On 7/21/2011 1:16 PM, Jason Resch wrote:
On Thu, Jul 21, 2011 at 1:30 PM, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 7/21/2011 11:03 AM, Jason Resch wrote:
On Thu, Jul 21, 2011 at 10:54 AM, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 7/21/2011 2:27 AM, Bruno Marchal wrote:
Axiomatics are already in Platonia so of course that
forces computation to be there.
The computations are concrete relations.
If the are concrete then we should be able to point to them.
If your mind is a computer, you don't even need to point to them,
everything you see and experience is direct evidence of the
existence of the computation implementing your mind.
Also, I don't think the "point test" works for everything that
has a concrete existence. How would a many-worlder point to the
other branches of the wave function, or an eternalist point to
the past? How would an AI or human in a virtual environment
point to the concrete computer that is rendering its environment?
They don't need axioms to exist. Then the numbers
relation can be described by some axiomatic.
And one can regard the numbers as defined by their relations.
So the "fundamental ontology" of numbers is reduced to a
description of relations.
Is a chair the same thing as a description of a chair, or an idea
of a chair?
The is no need to suppose they exist in the sense of tables
and chairs.
Assume both matter and number relations exist. With comp, the
existence of number relations explains the existence of matter,
That's the question. It seems that comp requires more than the
existence of number relations, it requires the existence of a UD
or equivalent.
The Fibonacci sequence is, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
It is defined by the simple number relation Fib(n) = Fib(n-1) +
Fib(n-2). This is a simple recursive definition. You might even say
the number line has a simple recursive definition, where Number(n) =
Number(n-1) + 1. Different recursive definitions result in different
sequences of numbers (different ways of progressing through the
integers). In some of these definitions, bits patterns (within the
number) may move around in well defined ways,
There's the rub. Nothing changes in Platonia. Nothing "moves around"
or "computes". Bit patterns are physical things, like 101101. Numbers
are not.
some of these bit patterns become self-reproducing, and may even
evolve into more complex bit patterns, which are better able to
reproduce themselves. Some of these bit patterns may even evolve
consciousness, as they build brains which attempt to discern and
predict future observations of bit patterns within the number. Let's
call this function Universe. There may be bit patterns (life forms)
in Universe(n) which improve their survival or reproductive success by
correctly predicting parts of Universe(n+x). There are number
relations which define such sequences of numbers; you cannot deny
their existence without denying the Fibonacci sequence or the number
line (these are just simpler instances of recursive relations).
I can deny that the numbers exist the way tables and do and still accept
that certain relations are true of them; just like I can accept that
John Watson was a friend of Sherlock Holmes.
Brent
Jason
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