Does the Matrix Possibility Mean Anything Can Happen?
Kingasaurus asked the million dollar question about assigning 0% Bayesian prior probabilities to claims:
Kingasaurus, those type of scenarios are literally a dime a dozen. Did you see the "Men in Black" movie where a a cat wears a charm which is another whole universe? I could be nothing but brains in a vat. A demon might be deceiving me. The whole universe might be growing larger every second, or smaller, along with us in it. I've written about a few of them before. Technically they are all mathematical possibilities, but they not only cancel each other out, they're to be regarded by those of us living in this reality as impossibilities.
How can we choose which one of these multitude of scenarios is actually the case? Hitchens said "That which can be asserted without evidence, can be dismissed without evidence." Dismissed. Just as Bayes cannot deal with claims that have no prior data to compare with, so also these scenarios can all be dismissed until such time as there is evidence for one over any of the lot of them.
Take the problem induction for instance. Induction is the basis for science. How do we know the universe acts uniformly such that gravity will still work tomorrow? The answer is there hasn't been a single case where the world acted differently under the same test conditions, so that's solid objective evidence we can do science based on a uniform world.
Math does not adequately reflect reality. We know this. We make it up and it seems to correspond close enough to reality, but not perfectly. Technically speaking, one plus one does not equal two. Look also at Borels' Law where any event probability below 1 in 10 to the 50th power will never happen. Beyond that, infinity to 1 odds is equivalent to 0 odds because infinity is not actually a number. So in the real world, virtual impossibilities are good enough. The math does not adequately reflect the true nature of real world impossibilities. Mathematical "virtue impossibilities" are real world "impossibilities."
Could we still be deceived? No, not unless we're insane. For even if we live in a Matrix we should still act and think and calculate as if we don't. Even if the Matrix dictates reality, that's our reality. In that reality no one can jump off a cliff and hope to survive. No one should shoot themselves either. So we have zero hope that pigs can fly and still remain pigs, or that amputated arms don't magically reattach themselves.
John, isn't there a non-zero chance that we're all living in the Matrix and the programming could always be changed so that pigs do fly and amputated arms are "magically" re-attached?Great question!
Wouldn't this make the possibility of absolutely anything and everything non-zero?
Kingasaurus, those type of scenarios are literally a dime a dozen. Did you see the "Men in Black" movie where a a cat wears a charm which is another whole universe? I could be nothing but brains in a vat. A demon might be deceiving me. The whole universe might be growing larger every second, or smaller, along with us in it. I've written about a few of them before. Technically they are all mathematical possibilities, but they not only cancel each other out, they're to be regarded by those of us living in this reality as impossibilities.
How can we choose which one of these multitude of scenarios is actually the case? Hitchens said "That which can be asserted without evidence, can be dismissed without evidence." Dismissed. Just as Bayes cannot deal with claims that have no prior data to compare with, so also these scenarios can all be dismissed until such time as there is evidence for one over any of the lot of them.
Take the problem induction for instance. Induction is the basis for science. How do we know the universe acts uniformly such that gravity will still work tomorrow? The answer is there hasn't been a single case where the world acted differently under the same test conditions, so that's solid objective evidence we can do science based on a uniform world.
Math does not adequately reflect reality. We know this. We make it up and it seems to correspond close enough to reality, but not perfectly. Technically speaking, one plus one does not equal two. Look also at Borels' Law where any event probability below 1 in 10 to the 50th power will never happen. Beyond that, infinity to 1 odds is equivalent to 0 odds because infinity is not actually a number. So in the real world, virtual impossibilities are good enough. The math does not adequately reflect the true nature of real world impossibilities. Mathematical "virtue impossibilities" are real world "impossibilities."
Could we still be deceived? No, not unless we're insane. For even if we live in a Matrix we should still act and think and calculate as if we don't. Even if the Matrix dictates reality, that's our reality. In that reality no one can jump off a cliff and hope to survive. No one should shoot themselves either. So we have zero hope that pigs can fly and still remain pigs, or that amputated arms don't magically reattach themselves.
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