On 26 Nov 2012, at 13:42, Craig Weinberg wrote:
On Friday, November 23, 2012 11:54:57 AM UTC-5, Bruno Marchal wrote:
On 22 Nov 2012, at 18:38, Stephen P. King wrote:
How exactly does the comparison occur?
By comparing the logic of the observable inferred from observation
(the quantum logic based on the algebra of the observable/linear
positive operators) and the logic obtained from the arithmetical
quantization, which exists already.
How does the comparison occur? I will not ask what or who is
involved, only how. What means exists to compare and contrast a
pair of logics?
The logic exists, because, by UDA, when translated in arithmetic,
makes a relative physical certainty into a true Sigma_1 sentence,
which has to be provable, and consistent. So the observability with
measure one is given by []p = Bp & Dt & p, with p arithmetical
sigma_1 (this is coherent with the way the physical reality has to
be redefined through UDA). Then the quantum logic is given by the
quantization []<>p, thanks to the law p -> []<>p, and this makes
possible to reverse the Goldblatt modal translation of quantum logic
into arithmetic.
Comparison is used in the everyday sense. Just look if we get the
quantum propositions, new one, different one, etc.
The question is straightforward to me - what makes logical
comparison happen? Let me try to tease out what you answer is here,
because it is not obvious.
The logic exists, because,
so far so good.
by UDA,
Isn't UDA a logical construct already?
UDA refers to an argument. It is the argument showing that if we are
machine (even physical machine) then in fine physics has to be
justified by the arithmetical relations, and some internal views
related to it.
Is your answer to 'what makes logic happen?' rooted in the
presumption of logic?
At the basic ontological level, I can limit the assumption in logic
quite a lot. Actually we don't need logic at the base ontological
level, only simple substitution rules and the +, * equality axioms.
Only later we candefine an observer, in that ontology, as a machine/
number having bigger set of logical beliefs. But the existence of
such machine does not require the belief or assumptions in that logic.
That's ok with me, but you don't need any smoke or mirrors after
that, you are pretty much committed to 'because maths' as the alpha
and omega answer to all possible questions.
On the contrary. The math is used to be precise, and then to realize
that we don't have the answers at all, but we do have tools to make
the questions clearer, and sometimes this can give already some shape
of the answer, like seeing that comp bactracks to Plato's conception
of reality (even Pythagorus).
This is not much. Just a remind that science has not decided between
Plato and Aristotle in theology.
when translated in arithmetic, makes a relative physical certainty
into a true Sigma_1 sentence, which has to be provable, and
consistent.
Proof and consistency, again, are already features of logic. What
makes things true? How does it actually happen?
We assume some notion of arithmetical truth. I hope you can agree with
proposition like "44 is a prime number or 44 is not a prime number".
Not much is assumed, except for UDA, where you are asked if you are
willing to accept a computer in place of your brain. The computer is
supposed to be reconfigured at some level of course. We assume also
Church thesis, although it is easy to avoid it, technically (but not
so much "philosophically").
So the observability with measure one is given by []p = Bp & Dt & p,
with p arithmetical sigma_1 (this is coherent with the way the
physical reality has to be redefined through UDA). Then the quantum
logic is given by the quantization []<>p, thanks to the law p ->
[]<>p, and this makes possible to reverse the Goldblatt modal
translation of quantum logic into arithmetic.
Way over my head, but it sounds like logic proving logic again.
It is not your fault. Nobody knows logic, except the professional
logicians, who are not really aware of this.
I talk about logic, the branch of math, not logic the adjective for
all simple rational behavior that we all know. UDA does not use logic-
branch-math, but of course it use the logic that you are necessarily
using when sending a post to a list (implicitly).
AUDA needs logic-the branch of math, due to the link between computer
science and mathematical logic.
Comparison is used in the everyday sense.
Yes! Now that I understand. What's wrong with the 'everyday sense'
being the reality
That would cut all the funding in fundamental sciences, as this answer
everything. It is a bit like "why do you waste your time trying to
understanding the thermo-kinetics of car motor and how car moves? Why
not just accept that car moves when we press on the pedal?"
The everyday sense is a part of reality, and I would understand it in
term of the simplest assumption possible. Then my point is only that
if comp is true (that is, roughly, if we are machine) then we can
already refute the lasting current idea that there is a primitive
physical universe. It gives at least another rational conception of
reality, which gives the hope to get the origin of the physical laws,
and the material patterns.
and the specialized logic being one category of specialized
mechanisms within that?
Logic is not fundamental at all, for UDA, you need only the everyday
logic that you need to be able to do a pizza. Arithmetic is far more
important, if only to understand how a computer functions.
Yet more advanced logic can help for two things, when doing reasoning:
-showing that a proposition follows from other propositions (deduction)
-showing that a proposition does not follow from other propositions
(independence).
Then, concerning the relation between mind, thinking, feeling, truth,
etc. many result in logic put some light, and that is not astonishing
once you bet on comp, even if temporarily for the sake of the argument.
In logic, the branch of math, the beginning is the most difficult,
because you have to understand what you have to not understand, like
formal expressions.
Logic is just like algebra, and those things imposes themselves once
we tackle precise theories, and relations between theories. It helps
for refuting them, or representing a theory in another, etc.
I know that comp invites to math, and that this seems to be a problem
for many.
Bruno
http://iridia.ulb.ac.be/~marchal/
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