From: Bruno Marchal
Sent: Monday, May 09, 2011 8:57 AM
Subject: Re: Against the Doomsday hypothesis
On 09 May 2011, at 13:35, Stephen Paul King wrote:
But this is problematic since dreams are 3p describable by the diary
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
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
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.
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.
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
How would we formulated this in your modal logic?
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.
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
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)
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.
“ 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
“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
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
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
Please elaborate on your point some more.
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
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
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.
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