Religion’s rules of inference

Besides defending quantum computing day and night, having drinks with Cosmic Variance‘s Sean Carroll, and being taken out to dinner at lots of restaurants with tablecloths, the other highlight of my job interview tour was meeting a friendly, interesting, articulate divinity student on the flight from San Francisco to Philadelphia, who tried to save my soul from damnation.

Here’s how it happened: the student (call him Kurt) was reading a Christian theological tract, while I, sitting next to him, was reading Russell on Religion. (This is true.) I sheepishly covered the spine of my book, trying to delay the inevitable conversation — but it finally happened, when Kurt asked me how I was liking ole’ Bert. I said I was liking him just fine, thank you very much.

Kurt then made some comment about the inadequacy of a materialistic worldview, and how, without God as the basis of morality, the whole planet would degenerate into what we saw at Virginia Tech. I replied that the prevention of suffering seemed like a pretty good basis for morality to me.

“Oh!” said Kurt. “So then suffering is bad. How do you know it’s bad?”

“How do you know it’s bad?”

“Because I believe the word of God.”

“So if God said that suffering was good, that would make it good?”

I can’t remember Kurt’s response, but I’m sure it was eloquent and well-practiced — nothing I said really tripped him up, nor did I expect it to. Wanting to change the subject, I asked him about his family, his studies, his job, what he’d been doing in the vipers’ den of San Francisco, etc. I told him a little about quantum computing and my job search. I mused that, different though we were, we both valued something in life more than money, and that alone probably set us apart from most people on the plane. Kurt said it was fitting that I’d gone to grad school at Berkeley. I replied that, as a mere Democrat, I was one of the most conservative people there.

Finally I blurted out the question I really wanted to ask. In his gentle, compassionate, way, Kurt made it clear to me that yes, I was going to roast in hell, and yes, I’d still roast in hell even if I returned to the religion of my ancestors (that, of course, being at best a beta version of the true religion). In response, I told Kurt that when I read Dante’s Inferno in freshman English, I decided that the place in the afterlife I really wanted to go was the topmost layer of hell: the place where Dante put the “righteous unbaptized” such as Euclid, Plato, and Aristotle. There, these pre-Christian luminaries could carry on an eternal intellectual conversation — cut off from God’s love to be sure, but also safe from the flames and pitchforks. How could angels and harps possibly compete with infinite tenure at Righteous Unbaptized University? If God wanted to lure me away from that, He’d probably have to throw in the Islamic martyr package.

San Francisco to Philadelphia is a five-hour flight, and the conversation ranged over everything you might expect: the age of the earth (Kurt was undecided but leaning toward 6,000 years), whether the universe needs a reason for its existence external to itself, etc. With every issue, I resolved not to use the strongest arguments at my disposal, since I was more interested in understanding my adversary’s reasoning process — and ideally, in getting him to notice inconsistencies within his own frame of reference. Alas, in that I was to be mostly disappointed.

Here’s an example. I got Kurt to admit that certain Bible passages — in particular, the ones about whipping your slaves — reflected a faulty, limited understanding of God’s will, and could only be understood in the historical context in which they were written. I then asked him how he knew that other passages — for example, the ones condemning homosexuality — didn’t also reflect a limited understanding of God’s will. He replied that, in the case of homosexuality, he didn’t need the Bible to tell him it was immoral: he knew it was immoral because it contradicted human beings’ biological nature, gay couples being unable to procreate. I then asked whether he thought that infertile straight couples should similarly be banned from getting married. Of course not, he replied, since marriage is about more than procreation — it’s also about love, bonding, and so on. I then pointed out that gay and lesbian couples also experience love and bonding. Kurt agreed that this was true, but then said the reason homosexuality was wrong went back to the Bible.

What fascinated me was that, with every single issue we discussed, we went around in a similar circle — and Kurt didn’t seem to see any problem with this, just so long as the number of 2SAT clauses that he had to resolve to get a contradiction was large enough.

