What I find fascinating is that Solomonoff Induction (and the related concepts from Kolmogorov complexity) very elegantly solves the classical philosophical problem of induction, as well as resolving a lot of other problems:
What is the correct “prior” in Bayesian inference, and isn’t the choice of prior all subjective?
What does Occam’s razor really mean, and what is a “simple” theory?
Why do physicists insist that their theories are “simple” when only they can understand them?
Despite this, it is almost unheard of in the general philosophical (analytic philosophy) community. I’ve read literally dozens of top-grade philosophers discussing these topics, with the implication that these are still big unsolved problems, and in complete ignorance that there is a very rich mathematical theory in this area. And the theory’s not exactly new either… dates back to the 1960s.
Possibly because .Solomonoff induction isnt very suitable to answering the kinds of questions philosophers want answered, questions of fundamental ontology.. It can tell you what programme would generate observed data, but it doesn’t tell you what the programme is running on..the laws of physics, Gods mind, .or a giant simulation. OTOH, traditional Occams razor can exclude a range of ontological hypotheses.
I don’t think Solomonoff Induction solves any of those three things. I really hope it does, and I can see how it kinda goes half of the way there to solving them, but I just don’t see it going all the way yet. (Mostly I’m concerned with #1. The other two I’m less sure about, but they are also less important.)
I don’t know why the philosophical community seems to be ignoring Solomonoff Induction etc. though. It does seem relevant. Maybe the philosophers are just more cynical than we are about Solomonoff Induction’s chances of eventually being able to solve 1, 2, and 3.
What I find fascinating is that Solomonoff Induction (and the related concepts from Kolmogorov complexity) very elegantly solves the classical philosophical problem of induction, as well as resolving a lot of other problems:
What is the correct “prior” in Bayesian inference, and isn’t the choice of prior all subjective?
What does Occam’s razor really mean, and what is a “simple” theory?
Why do physicists insist that their theories are “simple” when only they can understand them?
Despite this, it is almost unheard of in the general philosophical (analytic philosophy) community. I’ve read literally dozens of top-grade philosophers discussing these topics, with the implication that these are still big unsolved problems, and in complete ignorance that there is a very rich mathematical theory in this area. And the theory’s not exactly new either… dates back to the 1960s.
Anyone got an explanation for the disconnect?
Philosophers don’t read those things. If that explanation seems lacking, I feel like referring to Feynman.
Possibly because .Solomonoff induction isnt very suitable to answering the kinds of questions philosophers want answered, questions of fundamental ontology.. It can tell you what programme would generate observed data, but it doesn’t tell you what the programme is running on..the laws of physics, Gods mind, .or a giant simulation. OTOH, traditional Occams razor can exclude a range of ontological hypotheses.
There is also the problem that there is no absolute measure of the complexity of a programme: a programming language is still a language, and some languages can express some things more concisely than others, as explained in kokotajlods other comment. http://lesswrong.com/lw/jhm/understanding_and_justifying_solomonoff_induction/ady8
I don’t think Solomonoff Induction solves any of those three things. I really hope it does, and I can see how it kinda goes half of the way there to solving them, but I just don’t see it going all the way yet. (Mostly I’m concerned with #1. The other two I’m less sure about, but they are also less important.)
I don’t know why the philosophical community seems to be ignoring Solomonoff Induction etc. though. It does seem relevant. Maybe the philosophers are just more cynical than we are about Solomonoff Induction’s chances of eventually being able to solve 1, 2, and 3.