I almost dread entering into this discussion, but I think it should be
pointed out that this discussion occurs in various forms in both Leonard
Jimmie Savage's Foundations of Statistics and E T Jaynes Probability
Theory. I would also point out that you are missing key elements of both
the
On 31 Aug 2009, at 03:50, marc.geddes wrote:
On Aug 31, 4:19 am, Bruno Marchal marc...@ulb.ac.be wrote:
On 30 Aug 2009, at 10:12, marc.geddes wrote:
But look at this. I decide to do the following experience. I prepare
an electron so that it is in state up+down. I measure it in the
On Aug 31, 8:10 pm, Bruno Marchal marc...@ulb.ac.be wrote:
On 31 Aug 2009, at 03:50, marc.geddes wrote:
This assumes that qualia are completely determined by the wave
function, which (since Bohm is non-reductionist) I'm sure he'd
dispute. The wave function only predicts physical
On 31 Aug 2009, at 11:28, marc.geddes wrote:
On Aug 31, 8:10 pm, Bruno Marchal marc...@ulb.ac.be wrote:
On 31 Aug 2009, at 03:50, marc.geddes wrote:
This assumes that qualia are completely determined by the wave
function, which (since Bohm is non-reductionist) I'm sure he'd
dispute.
On Aug 30, 7:23 pm, Bruno Marchal marc...@ulb.ac.be wrote:
On 30 Aug 2009, at 07:06, marc.geddes wrote:
It’s true that there is no wave function collapse in Bohm, so it uses
the same math as Everett. But Bohm does not interpret the wave
function in ‘many world’ terms, in Bohm the wave
On Aug 30, 7:05 pm, Bruno Marchal marc...@ulb.ac.be wrote:
This does not make sense.
You said;
The truth of Gödel sentences are formally trivial.
The process of finding out its own Gödel sentence is
mechanical.
The diagonilization is constructive. Gödel's
proof is constructive. That is what
On 30 Aug 2009, at 10:12, marc.geddes wrote:
On Aug 30, 7:23 pm, Bruno Marchal marc...@ulb.ac.be wrote:
On 30 Aug 2009, at 07:06, marc.geddes wrote:
It’s true that there is no wave function collapse in Bohm, so it
uses
the same math as Everett. But Bohm does not interpret the wave
On 30 Aug 2009, at 10:34, marc.geddes wrote:
On Aug 30, 7:05 pm, Bruno Marchal marc...@ulb.ac.be wrote:
This does not make sense.
You said;
The truth of Gödel sentences are formally trivial.
The process of finding out its own Gödel sentence is
mechanical.
The diagonilization is
On 30 Aug 2009, at 18:55, Bruno Marchal wrote:
Not at all. Most theories can formally determined their Gödel
sentences, and even bet on them.
They can use them to transform themselves into more powerful, with
respect to probability, machines, inheriting new Gödel sentences, and
they can
On Aug 31, 4:55 am, Bruno Marchal marc...@ulb.ac.be wrote:
On 30 Aug 2009, at 10:34, marc.geddes wrote:
On Aug 30, 7:05 pm, Bruno Marchal marc...@ulb.ac.be wrote:
This does not make sense.
You said;
The truth of Gödel sentences are formally trivial.
The process of finding
On Aug 31, 4:19 am, Bruno Marchal marc...@ulb.ac.be wrote:
On 30 Aug 2009, at 10:12, marc.geddes wrote:
But look at this. I decide to do the following experience. I prepare
an electron so that it is in state up+down. I measure it in the base
{up, down}, and I decide to take holiday
marc.geddes wrote:
On Aug 31, 4:19 am, Bruno Marchal marc...@ulb.ac.be wrote:
On 30 Aug 2009, at 10:12, marc.geddes wrote:
But look at this. I decide to do the following experience. I prepare
an electron so that it is in state up+down. I measure it in the base
{up,
On Aug 31, 3:23 pm, Brent Meeker meeke...@dslextreme.com wrote:
marc.geddes wrote:
A weakness of MWI is that it does not describe the reality we actually
see - additional steps are needed to convert wave function to human
observables - Bohm makes this clear, MWI just disguises it.