In the study of rationality, there’s a well-known party game: the one where everyone throws a number from 0 to 100 into a hat, and that player wins whose number was closest to two-thirds of the average of everyone’s numbers. It’s easy to see that the only Nash equilibrium of this game — that is, the only possible outcome if everyone is rational, knows that everyone is rational, knows everyone knows everyone is rational, etc. — is for everyone to throw in 0. Why? For simplicity, consider the case of two people: one can show that I should throw in 1/2 of what I think your number will be, which is 1/2 of what you think my number will be, and so on ad infinitum until we reason ourselves down to 0.

On the other hand, how should you play if you actually want to win this game? The answer, apparently, is that you should throw in about 20. Most people, when faced with a long chain of logical inferences, will follow the chain for one or two steps and then stop. And, here as elsewhere in life, “being rational” is just a question of adjusting yourself to everyone else’s irrationalities. “Two-thirds of 50 is 33, and two-thirds of that is 22, and … OK, good enough for me!”

I’ve heard it said that the creationists are actually perfectly rational Bayesians; they just have prior probabilities that the scientifically-minded see as perverse. Inspired by conversations with Kurt and others, I hereby wish to propose a different theory of fundamentalist psychology. My theory is this: fundamentalists use a system of logical inference wherein you only have to apply the inference rules two or three times before you stop. (The exact number of inferences can vary, depending on how much you like the conclusion.) Furthermore, this system of “bounded inference” is actually the natural one from an evolutionary standpoint. It’s we — the scientists, mathematicians, and other nerdly folk — who insist on a bizzarre, unnatural system of inference, one where you have to keep turning the modus ponens crank whether you like where it’s taking you or not.

Kurt, who looked only slightly older than I am, is already married with two kids, and presumably more on the way. In strict Darwinian terms, he’s clearly been more successful than I’ve been. Are those of us who can live with A→B or B→C or C→not(A) but not all of them at once simply evolutionary oddities, like people who have twelve fingers or can’t stand sunlight?

186 Responses to “Religion’s rules of inference”

  1. Greg Kuperberg Says:

    Are those of us who can live with A→B or B→C or C→not(A)

    Which, on the other hand, is unlikely to be the way that he counts his money. I’m sure that he isn’t that stupid, when his time or money are at stake.

    This whole silly conversation proves no more than that people like him, and maybe fundamentalists in general, put intellectual loyalty over reason for hypothetical questions. The conversation was possible because neither his position nor yours much matters to you two personally.

    I think that what makes science different is the ideal of staying loyal to reason even when there is no personal need to do so. (Although there may be indirect incentives, such as peer pressure or employment.) Since you bring up evolution of humans, a few stone-age societies still exist today (e.g., in the Amazon and in New Guinea) and you can look at how they behave. If the question is planning a raid or weaving a hammock, they can be as rational as Isaac Newton. But when they are faced with questions that aren’t important (like astronomy) or problems that they know they can’t solve (like cancer), then they are deeply irrational. After all, how can you expect academic reason without literacy? Certainly writing is a post-evolutionary phenomenon.

    Maybe indirect incentives explain why ideological unreason is so irritating. You might have a career incentive to spout creationism, for instance if you are a priest (or a divinity student!). But even if it doesn’t hurt you personally to believe anti-scientific doctrines, the incentive to do so can be bad for society. I don’t blame most creationists (although a few of them are real stinkers), but creationism itself is a counterproductive, yet self-perpetuating meme.

  2. john faughnan Says:

    I advise some care in these discussions. If you did cause him to detect the flaws in his logic chain, he would likely be devastated. The joy of a crushing victory might would then be balanced by the need to sit next to someone who’s life has just fallen apart. Not to mention that you might feel a bit guilty.

    Existential crises are bad enough, but an induced existential crisis is probably worse.

    It’s fine to have theological discussions with Jesuits and the like — they enjoy the game and sophisticated theists have long explored these boundaries. I do urge caution about dangerous discourse with naive theists and fundamentalists, you probably don’t want to undo their worldview. I’m glad you didn’t use your stronger arguments.

    BTW, I think one of the stronger differences between geeks and neurotypicals is the ability to handle probability and indirection. Might be connected to your observations.

  3. Bram Cohen Says:

    Why didn’t you tell him that bert’s book was boring and uninteresting? That would easily have avoided the conversation.

