On 14 Jan 2015, at 08:05, 'Roger' via Everything List wrote:
I have to admit I have a hard time going with the idea of Platonism
or mathematical constructs existing somewhere that no one can see or
test. I sure can't rule it out, but I'd like to be able to know
where it is.
Where? You seem to assume a sort of geometry at the start, but with
computationalism, geometry is among the emergent phenomena.
"Where" does not apply to numbers, except in the large sense of
being between two numbers, with the usual ordering (defined by x < y
if Ez(x+z = y)).
All you need to believe in is that proposition like (786899543211 is
prime or is not prime) is true independently of you and me. Of
course by 786899543211, I mean the number denoted by this base ten
description of a natural number. Are you OK with this? that type of
assumption is weaker than the assumption most scientist are doing
when using mathematics in their domain. The arithmetical
"platonism" (realism) used in computationalism is the same amount
than the one used in computer science, physics, etc.
Roger: My view is that propositions like "786899543211 is prime or
is not prime", "1+1=2", etc. are mental constructs/entities that
exist in our minds (e.g., in our heads from my materialist point of
view) in order to describe existent entities that exist outside the
mind such as 786899543211 existent entities, an entity and another
one next to it, respectively.
What might be in your head are the sentences descriptions and the
numbers description, not what is referred by those description. There
is a difference between the number five, and a representation of the
number five in some hardware (if that exists).
Mathematics and arithmetic are mental constructs we've created to
manipulate these outside the mind entities.
How do you know that "outside of the mind" is not also a mental
construct? You assume a primary physical reality, but then the UD
Argument shows that you need to put some non computable stuff in the
brain and in matter.
Do you believe that the prime twin conjecture depends on the human
mind? Do you believe that the prime twin conjecture would not be true,
or false, in case life did not appear on Earth?
When I say "Please point out this Platonic realm", what I'm getting
at is that I don't think propositions or anything else can exist
somewhere that's not in the mind/head or in the physical universe
outside the mind. Where else would such propositions exist?
Propositions does not exist. A proposition is true or false. They
might exist in a metatheory, which might be a part of the theory, but
then propositions will be realized by sentences, and they will exist,
in the mind of some universal numbers, again in a sense similar to
"prime number exists", which I think is clear enough for not adding
metaphysical obscurity.
I'll need something more than just a statement affirming that
"where does not apply to numbers". This doesn't seem to be evidence.
This is because you seem to have decided that what exist are the
physical things, but this idea has failed on the mind-body problem,
and we don't have any evidence for it, and then with computationalism,
it prevents progressing on the question (by the UDA+MGA).
Postulating matter/physical avoids the question: where does the
physical things come from, and it introduces magic in the relation
between consciousness and matter, or worst: it eliminates
consciousness. It also avoids the question of the effectiveness of
mathematics in the description of the physical. Computationalism does
handle very well all those questions: it explains why physics is
mathematical, where it comes from, and why it is related to
consciousness, with both the sharable quanta part and the unsharable
private qualia. Only problem: the many complex open problems to
extract the whole of physics: but those are interesting mathematical
problems.
My feeling is that you confuse the arithmetical reality, with the
human and very partial theories which can put some light on that
arithmetical reality, but cannot be identified with it. Today, we know
that there is just no complete theory capable of describing the
arithmetical reality. With computationalism, the arithmetical reality
is provably quite beyond each of us.
You are not asked to believe in some realm where the numbers would
exist, you are only asked if we can agree on simple proposition like
"all natural numbers have a successor, different numbers have
different successors, 0 is not the successor of a number, x + 0 = x,
x* 0 = 0, addition laws, multiplication laws.
From this we define the mind (the possible beliefs of a universal
numbers + the intensional variants of those beliefs) and matter (what
is invariant for machine's bet on all relative computations). This
does explain quanta and qualia in a unified way, without any "magic
primary matter" (a god of the gap), nor magic power in the mind.
Even without the intrinsic difficulties of the mind-body problem
brought by the postulation of matter, this postulation take for
granted what I want to explain: where the physical reality comes from
and what could be its nature, and how is it related to consciousness?
Bruno
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