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Arielgenesis comments on Open thread, Jul. 25 - Jul. 31, 2016 - Less Wrong
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This, and your links to Lob's theory, is one of the most fear inducing piece of writing that I have ever read. Now I want to know if I have understand this properly. I found that the best way to do it is to first explain what I understand to myself, and then to other people. My explanation is below:
I suppose that rationalist would have some simple, intuitive and obvious presumptions a foundation (e.g. most of the time, my sensory organs reflect the world accurately). But apparently, it put its foundation on a very specific set of statement, the most powerful, wild and dangerous of them all: self-referential statement:
*Rationalist presume Occam's razor because it proof itself *Rationalist presume Induction razor because it proof itself *etc.
And a collection of these self-referential statement (if you collect the right elements) would reinforce one another. Upon this collection, the whole field of rationality is built.
To the best of my understanding, this train of thought is nearly identical to the Presuppositionalism school of Reformed Christian Apologetics.
The reformed / Presbyterian understanding of the Judeo-Christian God (from here on simply referred to as God), is that God is a self-referential entity, owing to their interpretation of the famous Tetragrammaton. They believe that God is true for many reasons, but chief among all, is that it attest itself to be the truth.
Now I am not making any statement about rationality or presuppositionalism, but it seems to me that there is a logical veil that we cannot get to the bottom of and it is called self-reference.
The best that we can do is to get a non-contradicting collection of self-referential statement that covers the epistemology and axiology and by that point, everyone is rational.
Very close, but not quite. (Or, at least not quite my understanding. I haven’t dug too deep.)
A reply to Presuppositionalism
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.
Brief detour
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.)
General conclusions
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.
That assumes that a rational person is one who holds beliefs because of a chain of logic. Empricially Superforcasters don't simply try to follow a chain of logic to get their beliefs. A rational person in the LW sense thus is not one that holds beliefs because of a chain of logic.
Tedlock gives in his book a good outlook about how to form beliefs about the likelihood that beliefs are true.
Neither do bad forecasters, or cranks, or schizophrenics. The suppressed premiss here is that superforcasters are right or reliable. But that implies that their claims are tested or testable and that implies some basic presumptions of logic or empricism.
Tedlock lays out a bunch of principles to come to correct conclusions. One of the principles is being a fox that uses multiple chains instead of trying to use one correct chain that rests on a foundation based on which other beliefs can be logically deduced.
The paradigm that Arielgenesis proposes is to follow a hedgehog system where a single chain of logic can be relied on because certain basic presuppositions are accepted as true.
Holding a belief because of a chain of logic has little to do with the principle of empricism.
There are many ways to do bad forecasts. As far as the examples of cranks and schizophrenics go, those are usually hedgehogs. A lot of cranks usually follow a chain of logic. If you take people who think there are illegal tricks to avoid paying income tax, they usually have elaborate chains of logic to back up their case.
How do you know that I hold my belief based on a "suppresed premiss"? If something is supressed and you can't see it, maybe the structure of my reasoning process isn't the structure you guess.
Missing the point. The point is how their conclusions are verified.
Logic is implicit in empricisicm because the idea that contradictions are false is implicit in the idea of disproof by contradictory evidence.
Missing the point. I didn't say that logic is sufficient for correctness. I am saying that if you have some sort of black-box, but effective reasoning, then some kind of presupposition is going to be needed to verify it.
If you have other reasoning show it. Otherwise that was an irrelevant nitpick.
I think Science and Sanity lays out a framework for dealing with beliefs that doesn't categories them into true/false that is better than the basic true/false dichomity.
I care more about what Science and Sanity called semantic reactions than I care about presuppositions.
Basically you feed the relevant data into your mind and then you let it process the data. As a result of processing it there's a semantic reaction. Internally the brain does that with a neural net that doesn't use logical chains to do it's work.
When I write here I point out the most important piece of the data, but not all of what my reasoning is based on because it's based on lots of experiences and lots of empiric data.
Using a ramified logic with more than two truth values is not the same as not using logic at all!
That is such a vague description of reasoning that it covers everything from superforecasting to schizobabble. You have relieved yourself of the burden of explaining how reasoning works without presupposiitons by not treating reasoning as something that necessarily works at all.
Could you define what you mean with "logic" if not thinking in terms of whether a statement is true?
Thinking about how probable it is, or how much subjective credence it should have. There are formal ways of demonstrating how fuzzy logic and probability theory extend bivalent logic.
Science and Sanity is not about probability theory or similar concepts of having numbers between 0 and 1.
"The map is not the territory" doesn't mean "The map is the territory with credence X that's between 0 and 1". It's rather a rejection about the concept of the is of identity and instead thinking in terms like semantic reactions.
If you agree that it covers superforcasting than my argument is right. Using presuppotions is a very particular way of reasoning and there are many other possible heuristics that can be used.
A LW comment also isn't long enough to lay out a complete system of reasoning as complex as the one proposed in Science and Sanity or that proposed in Superforcasting. That why I refer to general arguments are refer to the books for a more detailed explanation of particular heuristics.
There's basically two kinds of reasoning - the kind that can be made manifest (explicit,etc) and the kind that can't. The gold standard of solving of solving the problem of presuppositions (foundations, intuitions) is to show that nothing presupposition-like is needed in explicit reasoning. Failed attempts tend to switch to implicit reasoning, or to take it that sufficiently obvious presupposiitons don't count as presuppositions (We can show this with induction...we can show this with empiricism).
I don't think that's the case. Trying to put complex concepts into two boxes binary boxes is done very frequently in the Western tradition but there no inherent argument that it's the best way to do things. Science and Sanity argues in detail why binary thining is limiting.
As far as this particular case of the implicit/explicit distinction, most kinds of reasoning tend to be a mix. Reasoning that's completely explicit is the kind of reasoning that can be done by a computer with very limited bandwith. For many problems we know that computers can't solve them as easily as calculating 23472349 * 5435408 which can be done completely explicitely. If you limit yourself to what can be made completely explicit you limit yourself to a level of intelligence that can't outperform computers with very limited memory/CPU power.
Eliezer ruminates on foundations and wrestles with the difficulties quite a bit in the Metaethics sequence, for example:
Thank you. This reply actually answer the first part of my question.
The 'working' presuppositions include: * Induction * Occam's razor
I will quote most important part from Fundamental Doubts
And this have a lot of similarities with my previous conclusion (with significant differences about circular logic and meta loops)