    Your strongest argument probably wouldn’t have been a logical one at all, but to say that it sounds like a very unpleasant existence believing that most people are doomed to hell, and that it’s his choice to believe that, and that he could live in a much happier world if he so chose. It absolutely wouldn’t have convinced him then, but might have had an impact on his thought processes later. Probably for the better, I mean, yeesh, would you want to go through life constantly obsessed with everyone going to hell?

  4. Osias Says:

    Good morning , Scott! I liked this post. I wonder what if the guy read this post.

    He’ll probaly cite as an impious piece on some preaching.

  5. Ran Says:

    Nice post, I enjoyed reading it. The experience is indeed familiar.

    @faughnan – People’s world view don’t fall apart so easily, cognitive dissonance and similar biases make sure we remain blissfully ignorant. :)

  6. Robin Hanson Says:

    Maybe the difference between people is just how long a contradictory chain needs to be so they cannot see the contradiction. Then we would each elaborate justifications for what we want to believe until we reached the point where we could no longer see the contradictions. People with longer chains would then shake their heads at the irrational speck in the eyes of those with shorter chains, not realizing the irrational log in their own eyes.

  7. Craig Says:

    I can think of a billion muslims who would consider the religion of your ancestors to be an alpha version of the true religion.

  8. roland Says:

    >Maybe the difference between people is just how long a >contradictory chain needs to be so they cannot see the >contradiction.

    that line of thought is not very deep itself.

  9. Scott Says:

    Robin: After thinking about your proposed modification for a few minutes, I can’t find anything wrong with it, and will therefore add it to my worldview. :-)

  10. John Sidles Says:

    A useful resource in theological discussions is Wittgenstein’s notion of “aspect blindness”, which is discussed in his Philosophical Investigations.

    Modern cognitive science has established compelling physiological mechanisms that generate aspect blindness. Furthermore, be aware that academic specialists are by no means immune to this phenomenon. Indeed, academia is particularly susceptible to it.

    To experience aspect blindness yourself, merely ask, what are the most common aspects of the human condition to which quantum information theorists are commonly aspect-blind?

    That is to say, not just ignorant, but cognitively challenged to think about?

  11. ChristopherH Says:

    If there’s a high enough error rate per inference, then a restriction to short arguments (I visualize it as a small “consistency horizon”) might have greater expected utility for most humans than a willingness to consider longer arguments, even if the latter make fewer assumptions.

    If I hear two contradictory arguments:
    1) { A -> C, B -> C, my mom told me A and B } |- C
    2) { A -> C, C -> D, D -> (E | F), E -> ~D, F -> ~C } |- ~C

    Unless I (or my genes, if we’re speaking evolutionarily) have the utmost confidence in the accuracy and precision of my reasoning, I may be better off choosing C than ~C.*

    The “Kurt” error (not taking things to their logical conclusion) may have fewer detrimental effects on average than the, um, “Crank” error (assembling convoluted chains of reasoning full of holes and believing them to be ironclad).

    As a scientist or a mathematician or a computer scientist, you develop the skills to make and verify long precise arguments, and establish trust in your own reasoning abilities and those of your colleagues. But most people have understandably limited ability to distinguish rigorous argument from sophistry, and they’re going to experience many more sophistries than proofs in their day-to-day lives.

    Possible conclusion: It’s imperative to first teach critical thinking, bringing enough people up to basic single-step logical literacy (contrapositive, Bayes rule, etc.) before unleashing proofs reductio ad absurdum. Otherwise, you risk replacing the errors of local reasoning (excess certainty in locally-plausible beliefs) with worse ones (dire certainty in completely implausible beliefs due to faulty reasoning, escalating casual unreason to anti-reason backlash).

    * Ironically, I proved my point by making an error in the first draft of formula 2. :-/

  12. Greg Kuperberg Says:

    Maybe the difference between people is just how long a contradictory chain needs to be so they cannot see the contradiction.

    Again, there is a difference between “cannot see the contradiction” and “don’t care to consider the contradiction”. I refuse to believe that a fundamentalist like the one that Scott met is an imbecile. It would be too easy to steal money from him if he really can’t sustain a logical chain of length 3.