On Aug 29, 5:30 am, Brent Meeker meeke...@dslextreme.com wrote:
marc.geddes wrote:
See for example ‘Theory and Reality’ (Peter Godfrey Smith) and
debates in philosophy about prediction versus integration. True
explanation is more than just prediction, and involves *integration*
of
marc.geddes wrote:
On Aug 29, 5:21 am, Brent Meeker meeke...@dslextreme.com wrote:
Look at Winbugs or R. They compute with some pretty complex priors -
that's what Markov chain Monte Carlo methods were invented for.
Complex =/= uncomputable.
Techniques such the Monte Carlo
marc.geddes wrote:
On Aug 29, 5:30 am, Brent Meeker meeke...@dslextreme.com wrote:
marc.geddes wrote:
See for example ‘Theory and Reality’ (Peter Godfrey Smith) and
debates in philosophy about prediction versus integration. True
explanation is more than just prediction, and
On Aug 29, 6:41 pm, Brent Meeker meeke...@dslextreme.com wrote:
marc.geddes wrote:
On Aug 29, 5:30 am, Brent Meeker meeke...@dslextreme.com wrote:
marc.geddes wrote:
*Before* you can even begin to assign probabilities to anything, you
first need to form symbolic representations of
On Aug 29, 6:16 pm, Brent Meeker meeke...@dslextreme.com wrote:
Stathis once pointed on this list that crazy people can actually still
perform axiomatic reasoning very well, and invent all sorts of
elaborate justifications, the problem is their priors, not their
reasoning; so if you
On Aug 29, 6:50 pm, Brent Meeker meeke...@dslextreme.com wrote:
marc.geddes wrote:
Ok, probablistic/axiomatic, none of it works without the correct
priors, which Bayes can't produce.
Bayes explicitly doesn't pretend to produce priors - although some have
invented ways of producing
marc.geddes wrote:
On Aug 29, 6:41 pm, Brent Meeker meeke...@dslextreme.com wrote:
marc.geddes wrote:
On Aug 29, 5:30 am, Brent Meeker meeke...@dslextreme.com wrote:
marc.geddes wrote:
*Before* you can even begin to assign probabilities to anything, you
marc.geddes wrote:
On Aug 29, 6:50 pm, Brent Meeker meeke...@dslextreme.com wrote:
marc.geddes wrote:
Ok, probablistic/axiomatic, none of it works without the correct
priors, which Bayes can't produce.
Bayes explicitly doesn't pretend to produce priors - although
On Aug 29, 7:34 pm, Brent Meeker meeke...@dslextreme.com wrote:
marc.geddes wrote:
No, I think the buck stops with analogical reasoning, since no form of
reasoning is more powerful. Analogical reasoning can produce priors
and handle knowledge representation (via categorization),
On 29 Aug 2009, at 07:15, marc.geddes wrote:
On Aug 29, 2:36 am, Bruno Marchal marc...@ulb.ac.be wrote:
Obviously (?, by Gödel) Arithmetic (arithmetical truth) is infinitely
larger that what you can prove in ZF theory.
Godel’s theorem doesn’t mean that anything is *absolutely*
On 29 Aug 2009, at 08:09, marc.geddes wrote:
Bohm's interpretation of QM is utterly precise and was published in a
scientific journal (Phys. Rev, 1952). In the more than 50 years
since, no technical rebuttal has yet been found, and it is fully
consistent with all predictions of standard
On 29 Aug 2009, at 14:10, Bruno Marchal wrote:
This is the case for the p modalities. They are provably
necessarily non axiomatisable. They lead to the frst person, which,
solipstically, does separate truth and provability.
I mean does NOT separate truth and provability (like solipsist).
