comment by WhySpace_duplicate0.9261692129075527 ·
2016-07-29T16:45:03.005Z · LW(p) · GW(p)
Very close, but not quite. (Or, at least not quite my understanding. I haven’t dug too deep.)
A reply to Presuppositionalism
Rationalist presume Occam's razor because it proof itself Rationalist presume Induction razor because it proof itself *etc.
I wouldn’t say that we should presume anything because it proves itself. Emotionally, we may have a general impulse to accept things because of evidence, and so it is natural to accept induction using inductive reasoning. So, that’s likely why the vast majority of people actually accept some form of induction. However, this is not self-consistent, according to Lob’s theorem. We must either accept induction without being able to make a principled argument for doing so, or we must reject it, also without a principled reason.
So, Presuppositionalism appears to be logically false, according to Lob’s theorem.
I could leave it at that, but it’s bad form to fight a straw man, and not the strongest possible form of an argument. The steel man of Presuppositionalism might instead take certain propositions as a matter of faith, and make no attempt to prove them. One might then build much more complex philosophies on top of those assumptions.
Before I reply to that, let me back up for a moment. I Agree Denotationally But Object Connotationally with most of the rest of what you said above. (It seems to me to be technically true, but phrased in such a way that it would be natural to draw false inferences from it.)
If I had merely posited that induction was valid, I suspect it wouldn’t have been disconcerting, even if I didn’t offer any explanation as to why we should start there and not at “I am not dreaming” or any of the examples you listed. You were happy to accept some starting place, so long as it felt reasonable. All I did was add a little rigor to the concept of a starting point.
However, by additionally pointing out the problems with asserting anything from scratch, I’ve weakened my own case, albeit for the larger goal of epistemic rationality. But since all useful philosophies must be based in something, they also can’t prove their own validity. The falling tide lowers all ships, but doesn’t change their hull draft) or mast height.
So, we still can’t then say “the moon is made of blue cheese, because the moon is made of blue cheese”. If we just assume random things to be true, eventually some of them might start to contradict one another. Even if they didn’t, we’d still have made multiple random assertions when it was possible to make fewer. It’s not practically possible not to use induction, so every practical philosophy does so. However, adding additional assertions is unnecessary.
So, I agree connotationally when you say “The best that we can do is to get a non-contradicting collection of self-referential statement that covers the epistemology and axiology”. This infers that all possible sets of starting points are equally valid, which I don’t agree with. I’ll concede that induction is equally as valid as total epistemic nihilism (the position that nothing is knowable, not to be confused with moral nihilism, which has separate problems). I can’t justify accepting induction over rejecting it. However, once I accept at least 1 thing, I can use that as a basis for judging other tools and axioms.
A reply to the Presuppositionalism steel man
Lets go back to the Presuppositionalism steel man. Rather than making a self-referential statement as a proof, it merely accepted certain claims without proof. Any given Presuppositionalist must accept induction to function in the real world. If they also use that induction and accept things that induction proves, then we can claim to have a simpler philosophy. (Simpler being closer to the truth, according to Occam’s razor.)
They might accept induction, but reject Occam’s razor, though. I haven’t thought through the philosophical implications of trying to reject Occam’s Razor, but at first glance it seems like it would make life impractically complicated. It doesn’t necessarily lead to being unable to conclude that one should continue breathing, since it’s always worked in the past. So, it’s not instant death, like truly rejecting induction, but I suspect that truly rejecting Occam’s razor, and completely following through with all the logical implications, would cause problems nearly as bad.
For example, overfitting might prevent drawing meaningful conclusions about how anything works, since trillions of arbitrarily complex function can all be fit to any given data set. (For example, sums of different sine waves.) It may be possible to substitute some other principle for Occam’s razor to minimize this problem, but I suspect that then it would then be possible to compare that method against Occam’s Razor (well, Solomonoff induction) and demonstrate that one produced more accurate results. There may already be a proof that Solomonoff induction is the best possible set of Bayesian Priors, but I honestly haven’t looked into it. It may merely be the best set of priors known so far. (Either way, it’s only the best assuming infinite computing power is available, so the question is more academic than practical.)
So, it looks like this is the least bad possible philosophy, or at least quite close. It’s a shame we can’t reject epistemic nihilism, but pretty much everything else seems objectively suboptimal, even if some things may hold more aesthetic appeal or be more intuitive or easy to apply. (This is really math heavy, and almost nothing in mathematics is intuitive. So, in practice we need lots of heuristics and rules of thumb to make day to day decisions. None of this is relevant except when these more practical methods fail us, like on really fundamental questions. The claim is just that all such practical heuristics seem to work by approximating Solomonoff induction. This allows aspiring rationalists to judge potential heuristics by this measure, and predict what circumstances the heuristic will work or fail in.)
It is NOT a guarantee that we’re right about everything. It is NOT an excuse to make lots of arbitrary presuppositions in order to get the conclusions we want. Anything with any assumptions is NOT perfect, but this is just the best we have, and if we ever find something better we should switch to that and never look back.