On 17 Jul 2014, at 01:20, Craig Weinberg wrote:
On Wednesday, July 16, 2014 2:22:46 PM UTC-4, Bruno Marchal wrote:
On 16 Jul 2014, at 15:05, Craig Weinberg wrote:
So much of our attention in logic and math is focused on using
processes to turn specific inputs into even more specific binary
outputs. Very little attention is paid to what inputs and outputs
are or to the understanding of what truth is in theoretical terms.
Come on!
?
The possibility of inputs is assumed from the start, since no
program can exist without being 'input' into some kind of material
substrate which has been selected or engineered for that purpose.
In which theory?
What theory details the ontology of inputs?
Arithmetic. The subset of true sigma_1 sentences emulate the UD, that
is the activity of all programs on all inputs.
You can't program a device to be programmable if it isn't already.
Overlooking this is part of the gap between mathematics and reality
which is overlooked by all forms of simulation theory and
emergentism.
You are quick. Correct from the 1p machine's view on their own 1p.
You do confuse []p and []p & p.
So you are saying that programmability is universal outside of 1p
views?
At least in the same sense that 23 is prime "outside 1p views".
Like infinite computational resources in a dimensionless pool?
You can see it that way.
Without some initial connection between sensitive agents which are
concretely real and non-theoretical, there can be no storage or
processing of information. Before we can input any definitions of
logical functions, we have to find something which behaves
logically and responds reliably to our manipulations of it.
The implications of binary logic, of making distinctions between
true/go and false/stop are more far reaching than we might assume.
I suggest that if a machine's operations can be boiled down to true
and false bits, then it can have no capacity to exercise
intentionality. It has no freedom of action because freedom is a
creative act, and creativity in turn entails questioning what is
true and what is not. The creative impulse can drive us to attack
the truth until it cracks and reveals how it is also false.
Creativity also entails redeeming what has been seen as false so
that it reveals a new truth. These capabilities and appreciation of
them are well beyond the functional description of what a machine
would do. Machine logic is, by contrast, the death of choice. To
compute is to automate and reduce sense into an abstract sense-of-
motion. Leibniz called his early computer a "Stepped Reckoner", and
that it very apt. The word reckon derives from etymological roots
that are shared with 'reg', as in regal, ruler, and moving straight
ahead. It is a straightener or comb of physically embodied rules. A
computer functionalizes and conditions reality into rules, step by
step, in a mindless imitation of mind. A program or a script is a
frozen record of sense-making in retrospect. It is built of
propositions defined in isolation rather than sensations which
share the common history of all sensation.
The computing machine itself does not exist in the natural world,
but rather is distilled from the world's most mechanistic
tendencies. All that does not fit into true or false is discarded.
Although Gödel is famous for discovering the incompleteness of
formal systems, that discovery itself exists within a formal
context. The ideal machine, for example, which cannot prove
anything that is false, subscribes to the view that truth and
falsehood are categories which are true rather than truth and
falsehood being possible qualities within a continuum of sense
making. There is a Platonic metaphysics at work here, which
conjures a block universe of forms which are eternally true and
good. In fact, a casual inspection of our own experience reveals no
such clear-cut categories, and the goodness and truth of the
situations we encounter are often inseparable from their opposite.
We seek sensory experiences for the sake of appreciating them
directly, rather than only for their truth or functional benefits.
Truth is only one of the qualities of sense which matters.
The way that a computer processes information is fundamentally
different than the way that conscious thought works. Where a
consistent machine cannot give a formal proof of its own
consistency, a person can be certain of their own certainty without
proof. That doesn't always mean that the person's feeling turns out
to match what they or others will understand to be true later on,
but unlike a computer, we have available to us an experience of a
sense of certainty (especially a 'common sense') that is an
informal feeling rather than a formal logical proof. A computer has
neither certainty nor uncertainty, so it makes no difference to it
whether a proof exists or not. The calculation procedure is run and
the output is generated. It can be compared against the results of
other calculators or to employ more calculations itself to assess a
probability, but it has no sense of whether the results are certain
or not. Our common sense is a feeling which can be proved wrong,
but can also be proved right informally by other people. We can
come to a consensus beyond rationality with trust and intuition,
which is grounded the possibility of the real rather than the
realization of the hypothetical. When we use computation and logic,
we are extending our sense of certainty by consulting a neutral
third party, but what Gödel shows is that there is a problem with
measurement itself. It is not just the ruler that is incomplete, or
the book of rules, but the expectation of regularity which is
intrinsically unexpected.
