On 12 Jun 2016, at 00:50, John Clark wrote:
On Sat, Jun 11, 2016 at 6:14 PM, Brent Meeker <[email protected]>
wrote:
>> As I've said 6.02*10^23 times it's irrelevant if matter
is primary or not, matter is still necessary to make calculations
or perform intelligent behavior or produce consciousness.
> I think Bruno agrees with that
That's news to me. If so Bruno should have said that several years
ago and a great many electrons wouldn't have had to give up their
lives.
>> And even if matter isn't primary that doesn't necessarily
mean mathematics is.
> The question is can one be derived from the other?
I think so, but neither may be primary.
X is primary means that we need to assume X, or something equivalent,
if we want it existing.
So X is primary means mainly that we cannot derive the existence of X,
or the appearance of X, from something judged conceptually simpler.
With mechanism, we need the natural numbers, but we can assume any
Church-Turing universal system. Once you assume one of them, you get
all of them. You can define the numbers in the language of the SK-
combinators, and vice versa. But without assuming at least one
universal system, you cannot get it from anything simpler (trivially,
because if you can get a universal system A from some system B, B is
proven universal!
Now, elementary arithmetic, and its standard semantics, is assumed by
virtually all scientists.
UDA shows that with computationalism, we cannot assume anything more
than that, nor anything less. I mean in the fundamental theory. In the
evryday life, it is quite different, and we assume all the time much
more.
> William S. Cooper, "The Origin of Reason" makes an argument
that mathematics is a way of brains thinking about things that was
found by evolution, just like mobility, metabolism,
reproduction,...and a lot of other functions.
I agree with that, but evolution works according to the laws of
physics so a animal who thought 1+1=0 would have fewer offspring
than one who believed 1+1=2. So we'd agree with ET's mathematics
because it's the language of physics.
I bet alien's among those we can discuss with would have the same
arithmetic, but humans already disagree easily on analysis. Now,
thanks to the fact that they agree on arithmetic, they do agree on the
consistency on the consistency of classical (second-order) analysis,
but none really agree on what they mean, or if they are the last
theory or not. There are many ways to reintroduce infinitesimals. They
are proved coherent by mathematical logic technics, for example.
Arithmetic and digital (universal) system are very special in that
regard. Everyone agrees that for all natural number n, we have that 1
+ 2 + 3 + ... + n = n(n+1)/2.
Bruno
John K Clark
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