On 1/10/2014 7:33 PM, LizR wrote:
On 11 January 2014 16:02, meekerdb <[email protected] <mailto:[email protected]>>
wrote:
On 1/10/2014 4:06 PM, LizR wrote:
On 11 January 2014 12:54, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 1/10/2014 1:42 AM, Bruno Marchal wrote:
Second, a reality can exist without being computed. the best and simple
example is arithmetic. Only a very tiny part of it is computable (this
is
provable if you accept the Church Turing thesis).
But it's questionable whether it "exists".
Does it kick back? Could two beings in different universes, with different
laws of
physics (if such exist) discover it independently?
Of course "discover" begs the question.
No it doesn't. It /is/ the question. I used "discover" in the sense of making a
discovery, as opposed to inventing something.
That's what "begs the question" means, the form of your question implicitly assumes the
answer you presuppose. "Discover" implies existence independent of invention. But that's
the point I'm questioning. When we count are we discovering 1,2,3,... or are we inventing
the concept of several things consitituting a numberable set.
If alien mathematicians start from whatever axioms the humans mathematicians start from,
and find themselves led inexorably to the same logical conclusion as the humans, then I
would say they are "discovering" something about the nature of reality. If they start
from the same premises and arrive at a different conclusion (and neither sets of
mathematicians have made any mistakes), then I would say they are "inventing" something.
That's the sense in which I asked if they would "discover" the (alleged) facts of maths.
It seems to me a perfectly reasonable way to ask the question. Would they independently
discover the same results, or wouldn't they? What's wrong with that?
Why couldn't they invent the same concepts?
I suppose I could have assumed my audience were drongoes and added something like "...or
would they invent completely different results?" But I didn't bother to insult my
audience like that, because it seems to me that was implicit in the way I'd asked the
question. In fact I'd very neatly /summarised/ the entire question through the use of
that one word - "discover".
If so, it exists by any reasonable definition (including Stephen's)
Two beings with different laws of physics in different universes could
invent the
game of rock, paper, scissors. Does that mean the game exists? Did it
exist before
they invented it?
That isn't the same as being led to one specific conclusion by applying logic to a given
set of axioms, though, which is what "discover" implies.
I think it is the same. R<P<S<R is not so complicated it couldn't be "discovered" in
almost all worlds.
Does the continuum exist?
I don't know. I assume it exists as a mathematically discoverable entity (or is there a
problem with that?) I don't know if it exists in the physical sense of space-time being
one. As I mentioned elsewhere recently, the jury is out on this one due to the GRB data
still being relatively scarce. Watch this space.
I don't have any problem with "exists in mathematics" or "in Platonia" or in "the realm of
fiction" (e.g. where Sherlock Holmes "exists") so long these can be given some reasonable
definition. But it seems like a leap to say that because we can make up rules about
creating sentences (inference from axioms) that makes things exist. Did we invent
insurance or discover it? What about the non-standard models of arithmetic? Are we to
say they don't exist because...why exactly?...we didn't think of them first?
I think of them all as models, some are just models of little pieces of reality (e.g.
numbers->things we can count) others try to be models to much big parts (e.g. quantum
field theory) and "exists" is relative to the model.
Brent
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