On 05 Apr 2017, at 22:51, David Nyman wrote:
On 5 Apr 2017 7:46 p.m., "Brent Meeker" <meeke...@verizon.net> wrote:
On 4/5/2017 1:54 AM, Bruno Marchal wrote:
On 04 Apr 2017, at 16:47, David Nyman wrote:
I've been thinking about the Lucas/Penrose view of the purported
limitations of computation as the basis for human thought. I know
that Bruno has given a technical refutation of this position, but
I'm insufficiently competent in the relevant areas for this to be
intuitively convincing for me. So I've been musing on a more
personally intuitive explication, perhaps along the following lines.
The mis-step on the part of L/P, ISTM, is that they fail to
distinguish between categorically distinct 3p and 1p logics which,
properly understood, should in fact be seen as the stock-in-trade
of computationalism. The limitation they point to is inherent in
incompleteness - i.e. the fact that there are more (implied)
truths than proofs within the scope of any consistent (1p) formal
system of sufficient power. L/P point out that despite this we
humans can 'see' the missing truths, despite the lack of a formal
proof, and hence it must follow that we have access to some non-
algorithmic method inaccessible to computation. What I think
they're missing here - because they're considering the *extrinsic
or external* (3p) logic to be exclusively definitive of what they
mean by computation - is the significance in this regard of the
*intrinsic or internal* (1p) logic. This is what Bruno summarises
as Bp and p, or true, justified belief, in terms of which
perceptual objects are indeed directly 'seen' or apprehended.
Hence a computational subject will have access not only to formal
proof (3p) but also to direct perceptual apprehension (1p). It is
this latter which then constitutes the 'seeing' of the truth that
(literally) transcends the capabilities of the 3p system
considered in isolation.
I don't think so. It is not direct perceptual "seeing the truth";
it is an inference in language and depends on language. The fallacy
of L/P is they assume you can know what machine you are and
therefore you can "see" the truth of your Godel sentence, but in
fact you don't know what algorithmic machine you are.
That's an interesting point also, but I'm not sure you've quite
taken my meaning. I'm specifically making use of Tarski's criterion
of truth as correspondence with the facts. When considering
matters in the first-person, the "facts" in question are in the
first instance perceptual and hence as such directly apprehended.
Hence we have access to a second means of judging truth, in this
specific sense, over and above the restrictions of any purely
algorithmic procedure. In other words, we are able directly to
apprehend or "see" a correspondence *in concrete perceptual terms*
of an assertion with facts to which it purports to refer. And indeed
that's exactly how we are able to make the relevant distinction:
i.e. between working through a formal procedure, which we are
equally able to do, and at the same time grasping a directly
perceptible correspondence that eludes the restrictions of that
procedure. The linguistic part comes later in justifying our
judgement (to another or for that matter to ourselves) post hoc.
Yes, that is what I said, but you put it in a much more better way
than me! Consciousness is in the truth, or in its "direct perception
through sense". Note that happens in dreams too, where the cortex will
build the []p, and the stem is bringing the "p", which sometimes can
be random letting the [] in need of some imagination (dream weirdness).
A remark on entheogen:
I think that with cannabis, you blur the "p" in "[]p & p", and
with salvia you blur the "[]p" in "[]p & p". (with the surprise that
you still remain as a sort of conscious person).
Oops I have to go. Before I fall in the machine's blasphem ... More on
this later most probably.
Bruno
David
Brent
Exact. And going a little further, that is what the Gödel-Löbian
machine already says (or say out of time and space).
If the foregoing makes sense, it may also give a useful clue in
the debate over intuitionism versus Platonism in mathematics.
Indeed, perceptual mathematics (as we might term it) - i.e. the
mathematics we derive from the study of the relations obtaining
between objects in our perceptual reality - may well be
"considered to be purely the result of the constructive mental
activity of humans" (Wikipedia). However, under computationalism,
this very 'perceptual mathematics' can itself be shown to be the
consequence of a deeper, underlying Platonist mathematics (if we
may so term the bare assumption of the sufficiency of arithmetic
for computation and its implications).
Is this intelligible?
I have no critics. Your point is done by the machine through a
theorem of Grzegorczyk on one par: the fact that S4Grz, like S4,
formalises Intutionistic logic, and of Boolos and Goldblatt on
another par: the fact that the formula Grz *has to* be added to S4
to get the arithmetical completeness of the "[]p & p". Note that
this makes the intuitionist into a temporal logic, and attach
duration to consciousness, like with Bergson and Brouwer himself.
Eventually it is amazing and counter-intuitive, because it ascribes
consciousness to all universal numbers, probably the same before
they get the differentiation along the infinitely many computations
supporting them. Needless to say that such consciousness is in a
highly dissociated state at the start, a bit like after consuming
some salvia perhaps (!).
Your analysis can be extended on the intelligible and sensible
(neo)Platonist theory of matter, but with p restricted to the
sigma_1 sentences (which describe in arithmetic the universal
dovetailing), with or without the adding of "<>t", which typically
transform the notion of "belief []p" or "knowledge []p &
p" into notion of "probabilities".
In summary
p (truth, god, the one)
[]p (rational belief)
[]p & p (knowledge, intuitionist subject)
[]p & <>t (probability, quantum logic)
[]p & <>t & p (intuitionist probability, quale logic).
The quanta themselves appear to be qualia. In fact a quanta is a
sharable qualia by two universal number when supported by a same
universal number. That can be used to show that the "many worlds"
of the physicists (Everett theory) confirms Computationalism and
protect it from solipsism. The physical is indeed first person
PLURAL, and its sharableness comes from the linearity of the tensor
product. At each instant we all enter the same replication
machinery. The Z logics justifies the linearity and reversibility,
but not clearly enough to extract the unitarity and use Gleason to
make the measure unique. But this is for the next generation,
hopefully (as many seem to prefer the obscurantist statu quo alas).
Bruno
David
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