    In fact, such imbeciles exist, and they really are legally defrauded in a variety of ways. And I can see that charismatic fundamentalists, such as Pat Robertson, enjoy preaching to them, because it is highly profitable. But I remain skeptical that this divinity student that Scott met is one of them. Maybe on occassion he is that stupid — I would suppose that his irrational ideology does infect his real reasoning skills from time to time — but not all or even most of the time.

    Really a doctrine such as creationism more reflects a lack of respect for scientific reason than it does a lack of logic skills. After all, there was the creationist who got a PhD in dinosaur biology, for perfectly good work. Most creationists don’t even quite disrespect scientists; they just respect their own religious circle a lot more. If it were a question of money or medical treatment, then I guarantee you that 90% of creationists would easily attain a basic grasp of evolution.

  13. Scott Says:

    Thanks to Sean Seefried for correcting an error in my game theory example (5/6 → 1/2)

  14. ChristopherH Says:

    Slightly less convoluted summary: Given Kurt’s limited critical thinking ability, it was unconsciously wise of him to discount your arguments. If he’d accepted your (presumably sound and helpful) arguments, he’d be at risk of accepting other (presumably unsound and harmful) arguments, because he can’t tell the difference. Therefore, to convince Kurt, you first have to increase his confidence in his own intellectual authority and the trustworthiness of his mental processes. Only then can he trust himself to engage with your argument.

  15. Scott Says:

    Greg, I completely agree that people follow chains of inference further when they have a personal stake in the outcome. Indeed, one could even argue that the key insight needed to get science off the ground was that the same reasoning processes used to drive wildebeests off a cliff, detect a cheating mate, etc., can also be used to study the nature of the celestial bodies and the origin of the universe. You just have to act like it matters to you!

  16. Greg Kuperberg Says:

    I completely agree that people follow chains of inference further when they have a personal stake in the outcome.

    A couple of further thoughts on this theme:

    1) As Robin Hanson emphasizes, obviously we are all finite computers and can only sustain a chain of logic that is so long. The real problem is not the the numerical length of the chain, but having a good sense of when a particular chain of inference is reliable. That is when the game gets hard. It is a skill that is amenable to training, and belief in illogical things interferes with that training. The typical creationist may largely just be playing stupid out of loyalty; but most such people wouldn’t make good cardiologists.

    2) Nonetheless even scientists abandon their critical thinking skills from time to time out of emotionalism or loyalty. So Robin Hanson is also right that our chortles are somewhat hypocritical.

    One time I was at lunch at a conference on quantum algebra, and one of the attendees was afraid of the corn tortillas. He was from Germany, and his concern was that since the corn was American, it was probably genetically modified. He wasn’t just taking a theoretical political stand against genetic modification of food; he was actually worried that the food on his plate was going to hurt him. He had made no calculation of relative risks, nor did he know which foods had undergone what genetic modifications. He had been warned about corn, so corn was the problem. Tellingly, he also said that he didn’t enjoy discussing the issue.

  17. James Cook Says:

    If it were a question of money or medical treatment, then I guarantee you that 90% of creationists would easily attain a basic grasp of evolution.

    Indeed, there’s the example of the oil company executive who readily understood and accepted the scientific ages of rocks in the ground for professional purposes, despite believing in his personal life that the earth is 6,000 years old.

    Cases such as this suggest that, even among the lay public, religious fundamentalism involves more than just the inadeqaucies of people’s intellectual training. (Not that improving the latter wouldn’t still be a worthy goal in its own right.)

  18. Michael Says:

    Beautiful. And I now know what a ‘Shtetl’ is.

  19. rrtucci Says:

    Osias said “Good morning , Scott! I liked this post. I wonder what if the guy read this post.…He’ll probaly cite as an impious piece on some preaching.”

    Well, Osias, Kurt too has a blog, except one with a much larger readership. He calls it a sunday sermon. His reaction to Scott’s exalted logic was the following:

    And then the devil (well, okay, a short underling called Scott, Son of Aaron) took me to a great height (30 thousand feet to be precise). And then he tempted me with his exalted logic by saying that if I were really a son of God, I could jump off this mountain, for surely the angels would save me…

  20. Shaun Apple Says:

    Brilliant read!

