I don’t think you know how Bayes’ theorem works… if I say “A & B will both be true,” and it turns out that A is true, this is evidence for my original claim, despite the fact that it is implied by the meaning of the words… or rather in this case, because it is so implied.
Also, without induction, we can construct a probability estimate: take all the possibilities we know of, add the possibility “or something else”, and then say that each of possibilities is equally likely. Yes, this probability estimate isn’t likely to be calibrated but it will be the best we can do given the condition of not knowing anything about the relation of past and future.
How can one confirm that this happens without induction?
That said, I’m becoming somewhat more convinced of your point; I’m just not sure it’s of any practical value.
The issue is that any statement made about the real world requires induction. If we are speaking in the hypothetical, yes, if the sun rises tomorrow, then that increases the chance that the sun will rise for the next ten thousand days, in the same sense that if the next flozit we quivel is bzorgy, that increases the chance that the next 10,000 flozits we quivel will be bzorgy. It tells us nothing new or interesting about the actual world. Furthermore, we can never confirm that the conditional is fulfilled without sense data, the reliability of which presumes induction.
Just as you seem to think I underestimate the primacy of Bayes, I think you significantly underrate the depth of induction. A world without induction being valid is not so much one where the sun does not rise tomorrow as one that would make a drugged-out madman look like a Bayesian superintelligence. Without assuming the validity of induction, that there will be an earth or a sun or a tomorrow are all completely uncertain propositions. Without induction, far more is possible than we can ever hope to imagine. We can’t construct any meaningful probability estimate, because without induction we would expect the world to look something like more colorful TV static.
The fact that your senses are reliable may “presume induction”, just as it may also presume that you are not being deceived by Descartes’ evil demon. But when you say “that grass is green,” you don’t consider that the only reason you know it isn’t red is because there isn’t any demon… instead you don’t think of Descartes’ demon at all, and likewise you don’t think of induction at all. In any case, in whatever way “induction” might be involved in your senses, my article doesn’t intend to consider this, but induction considered just as a way of reasoning.
My point is that a year ago, you could have had a 90% probability estimate that the world would look like TV static, and a 10% probability of something else. But the 10% chance has been confirmed, not the 90% chance. Or if you say that there was no basis for the 10% chance, then maybe you thought there was a 100% chance of static. But in this case you collapse in Bayesian explosion, since the static didn’t happen.
In other words, “not assuming induction” does not mean being 100% certain that there will not be a future or that it will not be like the past; it means being uncertain, which means having degrees of belief.
I don’t think you know how Bayes’ theorem works… if I say “A & B will both be true,” and it turns out that A is true, this is evidence for my original claim, despite the fact that it is implied by the meaning of the words… or rather in this case, because it is so implied.
Also, without induction, we can construct a probability estimate: take all the possibilities we know of, add the possibility “or something else”, and then say that each of possibilities is equally likely. Yes, this probability estimate isn’t likely to be calibrated but it will be the best we can do given the condition of not knowing anything about the relation of past and future.
How can one confirm that this happens without induction?
That said, I’m becoming somewhat more convinced of your point; I’m just not sure it’s of any practical value.
The issue is that any statement made about the real world requires induction. If we are speaking in the hypothetical, yes, if the sun rises tomorrow, then that increases the chance that the sun will rise for the next ten thousand days, in the same sense that if the next flozit we quivel is bzorgy, that increases the chance that the next 10,000 flozits we quivel will be bzorgy. It tells us nothing new or interesting about the actual world. Furthermore, we can never confirm that the conditional is fulfilled without sense data, the reliability of which presumes induction.
Just as you seem to think I underestimate the primacy of Bayes, I think you significantly underrate the depth of induction. A world without induction being valid is not so much one where the sun does not rise tomorrow as one that would make a drugged-out madman look like a Bayesian superintelligence. Without assuming the validity of induction, that there will be an earth or a sun or a tomorrow are all completely uncertain propositions. Without induction, far more is possible than we can ever hope to imagine. We can’t construct any meaningful probability estimate, because without induction we would expect the world to look something like more colorful TV static.
The fact that your senses are reliable may “presume induction”, just as it may also presume that you are not being deceived by Descartes’ evil demon. But when you say “that grass is green,” you don’t consider that the only reason you know it isn’t red is because there isn’t any demon… instead you don’t think of Descartes’ demon at all, and likewise you don’t think of induction at all. In any case, in whatever way “induction” might be involved in your senses, my article doesn’t intend to consider this, but induction considered just as a way of reasoning.
My point is that a year ago, you could have had a 90% probability estimate that the world would look like TV static, and a 10% probability of something else. But the 10% chance has been confirmed, not the 90% chance. Or if you say that there was no basis for the 10% chance, then maybe you thought there was a 100% chance of static. But in this case you collapse in Bayesian explosion, since the static didn’t happen.
In other words, “not assuming induction” does not mean being 100% certain that there will not be a future or that it will not be like the past; it means being uncertain, which means having degrees of belief.