One of the trickiest problems with the gap between the theoretical
and the concrete us that the gap itself is real rather than
theoretical. There can be no theory of why reality is not just
information, since theory itself cannot access reality directly.
Reality is not only formal. Formality is not real. There is a bias
within formal logic which favors certainty. This is at the heart of
the utility of logic. In mathematician Bruno Marshall's
Marchal, actually.
Gack! Sorry about that. :( I changed in the blog post. My wife
babysits a by called Marshall so he might have gotten in there.
Thanks, no real problem.
book "The Amoeba's Secret", his view on dreams hints at what is
beneath the surface of the psychology of mathematics. He writes
"What struck me was the asymmetry existing between the states of
dreaming and of being awake: when you are awake, you can never be
truly sure that you are. By contrast, when dreaming, you can
sometimes perceive it as such."
Surely most of us have no meaningful doubt that we are awake when
we are awake.
That ambiguous. I agree we felt like that. but we felt like that in
contra-lucid dreams. In those dreams, we dream that we have no no
meaningful doubt that we are awake.
But in all cases any doubt or doubt of doubt could be right or wrong
in the same way. The awakeness we feel in our doubt of a lucid dream
is no more than the awakeness if waking life, so if we can trust the
lucidity of a dream we can surely trust the lucidity of actually
being awake.
Not really. It is the same for correctness. You can know that you have
been wrong, because you can see the error, but you cannot know that
you are correct, because "not seeing an error" is not a valid argument
that there are none. It is not symmetrical.
Of course there are intermediate. In dream I was flying, so I conclude
first that I was dreaming. But then I was not flying so well and I
eventually concluded that I was awake, as in dreams, I fly much better
than that!
The addition of the qualification of being "truly sure" that we are
awake seems to assume that there is a deeper epistemology which is
possible - as if being awake required a true certainty on top of
the mere fact of being awake. To set the feeling of certainty above
the content of experience itself is an inversion; a mistake of
privileging the expectations of the intellect over the very ground
of being from which those expectations arise.
p was before []p, and even p & []p happens before (in machine's self
development) []p.
There is no p at all. p is formatting of an input.
p is put for some true arithmetical statement.
Likewise, to say that we can sometimes perceive our dreaming in a
lucid dream is to hold the dream state to a different
epistemological standard than we do of being awake. If we could be
awake and not really be sure that we are, then certainly we could
think that we are having a lucid dream,
No. In the lucid dream, you know that you are dreaming.
You know that you are in a dream, but the part that knows that is
not completely dreaming and is more awake than usual during dreams.
OK. Some would say that for all dreams. It is an awaken hallucinated
and paralysed state. Just that in a lucid dream we know that we are
dreaming, that we know that we are "awaken", but in the hallucinated
state. But some use "awake" as contrary to be be "asleep".
When you are awake, well ypou might discover later that you were
not, but the fact that you don't know does not entail that you know
you are dreaming a priori.
If you really are awake, you will not discover later that you were
not. Knowing isn't relevant, because knowledge is not applicable to
states of awareness. Our dreaming state of awareness can think that
it is not dreaming, but that does not mean that the fully awake
state can be fooled - even if it can be fooled under rare
circumstances.
One is enough.
but could be similarly misinformed. We could be dead and living in
an afterlife from which we will never return or some such goofy
possibility. Mathematical views of reality seem to welcome a kind
of escapist sophism which gives too much credence to rabbit holes
and not enough to the whole rabbit.
That we sometimes tell when we are dreaming means only that we are
more awake within our dream than usual - not that our usual
awareness is any more true or sure than it ever is. If we are
uncertain in waking life and certain in dreams, it is because our
capacity to tell the difference is real and not a dream or theory.
There is no way to prove that we are awake, but neither is there
any need to prove it since it is self-evident.
So here the brain teaches to the soul that sometimes self-evidence
can be false. A lesson in (Löbian) modesty.
I think that the brain has nothing to do with it. It shows that
consciousness is primary,
Because you assume this at the start.
and proof is an comparative function within consciousness which does
not itself have any proof of its own validity.
I am OK with this, though.
Any proof that we could have could theoretically be duplicated in a
dream also, but that does not mean that there is no difference
between dream and reality.
Absolutely. Indeed there is a special level with stable observable.
We cant know it for sure, but we can be correct in some bets or act
of faith (like in front of the doctor).
What can know for sure?
Consciousness.
The difference is more than can be learned by 'proof' alone.
Indeed, from the 1p view. Only God knows the matches.
Why God? Why not just extra-cognitive sense modalities?
That's what I meant.
Bruno
Craig
Bruno
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