On 09 Jan 2012, at 19:36, acw wrote:
On 1/9/2012 19:54, Craig Weinberg wrote:
Sure, but that requires one to better understand what a physical
brain is. In the case of COMP(given some basic assumptions), matter
is explained as appearing from simpler abstract mathematical
relations, in which case, a brain would be an inevitable consequence
of such relations.
On Jan 9, 12:00 pm, Bruno Marchal<marc...@ulb.ac.be> wrote:
On 09 Jan 2012, at 14:50, Craig Weinberg wrote:
On Jan 9, 6:06 am, Bruno Marchal<marc...@ulb.ac.be> wrote:
I agree with your general reply to Craig, but I disagree that
computations are physical. That's the revisionist conception of
computation, defended by Deustch, Landauer, etc. Computations have
been discovered by mathematicians when trying to expalin some
foundational difficulties in pure mathematics.
Mathematicians aren't physical? Computations are discovered
living nervous system, one that has been highly developed and
conditioned specifically for that purpose.
Computation and mechanism have been discovered by many people since
humans are there. It is related to the understanding of the
between "finite" and "infinite". The modern notion has been
independently by many mathematicians, notably Emil Post, Alan
Alonzo Church, Andrzei Markov, etc.
With the comp. hyp., this is easily explainable, given that we are
somehow "made of" (in some not completely Aristotelian sense to be
They are making those discoveries by using their physical brain
We can implement
computation in the physical worlds, but that means only that the
physical reality is (at least) Turing universal. Theoretical
science is a branch of pure mathematics, even completely
And pure mathematics is a branch of anthropology.
I thought you already agreed that the arithmetical truth are
independent of the existence of humans, from old posts you write.
Explain me, please, how the truth or falsity of the Riemann
hypothesis, or of Goldbach conjecture depend(s) on anthropology.
Please, explain me how the convergence or divergence of phi_(j)
depends on the existence of humans (with phi_i = the ith computable
function in an enumeration based on some universal system).
The whole idea of truth or falsity in the first place depends on
humans capacities to interpret experiences in those terms. We can
this quality of truth or falsity into many aspects of our direct and
indirect experience, but that doesn't mean that the quality itself is
external to us. If you look at a starfish, you can see it has five
arms, but the starfish doesn't necessarily know it had five arms.
Yet that the fact the starfish has 5 arms is a fact, regardless of
the starfish's awareness of it. It will have many consequences with
regards of how the starfish interacts with the rest of the world or
how any other system perceives it.
If you see something colored red, you will know that you saw red and
that is 'true', and that it will be false that you didn't see 'red',
assuming you recognize 'red' the same as everyone else and that your
nervous system isn't wired too strangely or if your sensory systems
aren't defective or function differently than average.
Consequences of mathematical truths will be everywhere, regardless
if you understand them or not. A circle's length will depend on its
radius regardless if you understand the relation or not.
Any system, be they human, computer or alien, regardless of the laws
of physics in play should also be able to compute (Church-Turing
Thesis shows that computation comes very cheap and all it takes is
ability of some simple abstract finite rules being followed and
always yielding the same result, although specific proofs for
showing Turing-universality would depend on each system - some may
be too simple to have such a property, but then, it's questionable
if they would be powerful enough to support intelligence or even
more trivial behavior such as life/replicators or evolution), and if
they can, they will always get the same results if they asked the
same computational or mathematical question (in this case,
mathematical truths, or even yet unknown truths such as Riemann
hypothesis, Goldbach conjecture, and so on). Most physics should
support computation, and I conjecture that any physics that isn't
strong enough to at least support computation isn't strong enough to
support intelligence or consciousness (and computation comes very
cheap!). Support computation and you get any mathematical truth that
humans can reach/talk about. Don't support it, and you probably
won't have any intelligence in it.
To put it more simply: if Church Turing Thesis(CTT) is correct,
mathematics is the same for any system or being you can imagine.
I am not sure why. "Sigma_1 arithmetic" would be the same; but higher
mathematics (set theory, analysis) might still be different.
If it's wrong, maybe stuff like concrete infinities,
hypercomputation and infinite minds could exist and that would
falsify COMP, however there is zero evidence for any of that being
Not sure, if CT is wrong, there would be finite machines, working in
finite time, with well defined instructions, which would be NOT Turing
emulable. Hypercomputation and infinite (human) minds would contradict
comp, not CT. On the contrary, they need CT to claim that they compute
more than any programmable machines. CT is part of comp, but comp is
not part of CT.
Beyond this, I agree with your reply to Craig.
BTW, acw, you might try to write a shorter and clearer version of your
joining post argument. It is hard to follow. If not, I might take much
If any intelligent system capable of interpreting the same idea will
always reach the same conclusions about it (if they followed the
same steps), I'd call that an external truth, it's about as external
as it can get. If your consciousness or physics were a direct result
of such abstract relations, it would also be both an internal and
What about arabic numerals? Seeing how popular their spread has been
on Earth after humans, shouldn't we ask why those numerals, given an
arithmetic universal primitive, are not present in nature
independently of literate humans? If indeed all qualia, feeling,
color, sounds, etc are a consequence of arithmetic, why not the
numerals themselves? Why should they be limited to human minds and
I think you're confusing numerals with numbers. Numeral systems are
just an encoding we have for talking about numbers. Numeral
encodings are a matter of history, which is a matter of physics, and
in case of COMP, is a matter of arithmetic (or any other universal
computational system - they're all equivalent by the Church Turing
Thesis). In that sense, numeral systems(encodings) are a consequence
The encoding itself is irrelevant, you could use tally notation
(such as ||| + || = |||||) and it wouldn't matter. Nor is the choice
of the universal system - all that matters is the ability of
following simple finite rules and getting the same result each time
Us finding about the CTT or any other mathematical truth is also
such a consequence of arithmetic. In a less serious way, you could
say: "It's turtles all the way down!". In a more serious way, you
could think of quines and Kleene's recursion theorems about fixed
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To post to this group, send email to firstname.lastname@example.org.
To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com
For more options, visit this group at http://groups.google.com/group/everything-list?hl=en
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to email@example.com.
To unsubscribe from this group, send email to
For more options, visit this group at