On Wednesday, January 14, 2015 at 5:28:03 AM UTC-5, Bruno Marchal wrote:
>
>
> 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)...
>
...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.
>
Roger: There is, of course, a difference between the conception in our
minds of something and the thing it is we're conceiving. I've made this
exact point in a recent posting here. But, because of your Platonism
you're suggesting that if the thing we're conceiving is a number or
mathematical proposition, it would exist or be true even in the case of the
complete lack of all physically existent entities. What I'm suggesting is
that there would be no proposition about "786899543211 is prime or is not
prime" in the first place unless there are first existent entities and the
mental constructs called numbers and mathematics for describing these
entities. That is, to have a proposition *be* true or false, a proposition
first has to *be* or "exist". Basically, I think our disagreement comes
down to the idea that you believe that some propositions exist or are true
in a Platonic realm that is not part of space, time and the physical world.
I can't disprove this. But, no one can ever disprove or prove things they
can neither see evidence for or test. That's more a matter of faith.
>
>
> 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?
>
> Roger: Even if what is "outside the mind" is also a mental construct, and
even if the entirety of existence is some mental construct, you're
suggesting that mathematics or mathematical propositions would exist
outside that existence in a Platonic realm that doesn't exist like
everything else. Again, I can't disprove it, but it can't be proved either
because this realm can't be seen or experimented on.
For a prime twin conjecture to *be *true or false, there first has to
*be* a prime twin conjecture as well as primes. That is these things have
to *be* or exist somewhere. If you can point out to me where they exist
separately from being a mental construct, that'd be great.
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?
>
> 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?
>
>
> Roger: When you say "My feeling is that you confuse the arithmetical
reality...", you're making a very large and unprovable assumption that
there is an arithmetical reality separate from all physically existing
things. On the other hand, I'm only willing to assume what I can see or
test (if not now, then someday as technology develops). I can't disprove
that mathematical propositions can be true or false separate from all
physically existent entities, but neither can you prove them. So,
overall, I do lean towards the idea that all things are physical, as many,
if not most, in science do. You seem to have decided that mathematical
propositions can "be" true without accepting that these propositions first
have to "be" or exist. They can exist as a "physical" or "mental"
construct, but they have to first "be" or exist somewhere in order for them
to be true or false. As before, if someone can point out to me where they
exist that's not a mental construct, that'd be great.
In regard to "where does the physical things come from", the whole
point of this entire thread was about the question "Why is there something
rather than nothing?", and I mentioned and posted the link for my
physicalist/materialist type proposal for where the "physical things" or
"something" come from.
Overall, I think this is a disagreement where neither one of us can
prove our side to be correct. I just like to only assume what I can see or
test and not assume otherwise without evidence.
While we totally disagree, I do thank you for a great discussion!
Roger
>
>
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