On 14 Feb 2013, at 17:01, Stephen P. King wrote:

On 2/14/2013 10:40 AM, Bruno Marchal wrote:

On 13 Feb 2013, at 23:08, Stephen P. King wrote:

On 2/13/2013 2:46 PM, meekerdb wrote:
On 2/13/2013 8:04 AM, Bruno Marchal wrote:

On 13 Feb 2013, at 03:03, meekerdb wrote:

On 2/12/2013 5:28 PM, Russell Standish wrote:
On Tue, Feb 12, 2013 at 11:05:37AM -0800, Craig Weinberg wrote:
When we talk about a Bp, relating to consciousness is that we are making an assumption about what a proposition is. In fact, if we look closely, a proposition can only be another level of B. p is really nothing but a group of sub-personal Beliefs (logarithmically nested as B^n) which we are arbitrarily considered as a given condition...but there is no given condition in actual experience. All experiences are contingent upon what
the experiencer is capable of receiving or interacting with.

I don't really follow your remaining comments, but I agree with you
that the p in the Theatetical definition of knowledge makes me
uncomfortable, post Popper.

I'm happy for Bp&  p to apply to mathematical knowledge, with B
semantically equivalent to "prove", but when it comes to scientific knowledge, requiring absolute truth in things seems a step too far.

But I have no constructive suggestions as to how to modify Theatetus :(.


Intuitively Bp & p does not define knowledge.

Why? It obeys to the classical theory of knowledge (the modal logic S4), and in the comp context, we get the more stronger logic S4Grz1, and it works very well. It even makes the knower unnameable and close to the Plotinus "universal soul" or "inner God".



As Edmund Gettier pointed out Bp, where B stands for 'believes' as in non-mathematical discourse, can be accidental. Hence he argued that the belief must be causally connected to the fact of the proposition in order to count as knowledge.

We have already discussed this. Edmund Gettier seems to accept a notion of knowledge which makes just no sense, neither in comp, nor in platonism.

From http://en.wikipedia.org/wiki/Gettier_problem we read:

"A Gettier problem is any one of a category of thought experiments in contemporary epistemology that seem to repudiate a definition of knowledge as justified true belief (JTB). The category of problem owes its name to a three-page paper published in 1963, by Edmund Gettier, called "Is Justified True Belief Knowledge?". In it, Gettier proposed two scenarios where the three criteria (justification, truth, and belief) seemed to be met, but where the majority of readers would not have felt that the result was knowledge due to the element of luck involved."

    Bruno's notion involves betting, so luck is a factor! ;-)

Not with Bp & p. The betting is for observation, not knowledge.

Hi Bruno,

I don't understand the difference between knowledge and observation when considering 1p. Knowledge isn't just recollection of facts, it is always observation, event if purely internal experience of abstractions. I am aware of that I have knowledge of, especially when I am thinking of it.


Knowledge and observation can be related, but it is better to distinguish different notions. With comp and the naive Theaetetus, say, knowledge is given by Bp & p, and observation is given by the Bp & Dt. And feeling is given by Bp & Dt & p. This gives an intuitionist epistemic logic for the first person knowledge, with an antisymmetrical knowledge state evolution. Bp & Dt ( & p) gives, for observation, at the "*" level, a symmetrical structures, with a quantum like quasi orthomodular structure. It provides steps toward having the arithmetical frame to get a Gleason- like theorem, to solve the measure problem, in the way UDA explains to do.

With comp, a physical proposition is a true sigma_1 proposition pondered by the frequence of its proof in the universal dovetailing (UD*), or equivalently, in arithmetic. That follows from the global 1p indeterminacy, on UD*.

p is arithmetical truth. You can see it as Dennett intentional stance toward the set of the Gödel numbers of the true proposition, true in the standard model of Peano Arithmetic. Comp will explain notably why we cannot define that standard model. p plays the role of Plotinus' one.

Bp is a statement made by some number relatively to some universal number. It plays the role of Plotinus' discursive reasoner, or 'man' (that includes woman, as it is the generic term). Here it is the 3p, finitely describable machine, or its Gödel number, programs, etc. It is the 3p duplicable entity you can bet on.

Bp & p, is simply the same statement made in the case of p. It restrict the prover or justifier to truth, in a non necessary constructive way. The intensional interpretation of p can be given by the set of worlds, or of computations, satisfying (in some sense) p. Or p can represent some actual truth in this actual world. A lot of variation are possible, but I concentrate on the simplest case. It provides already something highly non trivial, despite being a simple common part of the possible knower. It corresponds to Plotinus' soul, and it has the unique quality, among the hypostases of not splitting between G and G* metatheories. Its logic is S4Grz1, and S4Grz1 = S4Grz1*.

Bp & Dt, is observation, and should give the logic of the observable. As UDA generalize Everett on arithmetic, the observable with certainty will be the provable-and-consistent propositions. You will be certain to get a cup of coffee in a WM-duplication experience, in case you get a cup of coffee in both W and M. But you have to take into account the act of faith, which is the fact that Dt has to be made explicit. Only G* knows that Dt is true about "you" (the correct machine), but you can't know that, and this will change the pov on the arithmetical truth. Like with Bp & p, actually. G* knows that Bp and Bp & p sees the same arithmetical reality, but they don't know that, and see it differently. It corresponds to Plotinus Intelligible Matter, with Dt playing the role of the non determinate, and his bastard calculus becoming the arithmetical "physical" probability theory.

Bp & Dt & p, is the Theaetetus definition reapplied on observation. It is the observation + that non communicable component related to the truth. It corresponds to Plotinus' sensible matter. The logic of both Bp & Dt, and Bp & Dt & p, are non transitive, and implements a notion of locus and proximity notions, like the theorem p -> BDp can help to figure out.

The naive scientist is classical, the soul is intuitionist, but on UD* get already quantum-like. Both sensible and intelligible matter are quantum-like. The generalization B^n p and D^m t (& p) provides a graded quantum structure.

The soul and the sensible matter marries both symmetry on the sigma_1 "bottom" (the UD*), and antisymmetry on whatever the machine can extract from that bottom. It is a chance that those logic does not collapse, it would have made comp implying there is no physics at all, only geographies. The multiverse would be a continuum of all physical laws, F = ma^3 would be realized somewhere. By the non collapse, we have a much more less trivial physics, but not entirely digital.

You can take this as a toy theology, but it is the only way I know of to get quanta and qualia when taking into account the (global) first person indeterminacy. The measure one, the laws of physics, are determined by the logic of self-reference, and the intensional variants described by the "intelligible and sensible" matter.

Bruno





The betting is handled with Bp & Dt & p. Somehow, we impose the consistency: that is, for machine talking first person logic, the existence of at least one reality (Dt).

(By Gödel's completeness theorem (not incompleteness !) we have that Dt is true iff "B" has a model (a mathematical reality "satisfying" his beliefs)). Bp & Dt (& p) makes p true in all the accessible realities in the neighborhood, so the "p" has measure one, and the corresponding logic is the logic of the "probability" one.

Bruno



--
Onward!

Stephen

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http://iridia.ulb.ac.be/~marchal/



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