So when we are aware that nothing can ever be 100% conclusive, we are unable to be truely satisfied?

@waffle
I'm willing to reduce my claims to match the Carroll article. There's really nothing crucial to my line of argument that isn't covered in the article, and since you're willing to accept it as written, it might make a better starting point.

@drache
The first ones that come to mind are "Why is there a Mandelbrot Set?" "Why is pi irrational?" and "Why is the golden ratio the number that it is?" . Any "why" question will be necessarily outside the Bayesian realm. Of course, EY would almost certainly reply that those are not things we "need" to know, but that itself serves to highlight the subjectivity of his language. Who decides?

A more pointed example of a non-Bayesian question that EY seems to mistakenly include in the Bayesian universe of discourse is the worth of ZFC. ZFC is not something that has a greater or lesser probability of being true, it's one of a set of axiomatic systems capable of serving as a foundation for mathematics. Other axiomatic systems aren't more right or wrong, they are just different, in the same way that Non-Euclidian geometry isn't more right or wrong than Euclidian geomoetry.

The choice of a set of axioms is a functional one, it isn't empirical, and it isn't probabilistic. It serves both as a counter-example to EY's assumption that all things of interest are Bayesian and as a warning (along with his apparent ignorance of the definition of "ordinal") of the shallowness of his understanding.

Axiomatic systems aren't right or wrong, but they are consistent or inconsistent, and the only reason anyone chooses axioms like ZFC is the presumption that they're consistent. Personally I think the chance of inconsistency is so ridiculously low that I would normally ignore it, but really that's only based on how it works in practice, so I have a tough time saying my extremely high confidence is so fundamentally different than for the other empirical certainties we've been talking about.

And I'll second that you're wrong, most people seem satisfied with high-confidence answers. The difference between 100% and 99.999999999999% may be significant from a philosophical perspective, but when your concern is more about understanding whatever subject they pertain to, the difference in satisfaction is less than negligible. You've said you don't want to press this, but I'm not sure what other point "science as a faith" refers to any more.

It's very very peculiar that you say the above, and then say the following:



I'm not sure those are great questions as counterexamples. 'Because by the way you built it, it had to exist' for Mandelbrot, and 'It follows from the definition' for the others. Why pi is transcendental doesn't seem deep to me. If you don't accept the surface answer, then nothing will satisfy you. Same with the others.



No, Kitoba. You've rather missed the boat with this one.

Mathematical truth is the map from sets of axioms to their consequences - not a single choice of axioms. You can navigate and acquire mathematical knowledge while using a Bayesian framework (though a trivial one as almost all of the probabilities will be extremes).

If you use mathematics to model the world, you need to choose what axioms you will use. Which set of axioms fits the world best is an empirical matter.

So the concept is since that it's provably unprovable that ZFC is consistent, we'll assign some sort of probability to the idea that it's inconsistent and treat it like a statistical problem? That still seems really off to me, but let's let that go.

Assuming that's what EY actually means --and it does seem like that's the most likely way to read him --then he in this article stands as an example of what I was talking about (maybe that's why drache cited him in the first place?). He isn't satisfied with what he views as a high confidence situation, he explicitly admits that it takes faith to go beyond that, and --presumably --he's willing to make that move of faith.



I'm entirely dropping this claim. It isn't doing any philosophical work for me anyway. The new claim is that there exist some people --such as, potentially, EY --who aren't satisfied with high-confidence answers.

@drache -- wrote this post before reading yours. I have a reply, but don't have time to write it up now, will try to post it this evening.

Would you say that Euclidian geometry versus non-Euclidian geometry is an empirical problem? In the case of a specific set of figures charted, say, on a plane vs on a sphere, one set of axioms is going to match a lot better. But in terms of which is "right" or "wrong" as mathematics? It doesn't even make sense to frame the question that way.

And in the specific case of ZFC versus its chief rivals, you can derive all standard mathematics from any of them. Whether or not you include the Axiom of Choice or a different axiom is --appropriately enough --a matter of choice. You get different systems, but the differences are at an extremely high level of abstraction.

I'm not saying that one system might not map onto some specific real world measurable better than the other, but that doesn't mean the other might not also map onto something different. You're just charting out different sections of the mathematical realm, not studying material objects with sensory qualities or that are subject to laws of probability.

But let me return to my core line of argument. From the first page:



I'm not sure of whether you've quoted EY approvingly or disapprovingly, but would you agree or disagree that the following opener to his article is much the same kind of blanket statement as point 1 quoted above?



This is explicitly a statement of "faith" (as defined by the speaker), and I would further argue that it is a statement of faith in three things, not two, with the third being that everything worth believing falls within the universe of discourse governed by his other articles of faith.

Not to restart this mess again, but I've got a question.

In the above, what is the difference between faith and apathy? Many people use inductive reasoning or empirical reasoning without much thought or care as to that threshold of surety. They may behave as if the results have surety. But there is no deep philosophical attachment to such a position. The results are used because they work and they can't be arsed to worry about the difference between high probability and surety.

