven: "The UDA
*proves* that the fundamental reality = arithmetic.”
But the “UDA proves that …” is not derived from “arithmetic is real”. It is
derived from x + 0 = x, etc.
You seem to confuse the theory/machine (and what its says) with the
arithmetical reality. Those do not belong to the same level of explanation. The
arithmetical reality proves nothing: it is not a theory.
I'm not confused. You made two statements that are implicitly contradictory:
(1) To assume arithmetic is real is ambiguous, if not non sensical.
It is unclear if by “assuming arithmetic” you are are assuming 0 + 0 = 0, 1 + 0
= 1, etc.
Ask yourself what you were assuming. It's your statement.
or if you are assuming that the theory exists and is consistent (that is:
assuming that a model of arithmetic exists, which when formalised assumes much
more, like infinite sets, etc.).
(2) The UDA *proves* that the fundamental reality = arithmetic.
UDA shows that we cannot use the assumption that there is a universe to explain
why we see a universe. It shows rigorously that this idea does not work.
But you can assume the UDA. Proofs are relative to their premises.
But that is beside my point: It is contradictory to say that to assume
proposition X is nonsense and also that proposition X can be proven.
Any proposition that can be proven (in any logical system) is a
proposition that can be consistently added to the axioms.
Brent
Of course, the neoplatonician udesrood this since long, but without the Church
thesis, their argument (mainly the dream argument) is not constructive, and
does not provide the means of verification.
I just made the contradiction explicit by pointing out that any proposition
that can be proven, cannot be ambiguous or nonsensical and hence can be
unambiguously assumed.
The expression “assuming arithmetic” is unclear. With mechanism (which is an
heavy assumption) we isolate by meta-reasoning a theory of everything which has
very few assumptions: just 0 + 0 = 0, 1 + 0 = 1, etc. That is quite different
than assuming that arithmetic is consistent, or make sense, etc.
There is a subtlety here, no doubt. As we assume as much math as we needed at
the meta-level, and for the internal phenomenology as well, but all this is
done without assuming more than elementary arithmetic at the fundamental
ontological level. Mechanism justifies such an approach. All the machine
interviews in the context of RA, believes far more proposition than RA.
Arithmetic explains why numbers believe (even “richly”) in much more than
arithmetic, indeed, they believe in most of the objects that they are dreaming…
Bruno
Brent
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