Abram Demski wrote:
Charles,
Again as someone who knows a thing or two about this particular realm...
Math clearly states that to derive all the possible truths from a numeric
system as strong as number theory requires an infinite number of axioms.
Yep.
I.e., choices. This is clearly impossible. To me this implies (but not
proves) that there are an infinite number of possible futures descending
from any precisely defined state.
Not quite.
An infinite number of axioms may be needed, but there is a right and
wrong here! We cannot choose any axioms we like. Well, we can, but if
we choose the wrong ones we will eventually derive a contradiction.
When we choose the right ones, we can't know that we have... we just
hold our breath and hope that no contradiction arises. :)
--Abram
Sorry. Thinking on it you are correct. Merely because the math ends up
consistent doesn't mean that it matches "reality". But we can't know
until after, quite possibly long after, we choose the axiom. Which
furthers the need for built in biases. (I wish I'd realized your point,
it would have made my argument stronger.)
OTOH, this is an argument by analogy, so it's not certain anyway. It
might be possible to derive a proof, but I sure couldn't do it.
-------------------------------------------
agi
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