On 27 Oct 2015, at 23:28, Brent Meeker wrote:
On 10/27/2015 3:04 PM, Stathis Papaioannou wrote:
On 28 Oct 2015, at 1:30 AM, John Clark <[email protected]> wrote:
On Mon, Oct 26, 2015 at 5:16 PM, Stathis Papaioannou <[email protected]
> wrote:
>> From examples in the physical world. You can give as
many botanical definitions of the word "tree" as you want but it
will just be a word defined by other words that are themselves
defined by yet more words that are.... If you tried to dig for
meaning all you'd find is a endless loop, it would just be a game
where words are manipulated
according to the rules of botany until somebody forgot about
definitions and pointed to the ASCII string "t-r-e-e" and then
pointed to a large photosynthesizing organism made largely of
cellulose that exists in the physical world. Then even a martian
would notice a correspondence between this game of manipulating
symbols called "botany" that humans had invented and the way these
large photosynthesizing organism made largely of cellulose live.
> What about a virtual world with trees and observers, and
no I/O devices connecting it to outside trees?
There would still be I/O devices connected to the virtual
trees made by a computer that operated according to the laws of
physics, if not the trees wouldn't even be virtual. And the books
on both virtual botany and real botany would still be more than a
just a symbol manipulation game, they would have semantic
content because there would be a correspondence between
the way the symbols are manipulated and the way the virtual
(or real) large photosynthesizing organism live. Regardless
of if they are virtual or real if you want to know how trees
live studying those botany symbols in virtual (or real) books will
help, so they must have semantic content .
The requirement that a computation be able to interact with the
real world puts a restriction on what qualifies as a computation.
You've challenged Bruno many times to perform a difficult
computation using his Platonic computer. Well, that computation is
occurring in front of you now in the thermal motion of the atoms in
your desk, which under an appropriate interpretation are
implementing a Turing machine. But you and Bruno don't have that
appropriate interpretation, and if you did, you would have the
result of the calculation already. In other words, the thermal
motion computation is not understandable as such in, and cannot
interact with, the world at the level of the substrate of its
implementation; so it would usually be said that either there is no
computation being implemented, or it is being implemented only in a
trivial and useless sense. But remove the requirement for
interaction in the real world, and this objection falls down. The
computation is being implemented, your difficult calculation has
been completed, and it is being appreciated by the virtual
observers who are clapping and cheering - even though you can't
hear them.
That's essentially Bruno's MGA, except it stops one step short.
Bruno takes the last step and says even if the atoms of your desk
were doing absolutely nothing there is an interpretation in which
that is a computation; hence the atoms are superfluous.
I do that in a context to prove something by a reductio ad absurdo.
The whole resoning showsh that the "atoms" have to be necessary, and
explain them by the logic of self-reference, which provides the needed
quantization exactly where computationalism predicts they must appear.
But clearly then it is the interpretation which is providing the
computation.
Exactly. And that is what universal numbers do, they interpret numbers
as programs and data, and do computations.
We just need to choose one universal number, to get a "base" in which
we describe all programs by numbers (to ease the things at the
fundamental level).
As Robinson arithmetic is already universal, we don't need to assume
anything more, beside Church-thesis, and the invariance of
consciousness for some digital transformation.
Bruno
Brent
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