  21. arakyd Says:

    I think that what makes science different is the ideal of staying loyal to reason even when there is no personal need to do so.

    Not only that, but the belief that the mind can say anything meaningful about things that are claimed to be divine revelation. Not reason, not science, the mind. That is the argument I get from my family (immediate, extended, and all college educated). The mind does not even apply. Most fundie apologists would not admit that, but their logic parsing is no better than this divinity student’s (in fact, it’s probably where he got his arguments from).

    There are lots of cases where people will be rational and empirical when the situation calls for it, regardless of how irrational they may be in other areas of life, but people also willingly die for religious beliefs to which they don’t believe the concept of “contradiction” even applies. I think arguments from bounded rationality (and maybe even minimal rationality) go a long way, but I’m afraid that if you pointed out that some of these arguments essentially boil down to A→B and B→C and C→not(A), many divinity students (at least those in the set of divinity students who lean towards a 6,000 year old earth) would eventually trot out some version of “reason does not apply.”

  22. mtraven Says:

    This is a very interesting discussion but misses the larger point, which is that faith is deliberately designed to be illogical, and the more illogical it is the better. Your flightmate may or may not be consciously aware of this, but you can be pretty sure that within his brain, the faith agents were all too happy to subvert the logic agents, because that’s part of their job.

    I’ve just been rereading Isaiah Berlin’s essay on Joseph de Maistre, who exemplified the religious mind’s opposition to reason. In this worldview, reason is not merely a weak tool but an extremely dangerous one that is constantly threatening to subvert the natural God-given order, which reason cannot grasp.

    Pacal Boyer’s work on the cognitive anthropology of religion takes a similar view. Religious ideas are counter-intuitive at their roots. That’s why we call them supernatural. They seem to have survival value despite their manifest illogicalities and falsehoods.

  23. James Andrix Says:

    So how do you know suffering is bad?

    How far do you follow that logic?

  24. Greg Kuperberg Says:

    This is a very interesting discussion but misses the larger point, which is that faith is deliberately designed to be illogical, and the more illogical it is the better.

    Except that major religions aren’t designed, they are evolved memes. But otherwise you are partly correct, in the sense that those elements of a religion that have scientific backing drift out of the definition of that religion. For example, the Bible posits that Judea had a king named Herod. Since this is also established history, it is not counted as an article of Christian faith.

  25. Dani Fong Says:

    ChristopherH,

    I think that the utility of bounding rationality is mostly not in improving prediction, but rather in reducing the cost of computation. Many people just can’t handle thinking things all the way through. It makes their head hurt.

    By the way, is this the same ChristopherH from TopCoder?

  26. Tim Says:

    Fascinatingly obvious points. I find it quite interesting how otherwise erudite blogs on rather esoteric topics (cf. Geoff Arnold’s at http://geoffarnold.com/ ) always need to pile on Christians by insulting their intellectual rigor or capacity just to shore up their own insecurities. What is it to you?

    I’m curious because the types of straw men – the Rortyesque notion of progressivism ethically succeeding with a quasi-transcendent idea of evil as suffering or rolling up evolutionary theories of natural history and experimentally provable genetic adaptation mechanisms as being epistemically equivalent – are so often cited with only high level and abstract argumentation. It is playing for a crowd – not arguing or establishing anything. Ironically, not unlike Pat Robertson’s practice- just the mirror for a different community. You take it as obvious that the areas you are arguing are true, yet you need to state the weaknesses of others reasoning about them instead of reasoning yourself – it is a sign of the very thing you criticize.

    While you may be attempting to layout the point of “Religion’s Rules of Inference,” I will speak of a different point you’ve made at the same time by your actions. People that are immersed in very hard problems of naturalistic science, computation, or complex systems – be it Quantum Computing, Evolutionary Biology, or (my own field) Artificial Intelligence and Natural Language Understanding – can tend to mistake their aptitude and/or rigor in that domain to be easily transferable to another domain with minimal effort. These people are already looking for a similarly structured argument with equal complexity to those areas they are comfortable with. Once they find it, they like the structure and difficulty of it and associate that with truth – rarely questioning the real premises or presuppositions of those arguments. They are captivated by structure and the almost Gnostic power of knowing the truth against the assumptions of the masses. It is a secular form of anointing.