Your argument hinges on the idea that a non-expert is taking the results of science and assuming surety. That final step, you state, is one of faith. Not trust. Faith. But such individuals have already expressed a distinct lack of interest in the mechanisms of science. They are content to use gigahertz or better computer processors, but I doubt they've sat down and figured out which quantum mechanical operators commutate to ensure there is no excessive tunneling among the computer circuits. Nor are they versed in electronic circuit design, Maxwell's Equations or the difference between a capacitor, transistor and indcutor. They haven't bothered to understand the theory of operation behind multiprocessor operating systems, to say nothing of multiprocess/multiprocessor operating systems. Nor have they bothered to understand the mathematics behind a packet switched information network, digital to analog signal conversion or the signal processing used to transmit information over an 802.11 network. It simply works, and that's good enough. But that's not faith. That's apathy.

But for the third the promotion to faith is, again, something entirely supposed by you. It seems to me just as easy to read as his high-confidence assessment of what's worth believing, based on his experience. Which is not quite the same thing as something formally empirically testable, but definitely much more akin to it. So except for the two postulates he uses to get induction going, I can't see any indication where EY isn't satisfied with high confidence, the way you assert.


I'm not sure I understand the point of the claim. You've already told us you're one of those people, and I'm not particularly skeptical of your existence of honesty. You can probably find the occasional person who mistakenly thinks science provides that extra satisfaction, but I think you will find most people who seem that way to you are more like drachefly, who talked about super-super-super-super-super-high confidence in the language you assumed should be reserved for something beyond that.

Nothing drache (in particular) has said sounds like faith to me. The way he has presented his views is entirely consistent with the way I expect people of a scientific frame of mind to present their views. I definitely don't think everyone here is being as careful, but we've already argued that point into the ground.

So instead of doing that again, I want to sum things up. While there have definitely been parts of this conversation where I haven't acquitted myself well, I think I have established my basic, minimal, original point --with the help of some of the links cited here:

On the one hand, we have EY, who self-identifies as having faith in two points that he assesses as likely but not provable. On the other, we have Sean Carroll, who acknowledges the existence of people who he feels can legitimately be described as falling into the "mistake" of "scientism." We also have the following comment on the Carroll article:



I think these examples together demonstrate that while it may not represent either legitimate or mainstream scientific thinking, the use of science as a locus of belief and thus as a direct rival to religious faith is not just a paranoid fantasy in the minds of fundamentalists.

----------------------------------------------

@waffle My first reaction was to ask how many more times I have to concede the claim! But that's not fair, you have a legitimate point you're making. I do think it's true that the majority of people don't have a firm grasp of science and its caveats, whether from apathy or from other causes.

It may be my turn to beat a dead horse, but that's why I think it's crucial for people who are versed in science to be careful in their language when speaking to a general audience, and to not make claims that sound absolutist to the under-educated listener. If nothing else, I think it neither serves the cause of science nor promotes a better understanding of what science actually is and does. It's not fair to expect people who aren't trained scientists to understand science is really all about (extremely) safe bets if it's instead presented in the language of eternal truths.

Actually, Eliezer is under normal circumstances very satisfied with high confidence answers. He's even quite accustomed to working with low-confidence answers, reasoning under ambiguity, and all that.

What he was specifically trying to do here - at least with the first thing (I don't see why you can't just construct your way out of the second) - was to point out that though you can use induction to get you really really far, including from very very early stages of reasoning, you can't use induction to establish that induction might be something worth considering.

My biggest beef with what he was saying in the article was the value judgement of categorizing things as being "worth knowing" or not. Whether or not something is worth knowing is subjective; what is of value to one person is not to another. Perhaps it isn't worth knowing for him, and I can completely accept that, but I reject the notion that there is nothing worth knowing outside of science's ability to observe.

Again, background. I think you underestimate the reach of Bayes. It can touch on things that mere science cannot - if you do care about something beyond observation, you can still formulate arguments, and those arguments will adjust your probability distribution over explanations, etc.

It's clear that you can appear to discuss matters outside the realm of science in the language of Bayes, but it's not clear that those analyses actually mean anything. How would you construct a coherent Bayesian argument on a subject where the probabilities themselves are unknown? Do you first calculate the probability of a given probability? There's a ninety percent chance something could happen fifty percent of the time?

If you open that door, all you have to do is conceal your biases in your determination of the relative probabilities, and you'll always get whatever answer you want.

That said, I'll admit I'm no expert on Bayes. Can you actually give an example (that avoids the pitfalls above) of a coherent Bayesian analysis of a topic outside of the reach of science?

The problem here is the 'teach the controversy' crowd attempting to push their own interpretation of their religion into the classroom under the guise of an alternative explanation. Creationism, intelligent design, whatever you want to call it, is poop. And I'm lifting my general rule on nice language here to make a point. Creationism is not science. It isn't even logical thinking. It is a lie, a trojan horse deliberately designed to take advantage of the normal instinct of scientists to place caveats on their claims in order to circumvent the Constitution and institute a religious education. It is an anti-intellectual movement specifically aimed at indoctrinating children. And the supporters of Creationism and Intelligent Design are aware of it, as has been demonstrated in a court of law.

