On 19 Nov 2010, at 22:37, Brent Meeker wrote:
On 11/19/2010 6:47 AM, Bruno Marchal wrote:
On 18 Nov 2010, at 06:10, Rex Allen wrote:
In this case, if we had sufficient mental capacity there would no
need
to think in terms of trees or forests - we could think exclusively
in
terms quarks, electrons, photons, and whatnot. Thinking in terms of
trees and forests is a "good enough" computational shortcut.
This is not obvious. Thinking might *necessitate* such approximation.
Thinking is a matter of relations among images or words or
concepts. So it must be approximate; it's usefulness in is
abstracting and generalizing.
Yes.
Obviously so once we assume that the brain (or whatever
consciousness supervene on) is a Turing emulable machine.
However, there is certainly no prediction I could make based on my
knowledge of trees and forests that would be as accurate or
precise as
the predictions I could make if I had the mental and sensory
capacity
to comprehend the forest at the level of it's constituent quarks and
electrons.
The only advantage of thinking in terms of trees and forests is
brevity and economy. Shortcuts.
If you had no need of brevity or economy, then you would have no
need
for concepts like trees and forests. Rather, you might as well
think
exclusively in terms of fundamental entities...quarks, electrons,
photons, and whatnot.
But quarks, electrons, etc. are themselves high level description
of what is eventually just relations between numbers. This is
derivable from digital mechanism, but is also corroborate from
physics itself.
Note that you would also have no need of "emergent" laws like
evolution or the laws of thermodynamics.
Further, given sufficient computational power there's no "abstract
interpretation" that you couldn't legitimately extract (via the
right
Putnam mapping) from the collection of electrons and quarks that
comprise the forest. It would be like looking for bunny-shaped
clouds
in the sky. Trees and forests and squirrels and hikers *might* be
the
most obvious higher-level interpretation of what exists...but
certainly not the only interpretation, and not privileged in any
way.
I doubt this.
Dowker and Kent have written a paper showing that there are many
possible, quite different quasi-classical worlds consistent with
quantum mechanics. So whether our world, or something similar, is
necessary seems to be an open question.
"Our world" is ambiguous.
But if by "our" you mean us the (hopefully sound) self-referentially
correct machine, then we might (re)define our physical worlds by the
set of things which we can observe, and this can be shown to be
necessary. With mechanism, there is no primitive physical laws, but
the laws of physics are necessary, all the (physical) rest is history
and geography.
My point being that, even assuming scientific materialism, trees and
forests only exist in your mind. They are part of how things seem
to
us. They are part of us. Like logic and reason and arithmetic
descriptions.
OK, but then everything is part of us. But I am quite skeptical
about the idea that elementary arithmetical truth is part of us.
Prime numbers did not wait for humans to have their remarkable
properties. I think you are confusing the discovery of numbers by
humans, and those numbers abstract properties which are not in the
category of time and space.
But why should not being in time and space excuse arithmetic from
depending on humans?
Are you serious about this? Do you really think that the fact that you
cannot cut 17 in two, that is "IIIIIIIIIIIIIIIII" is two equal parts
depend on humans? In such a case Church thesis and most of classical
mathematics is made false.
Price is not in spacetime and neither is love. I'd say that
spacetime and number are equally inventions.
Inventions by who? Are you taking the set of humans as what exists
primitively? Assuming mechanism, both matter and observers emerge from
something simpler: the laws of addition and the laws of multiplication.
Also, it can be proved that it is just impossible to derive arithmetic
from anything simpler than arithmetic, that is why arithmetic or
something implying arithmetic has to be assumed, and is the simplest
things to assume from which we can derive more complex things (like
the belief arithmetic and in space and time by machine/numbers).
Bruno
http://iridia.ulb.ac.be/~marchal/
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