    I’d call this the “Narcissism of Intellectual Transference” – i.e. if I’m smart enough to understand this difficult area through rigorous study, I can (with far less work) understand and deal with an area I presume to be vacuous. Those that disagree are either less intelligent or less rigorous, I just have to develop sufficient argumentation to dispose of or confuse those that challenge my premise. I say this not in judgment but as someone who appreciates the temptation here.

    Theology was at one time in the not too distant past known as the “Queen of the Sciences” because it promised to unify and explain underlying symmetries of reasoning and presuppositions between disparate systems and nomenclature – a grand proposition if ever there was one. It was a substantial reason that we named Universities as such (rather than Di-versities). In the present, this role has been supplanted (to a large degree) by theoretical physics and analytic philosophy with inklings of unification in information theory. The project has not succeeded – which does not disprove it, but may justify revisiting the real justification behind jettisoning the notion of Theology as unifier. The problem is that unification of discourse and reasoning through these newer approaches doesn’t carry the same implications for living as one through Theology. The very notion of a Theological unification (the worldview that your friend, “Kurt” was grasping at) implies obligations that most would like to avoid. This tension is actually at the heart of the worldview of the Theology he was working out – an ironic resonance.
    Perhaps it is not a shallowness of inference, but a more rigorous approach to question those premises that dispensed with historical consensus without providing a well grounded objection – just a well formed on?

    There is nothing brilliant in this “point” you’ve made. It is lazy sniping if you ask me. If you want to be praised for brilliance, then lay out a real argument. If it is cut and pasted from Dawkins, Dennett, Russell, or Martin, some of us will know. Your intelligence and capacity in your field is a given – or else I (and many others here) wouldn’t be subscribers. Beyond that field, however, your arguments need justification before grandstanding lest it be treated as mere opinion and begin to undermine credibility elsewhere.

  27. sigfpe Says:

    It most certainly is not about being able to make long chains of inferences. Ordinary people do this all the time and would be severely handicapped if they couldn’t.

    I just think of the ordinary things I have to do in my day that require long inference chains: the freeway has melted down (80 to 580 nr. SF Bay Bridge) from SF to the East Bay, therefore there are going to be traffic detours, and that will make the journey less pleasant, but everyone else knows the freeway has melted too, so they’ll all infer that there will be detours that make the journey unpleasant, therefore fewer people will drive to work, therefore there’ll be fewer cars making this journey each day. But any car that goes into work must come back again. The meltdown affects only the return journey. Therefore the reduced amount of traffic means the journey to work will become easier. (That’s just a sketch of the full argument, I don’t have all day…)

    I bet you that 90% of fundamentalists can understand this chain of reasoning, including the detour into epistemic logic, without any problem.

  28. Kurt Says:

    I certainly hope his name wasn’t really Kurt.

    Bram Cohen said: Why didn’t you tell him that bert’s book was boring and uninteresting? That would easily have avoided the conversation.

    Keeping in mind that a good offense is often the best defense, I would have suggested starting up a conversation about biting vaginas.

  29. roland Says:

    >Are those of us who can live with A→B or B→C or C→not(A) (…)

    Isn’t A→B or B→C a tautology already ?

  30. Domenic Denicola Says:

    “the student (call him Kurt) was reading a Christian theological tract, while I, sitting next to him, was reading Russell on Religion.”

    When I saw that, I knew we were in for a good blog post—and you didn’t disappoint :-D.

    Oooh, and the comments!

  31. Anonymous Says:

    “So if God said that suffering was good, that would make it good?”

    Perhaps if you assumed God said that you’d arrive at a contradiction. You might only end up proving that God wouldn’t say that.

  32. Dmitry Says:

    By the way, do you really like Russel’s writings on religion? I have once read his book “Why I Am Not A Christian?” — and I must admit that it seemed very stupid to me. It was a long time ago and I don’t remember any details at all, I just remember my overall impression (and it’s consistent with what I know about Russel in general).

