Hi Bruno,

    
From: Bruno Marchal 
Sent: Monday, May 09, 2011 8:57 AM
To: everything-list@googlegroups.com 
Subject: Re: Against the Doomsday hypothesis

On 09 May 2011, at 13:35, Stephen Paul King wrote:


  Dear Bruno,

      But this is problematic since dreams are 3p describable by the diary 
method, 

[BM]
A part of it only. You can write "I am conscious", but that is not a 
communication, at least in the strong sense of persuading some others. Dream 
are typically first person experiences. Malcolm wrote different books arguing 
that machine cannot be conscious, and that ... dreams does not exist. He is 
quite rational and coherent, and arguments against mechanism are often argument 
against the possibility of dreaming. Dreams plays some role in UDA, although 
"video-game" can be used instead.
Note that in the WM duplication experiment, the content of the diary is not 
communicable. "I am in W" does not convey a proof, as the guy in M can 
understand introspectively.
Dreams, and 1p can be approximated by memory and diary content, and that might 
be enough in some part of some reasoning (like in the UDA), but those are only 
approximations. 

[SPK]
    Does it matter that while dreaming all experiences, especially those that 
involve the appearance of other persons is purely solipsistic? In other words, 
When I dream, all that I could be aware of is purely a product of my brain. 
Well, let me weaken that claim a bit since it has been shown that noise and 
other stimuli in the environment of the sleeper has some appreciable effects on 
dream content, nevertheless the “what I am aware of” is clearly is not 
determined by external states of affairs.
    Malcolm, whoever that is..., is using the usual definition of existence 
that I rail against as it is dependent of physical instantiation, I am not sure 
that this would weaken his claims. But dreams as computations within 
computations (ala video games) seems unproblematic but it does not advance the 
discussion as far as I can tell, but the issue of “diary contents are not 
communicable” seems to weaken the argument for 1p indeterminism. I say this 
because unless there is some means to communicate the subjective experiences of 
our teleported and copied person to a witness that can compare the state of “I 
am in Moscow” and “I am in Washington” how are we to reason about the 1p of the 
person that is teleported? 
    We might be making a person into a zombie by teleporting them! How could we 
know that we are not unless we can communicate the content of the diary? I 
cannot just blindly accept the postulate of physical supervenience of 
subjective experience in this case since we do not have a clear and falsifiable 
model of consciousness/qualia yet! (Well, other than yours.)
**


  in that I usually have some memory of what I was dreaming once I awake that I 
can encode in using symbols for communications to others. It could be that the 
reported difficulty of becoming aware of the truth that one is dreaming, while 
one is in fact dreaming, is an answer.

[BM]
This is not so difficult. There are books explaining how to train oneself to 
become lucid in dreams. I don't see the relevance to the point, though.

[SPK]
    I, personally, have been trying to lucid dream for a long time and have not 
had any success at it, but I know people that report that they can. I can only 
bet that it occurs as I do not have 1 person knowledge that it is true, but 
even if I did have a lucid dream experience, how would I test to be sure that I 
am not hallucinating that I am lucid? This is a bit of a fly paper that we can 
get stuck on! The point is that dreamign seems to show a counter-example to the 
claim that consciousness requires self-awareness. It is my claim that 
self-awareness requires consciousness, but consciousness is a passive property 
that all logics (that have stone duals) have. (This claim is similar to 
Chalmer’s idea that consciousness is a basic property like mass and charge.) 
Self-awareness emerges from active updating self-modeling within and between 
the logics and requires some form of evolution; it is dependent on a “flow of 
time”.
**


  How would we formulated this in your modal logic?
[BM]
Bp v DDt   (I suggest this in "conscience et mécanisme": it makes the Malcolm 
argument against comp and against dreams equivalent). Don't mind this too much.


[SPK] 
    What would be the English version of Bp v DDt ? Could you give us an 
example of this?
**


      The difficulty I see in your reasoning is that Truth seems to require 
omniscience. 
[BM]
In what sense? 
What do you mean by omniscience? Do you mean the closure for the modus ponens 
rule (like in logic), or the God-like knowledge of everything, like in (pseudo) 
religion?

[SPK]
    It is related to the closure issue for modus ponens in the sense that the 
list of premises must be complete for the conclusion to be certain truth, thus 
for a conclusion to be True in an absolute sense, one must have an “omniscient 
list”.  My argument against the idea of a “pre-ordained harmony” that Leibniz 
proposed for his Monadology is relevant here. 
http://www.mail-archive.com/everything-list@googlegroups.com/msg19409.html

“   This problem can be traced even back to Leibniz’ Monadology where the 
“pre-ordained harmony” upon which Leibniz’ Monadology rests its explanation of 
how all of the internal evolutions of the Monads will be synchronized with each 
other. OTOH, we can still use the Monadology if we replace the need for a 
computation of the 3-p “initial conditions necessary” with a plurality of 
ongoing 1-p type computations within each Monad that act to continuously align 
pairs of Monads with each other. This is the distinction between 1 computation 
that must occur prior to the existence of Monads and many computations that 
co-exist with the monads. “

    In situations where it is not possible to know all of the premises, modus 
pones is not so useful. This is discussed by Peter Wegner in terms of 
computations that must interact with an environment that cannot be mapped 
completely into the algorithm of the computation. The difficulty of making 
robots that navigate unknown terrain illustrates this well. There is also the 
Paradox of "What the Tortoise Said to Achilles", by Lewis Carroll  discussed 
here: http://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achilles 

“The Wittgensteinian philosopher Peter Winch ... argued that the paradox showed 
that "the actual process of drawing an inference, which is after all at the 
heart of logic, is something which cannot be represented as a logical formula … 
Learning to infer is not just a matter of being taught about explicit logical 
relations between propositions; it is learning to do something" (p. 57). Winch 
goes on to suggest that the moral of the dialogue is a particular case of a 
general lesson, to the effect that the proper application of rules governing a 
form of human activity cannot itself be summed up with a set of further rules, 
and so that "a form of human activity can never be summed up in a set of 
explicit precepts".”

