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.
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.
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? Price is not in spacetime and neither is love.
I'd say that spacetime and number are equally inventions.
Brent
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