On Aug 30, 12:10 am, Bruno Marchal marc...@ulb.ac.be wrote:
http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems
The TRUE but unprovable statement referred to by the theorem is often
referred to as “the Gödel sentence” for the theory.
The sentence is unprovable within the
On Aug 30, 12:22 am, Bruno Marchal marc...@ulb.ac.be wrote:
On 29 Aug 2009, at 08:09, marc.geddes wrote:
Bohm's interpretation of QM is utterly precise and was published in a
scientific journal (Phys. Rev, 1952). In the more than 50 years
since, no technical rebuttal has yet been
On Aug 29, 7:12 pm, Brent Meeker meeke...@dslextreme.com wrote:
marc.geddes wrote:
There are many logicians who think that Bayesian inference can serve
as the entire foundation of rationality and is the most powerful form
of reasoning possible (the rationalist ideal).
Cox showed it
On Aug 28, 6:58 am, Brent Meeker meeke...@dslextreme.com wrote:
So how are you going to get around Cox's
theorem?http://en.wikipedia.org/wiki/Cox%27s_theorem
Cox's theorem is referring to laws of probability for making
predictions. I agree Bayesian inference is best for this. But it
On Aug 27, 7:35 pm, Bruno Marchal marc...@ulb.ac.be wrote:
Zermelo Fraenkel theory has full transfinite induction power, but is
still limited by Gödel's incompleteness. What Gentzen showed is that
you can prove the consistency of ARITHMETIC by a transfinite induction
up to
On 28 Aug 2009, at 10:47, marc.geddes wrote:
On Aug 27, 7:35 pm, Bruno Marchal marc...@ulb.ac.be wrote:
Zermelo Fraenkel theory has full transfinite induction power, but is
still limited by Gödel's incompleteness. What Gentzen showed is that
you can prove the consistency of ARITHMETIC
marc.geddes wrote:
On Aug 28, 6:58 am, Brent Meeker meeke...@dslextreme.com wrote:
So how are you going to get around Cox's
theorem?http://en.wikipedia.org/wiki/Cox%27s_theorem
Cox's theorem is referring to laws of probability for making
predictions. I agree Bayesian inference is
marc.geddes wrote:
On Aug 27, 7:35 pm, Bruno Marchal marc...@ulb.ac.be wrote:
Zermelo Fraenkel theory has full transfinite induction power, but is
still limited by Gödel's incompleteness. What Gentzen showed is that
you can prove the consistency of ARITHMETIC by a transfinite
On Aug 29, 2:36 am, Bruno Marchal marc...@ulb.ac.be wrote:
Obviously (?, by Gödel) Arithmetic (arithmetical truth) is infinitely
larger that what you can prove in ZF theory.
Godel’s theorem doesn’t mean that anything is *absolutely*
undecidable; it just means that not all truths can
On Aug 29, 5:21 am, Brent Meeker meeke...@dslextreme.com wrote:
Look at Winbugs or R. They compute with some pretty complex priors -
that's what Markov chain Monte Carlo methods were invented for.
Complex =/= uncomputable.
Techniques such the Monte Carlo method don’t scale well.
That which can be destroyed by the truth should be.
-- P.C. Hodgell
Today, among logicians, Bayesian Inference seems to be the new dogma
for all encompassing theory of rationality. But I have different
ideas, so I'm going to present an argument suggesting an alternative
form of reasoning. In
On 27 Aug 2009, at 08:19, marc.geddes wrote:
But is there a form of math more powerful than algebra? Yes,
Category/
Set Theory! Unlike algebra, Category/Set theory really *can* fully
reason about itself, since Sets/categories can contain other Sets/
Categories. Greg Cantor first
marc.geddes wrote:
That which can be destroyed by the truth should be.
-- P.C. Hodgell
Today, among logicians, Bayesian Inference seems to be the new dogma
for all encompassing theory of rationality. But I have different
ideas, so I'm going to present an argument suggesting an
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