Hi John,
On 24 Apr 2015, at 23:57, John Mikes wrote:
Liz and Friends of Nearer Geography:
I wrote so many times and nobody reflected so far.
WHY is 2 + 2 = 4 if there is a VALID concept like RANDOM?
Why not 2 + 2 = -----175,834? or even '1'? (Without
changing the game).
Without changing the game? I lend you 2 dollars, and then once again,
now you owe me 175,384 dollars.
Nice!
I deny random, it would eliminate all our technology, science,
physics, etc. etc.
Why would randomness eliminate technology? We can, and do, exploit
randomness. Also, some things can be random and other things being not
random. You need both to see the difference and get the concept.
My non-IndoEuropean mother tongue has no 'random, we use the
translation of the German "exbeliebig" (~ from what we like??) - well
I don't "LIKE" it, so I have no random?????
Russell wrote more than a decade ago: 'yes', it seems there
should be a 'relative random' - but nothing further from him.
Nor anybody else.
The math provides a tool for measuring a form of randomness inherent
from the number's perspective in arithmetic. A machine cannot
distinguish randomness from a non random production of a machine much
more complex than herself, so randomness is always based on
theoretical, and non random deeper beliefs/assumptions.
Randomly yours (no random qgnosticism, however)
I appreciate your agnosticism has no random reason.
You asked also: what is a number?
In science, we don't know.
But we can agree on some basic first principles and deduce from
there. Number can be defined axiomatically by axioms like:
0 ≠ (x + 1)
((x + 1) = (y + 1)) -> x = y
x = 0 v Ey(x = y + 1)
x + 0 = x
x + (y + 1) = (x + y) + 1
x * 0 = 0
x * (y + 1) = (x * y) + x
You, and all universal machines, are free to propose another theory,
but up to now, everyone agrees with the axioms above for the natural
numbers (0, 1, 2, ...), and in that theory, you can already prove the
existence of universal numbers, and of universal numbers developing
beliefs.
But that theory is not Löbian. It might be conscious in some "trivial"
sense, but it has no self-consciousness, for which you need to add the
infinitely many axioms of induction:
If P is true for zero, and if P is such that (if p is true for x then
P is true for x + 1) then you can derive that P is true for all x.
This makes the entity as much conscious than you and me, but with so
less prejudices than us, the humans, that you see the "theological"
first principle that such machine can't avoid when looking inward.
More on this in a reply to Brent.
Bruno
John Mikes
On Thu, Apr 23, 2015 at 8:02 PM, LizR <lizj...@gmail.com> wrote:
On 23 Apr 2015, at 08:37, meekerdb wrote:
2+2=1 in mod 3 arithmetic. If you change the game you change what
can be proven. You can't keep the old version and assume its
proofs apply to the new game.
But you haven't changed the game. 2+2=4, still, in normal
arithmetic, and unless you can change THAT you are still in the same
"game". (All you've done is to discover that there's more to the
game than you originally thought.)
I'm a little disappointed. Although I'm of the opinion that maths
isn't made up (based on its unreasonable effectiveness in the
physical sciences) I still expected a slightly more sophisticated
level of argument. If that's the type of argument that supposedly
shows maths is made up, it doesn't look like physicists need fear
that the mathematical rug they've been relying on for the last 300
years will be pulled out from beneath them anytime soon.
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