FAITH... WITH REASON

FAITH... WITH REASON Mar 5, 2017 18:06:38 GMT

Quote

Post by Eva Yojimbo on Mar 5, 2017 18:06:38 GMT

Mar 4, 2017 17:10:46 GMT fatpaul said:

Mar 3, 2017 17:51:07 GMT Eva Yojimbo said:

This is incorrect. Occam has been formalized via Solomonoff Induction, which is a bit too complex to fully explain in this post, but to reference the most relevant parts...

Solomonoff Induction itself is a mathematical justification for our bias, along with many other explanations, none of which are without their problems

First sentence is correct. I don't know what you mean by the bolded part.

I don't see how SI would even claim that OR is a real principle but rather a high likelihood that it could be real given that the theory itself is falsifiable. So I still stand by my statement, specifically that OR is a tendency for simplicity in us, not necessarily a tendency of the universe, or more precisely: OR is a tendency for simplicity, which we have, not necessarily a tendency to what's real.

Again you're confusing me. SI is a mathematical proof for Occam. Since SI is a method for finding hypothesis to explain empirical data (ie, reality), then the proof would mean that simpler explanations of that reality are more likely; ergo an ontological principle. I gave an example with the conjunction fallacy: the probability of A+B can never be greater than A or B alone. If we're talking about variable VS invariable laws, then with the latter we have A (the invariable laws that apply everywhere), while with the former we'd have A+B (plus perhaps many more). There's no way the invariable hypothesis can be more likely sans evidence.

Occam is also a heuristic technique, yes, but this does not prevent it from also being an ontological principle. In this case, it happens to be both. In fact, science chose it as a heuristic because it seemed to map well to reality. SI was just proof that it did.

It's also worth pointing out the "probability is in the mind" aspect of this. What we're really talking about isn't just reality, but hypotheses to explain reality. When dealing with hypotheses you ARE dealing with the mind because it's essentially the mind that's attempting to map reality. In constructing a hypothesis, every additional element you add has a probability of being wrong, and the more you add, the more the joint probabilities lowers the collective probability of the hypothesis. This is essentially what SI shows in a very rigorous manner, since all binary data adds 1-bit to a hypothesis that's either true/false (50/50). The more you add, the more that you need to be correct. You can think of it like a coin-flip: the sequence HHTTH will always be more likely than HTTHTH merely by virtue of the former being shorter/simpler. This is SI in a nutshell, and it supports the principle of Occam.