On 11 January 2014 16:02, meekerdb <meeke...@verizon.net> wrote:

>  On 1/10/2014 4:06 PM, LizR wrote:
>  On 11 January 2014 12:54, meekerdb <meeke...@verizon.net> 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. 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?

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 -

> 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.

> 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.

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