One of the horses I have been beating on lately is the nature and character of the replacement of scientific theories. All theories are confined by the observations already made. While it is possible for the Theory of Evolution to be modified or even replaced, whatever changes occur must conform to the empirical observations of evolution. I know you prefer the absolution of logical proof, but the actual odds against the observations of evolution: measurements of allele change, demonstrations of mutation rates, genetic comparisons between living species, observations of speciation, observations of new alleles arising, the fossil record, Mendel's peas and Darwin's finches, all of it; the odds of a significant portion of these observations proving inaccurate to the point where it modifies the constraints on a possible theory of evolution begger belief.

It is these observations that constrain the theory space. Any theory of evolution must contain within it an explanation of these observations of evolution. The observations are so numerous that any subsequent theory of evolution will very, very (very, very, very, very) likely reduce to the present Theory of Evolution for all areas we know that theory to work.

Again, to go to the more mathematical realm of gravity, Newton's Theory of Gravity was replaced by Einstein's General Relativity. In doing so, the orbit of Jupiter was disturbed not a whit. One of the first challenges of GR was demonstrating that it produced the exact same answers as Newton when it came to Jupiter because the orbit of Jupiter had already been measured. Jupiter's orbit serves as a constraint on any theory of gravity. Even now, as new theories of gravity are put forth to incorporate dark matter, such as Modified Newtonian Dynamics (MOND), one of the first tests is to reproduce the orbit of Jupiter.

It's actually even more exacting. GR reduces mathematically to Newton's gravity when one takes certain limits (speed of light to infinity, etc). MOND reduced mathematically to Newton's gravity when one takes the proper limits. This is a bit of a mathematical shortcut, but it serves to illustrate just what a replacement theory has to do.

This is the horse I am trying to beat. The Theory of Evolution is an empirical theory. It will be replaced by the empirical methods of science. Whatever replaces it will look exactly like the Theory of Evolution does right now.

And this is a very hard point to get across to the relatively engaged, intelligent and quite physically attractive crowd of sluggites.

Now let's go to high school. Every student is required to take an intro to science class (often folded into biology - bio gets no respect), a biology class, a chemistry class and maybe a really dull physics class (physics doesn't get interesting until the second year of college). The intro to science class is supposed to teach the above. It is supposed to teach all the caveats, the limits of empirical science and the difference between the facts of science and the truths of philosophy or religion. Most actually get this in grade school or junior high as well. We hit on it again for a final time in high school to try and drive the point home.

Once that is done, we generally don't mention it again unless it is important. This isn't being dishonest. It is no more being dishonest than not mentioning that a process may be swapped out of a kernel at any time while discussing an O(n log n) search algorithm in computer science. It is no more dishonest than failing to mention that when computing the orbit of Jupiter to very high precision, one should also toss in the effects of Mars and Saturn (at the least). Unless you're working out the orbit for NASA, it can be taken as read and just concentrate on understanding enough of two body mathematics to solve for Jupiter. Unless it bears on the problem, it is distracting to trying to understand the subject.

When we're discussing the Theory of Evolution, the Theory of Plate Tectonics, the Theory of Gravity, the Germ Theory of Disease, Quantum Field Theory or any of the other host of theories that touch on modern life, we assume we are talking to those with a high school education.

I disagree in the strongest terms with your assertion that leaving off the caveats is a disservice to science. Quite the opposite. I can demonstrate, with a painfully long list of recent articles on just how poorly understood this subject is, and how those with an ax to grind are using such dishonest tactics to attempt to replace science with their own flavor of religion. Just last week, there was a state supreme court justice who demonstrated (painfully) that he was unaware of the difference between a scientific theory and what theory means in the common vernacular. And you want more caveats and wishy washy language?

Look at the alleged controversy over global warming. This is a direct threat to the planet. And the evidence for it is about as incontrovertible as it gets. And we're actually having an argument over whether we can trust those scientists over this because they're living fat on grant money and, if you push them, they admit that they are not 100% sure with no room for doubt. Public policy is being built around using the limits of empirical science as a weapon against science.

So no, I think you are dangerously wrong here.

I think, waffle, that you and Kitoba are fighting different battles here.



Agreed. It's not science, the evidence suggests rather forcefully that it's false, it shouldn't be taught in schools. Alll agreed. But that's not the point of this thread. It's not what Kitoba's talking about.

It's clear that you've been burnt by that argument, somehow - someone, somehow, somewhere, has seriously bothered you on that front. Probably a lot of people. To the point where, when you meet an argument that looks vaguely like it might lead into the whole creationism thing, you react instinctively; you flinch away from the pain, you launch an attack on what you think the argument will be instead of on whatever is actually being talked about. (A likely result of this, incidentally, is that people trying to debate related points with you might eventually give up).

But that's not the point that Kitoba is trying to argue. Your instinctive pain reaction is preventing you from resonding to what Kitoba is actually saying.