    This article partly illustrates a problem that I have with the idea that we 
can reduce all experiences, even those of a flow of events, to static relations 
between numbers.

    This passage from the http://plato.stanford.edu/entries/logic-provability/ 
article is also related to my concerns:

“3.4 Topological semantics for provability logic
As an alternative to possible worlds semantics, many modal logics may be given 
topological semantics. Clearly, propositions can be interpreted as subsets of a 
topological space. It is also easy to see that the propositional connective ∧ 
corresponds to the set-theoretic operation ∩, while ∨ corresponds to ∪, ¬ 
corresponds to the set-theoretic complement, and → corresponds to ⊆. Modal 
logics that contain the reflection axiom □A →A enjoy a particularly natural 
interpretation of the modal operators as well. For these logics, ◊ corresponds 
to the closure operator in a topological space, while □ corresponds to the 
interior. To see why these interpretations are appropriate, notice that the 
reflection axiom corresponds to the fact that each set is included in its 
closure and each set includes its interior.

However, provability logic does not prove reflection, as the instantiation □⊥ 
→⊥ of reflection would lead to a contradiction with the axiom (GL).

Provability logic therefore needs a different approach. Based on a suggestion 
by J. McKinsey and A. Tarski (1944), L. Esakia (1981, 2003) investigated the 
interpretation of ◊ as the derived set operator d, which maps a set B to the 
set of its limit points d(B). To explain the consequences of this 
interpretation of ◊, we need two more definitions, namely of the concepts 
dense-in-itself and scattered. A subset B of a topological space is called 
dense-in-itself if B ⊆ d(B). A topological space is called scattered if it has 
no non-empty subset that is dense-in-itself. The ordinals in their interval 
topology form examples of scattered spaces. Esakia (1981) proved an important 
correspondence: he showed that a topological space satisfies the axiom GL if 
and only if the space is scattered. This correspondence soon led to the result, 
independently found by Abashidze (1985) and Blass (1990), that provability 
logic is complete with respect to any ordinal ≥ωω.

In recent years, topological semantics for provability logic has seen a 
veritable revival, especially in the study of Japaridze's bimodal provability 
logic GLB, an extension of GL (Japaridze 1986). The logic GLB turns out to be 
modally incomplete with respect to its possible worlds semantics, in the sense 
that it does not correspond to any class of frames. This feature places bimodal 
GLB in sharp contrast with unimodal GL, which corresponds to the class of 
finite transitive irreflexive trees, as mentioned above. Beklemishev et al. 
(2009) showed that GLB is, however, complete with respect to its topological 
semantics (see also Beklemishev (2010), Icard (2009)). Intriguing 
reverberations of Esakia's correspondence between GL and scattered topological 
spaces can even be found in recent topological studies of spatial and epistemic 
logics (see Aiello et al. (2007)).”

    I bet that this idea of “scattered spaces” is consistent with my crazy idea 
that we can identify the “particles” of physics (minus the properties of 
charge, mass, spin quantum number) with the Stone spaces that are dual to our 
logical structures. I will study this to be sure and report back. 
http://planetmath.org/encyclopedia/ScatteredSet.html seems to support my 
thinking.
**


  Please elaborate on your point some more.
[BM]
All what I was saying is that the constrains of consistency does not eliminate 
the WR, *per se*. Truth would, but we cannot use it because a machine cannot 
distinguish truth and provability from its first person view, and we are trying 
to eliminate the first person White Rabbits.
But then, the constraints of consistency, appears to be enough, thanks to the 
self-reference logics. The hypostases Bp & Dp (or Bp & Dt) does obey a kind of 
quantum logic, which might make the first person (plural) white rabbits 
vanishing away. 

Bruno

[SPK]
   Sure, the consistency constraint would allow for WR so long as they could be 
interpreted as hallucinations, noise, swamp gas, etc. So long as there is a 
means to ‘explain away” the WR in the 3p case, which is where we take into 
account the appearance of interactions between “machines”, then my claim would 
hold. The idea is like that in the Surprise 20 questions game, the sequential 
answers that any 1p would obtain of the states of affairs of the world that is 
experienced could be stochastic or random sampling of an ensemble (as in the 
SSA) but are constrained to not contradict any prior answer. 
    This idea requires “book keeping'” and thus seems to require a physical 
world to act as the persisting structure to record the past states of observer 
moments. It is as the physical world that is the “tape” for the UD in my 
thinking. OTOH, this “physical world” should not be considered as an 
ontologically primitive as it too is, ultimately, a fiction supervening on the 
bisimulations between quantum systems. In my ontology only quantum systems (as 
stone spaces) and their logics are primitive up to degeneracy in the limit of 
the totality of existence, AKA Nothing (as in Bertrand Russell’s neutral 
monism) .
    To put this idea into mythological terms, I ask that we consider that 
Creation of the Universe is an (ultimately eternal) ongoing process instead of 
a Special one-time event. I see this idea as consistent with the UD as per your 
discussions but it requires that the UD not be reducible to some a priori 
existing and static hypostase or number.

Onward!

Stephen
  snip

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