    I’m not a religious person at all (physics graduate student actually), but the famous anti-religion books (like those by Russel and Dawkins) usually seem very annoying and silly to me.

    We all know how many great scientists were religious, and it’s also clear that one can be a believer without actually believeing in Young Earth and all other crazy take-the-Bible-literally things.

  33. Robin Hanson Says:

    I agree that in addition to variance in how long a claim chain we can check for contradiction, there is also variance in how long a chain we want to check. We find it easier to see when others are averting their eyes from their own contradictions, and harder to see when we are doing this ourselves. We like to remember the occasions when others were doing so and we were not, and we forget or never noticed the occasions when we were more guilty.

  34. Dmitry Says:

    Oh, I somehow managed to misspell Russell three times in a row.

  35. chutzpan Says:

    Dmitry said: We all know how many great scientists were religious.

    Do we really? And would you really say it’s a significant ratio?
    Relgious people love to say how religious some great scientists were just because they used the word “God” etc. I would really like to know, however, how many such great scientists are actually religious.

    Keep in mind that if you’re going to include the boys from way back in the day, most of them only played religious so as to avoid getting ignored/exiled/killed. It used to be real tough to publish a physics text without calling it a study of God’s work.

  36. Greg Kuperberg Says:

    I’m not a religious person at all (physics graduate student actually), but the famous anti-religion books (like those by Russell and Dawkins) usually seem very annoying and silly to me.

    I sort-of agree. These books have some interesting zingers, but somehow they seem over-argued. Although I like Natalie Angier’s essay on this subject. I really like Stephen Weinberg’s quote in this essay, “Most scientists I know don’t care enough about religion even to call themselves atheists.” That is certainly where I am most of the time. The problem, as Angier points out, is that monotheism is all over the place, even on American currency. So how do you keep it from seeping into your life without ever addressing it? It’s like George Lakoff’s joke, “Don’t Think of an Elephant!”

    I attended grade school in a fairly religious area (Alabama). Certainly then, some of the other children were quite smug about the fact that their society had made Christianity the social default. In order to be an honest atheist, you had to ask for an exception from time to time, but then even asking would acknowledge Christianity and undermine the atheist position. (I.e., “If God isn’t important, why do you make such a big deal of His nonexistence?”) Although I admit that it was also partly a problem of my own making, just that I liked to argue too much.

  37. Greg Kuperberg Says:

    We find it easier to see when others are averting their eyes from their own contradictions, and harder to see when we are doing this ourselves.

    Yes, I agree, although it is easy to make too many relativist concessions. There is a real difference between Liberty University and UC Berkeley. I will grant that Berkeley society goes overboard in questions of doctrine; hypocrisy can be a problem there. But it is just not the same thing as the Liberty University approach, which is intolerant, anti-reason, and pseudo-intellectual from square one. The choice is not symmetrical.

  38. Matt S. Says:

    It can be lots of fun to shred the religious freaks with a simple argument, to devastate them with logic. But in such situations I am always reminded of the quote, and I do not remember who said it, but it is roughly, “You can’t reason someone out of a position they were not reasoned into.”

    In other words, logic will not work on them, it is like trying to use a wooden chisel to dismantle a brick wall. Good luck with that.

  39. Dmitry Says:

    chutzpan, no, I’m not saying that it’s a significant ratio (the number of religoius famous scientists). I don’t know what this ratio is, and I actually don’t care a lot. What I do care, is the following observation: the wiser a man is — the less odds are that he calls himself an atheist.
    You ask: “I would really like to know, however, how many such great scientists are actually religious” — well, that depends on the definition, doesn’t it?
    If by “religious” you mean going to some churh, praying in the prescribed manner et cetera, than probably very few are (if any). But my idea is the opposite: one can refuse to be called an atheist, believe in _something_, probably something very vague, and he can also be called “religious” in a way.
    Take Einstein. “I believe in Spinoza’s God, who reveals Himself in the lawful harmony of the world, not in a God Who concerns Himself with the fate and the doings of mankind.” By his own definition, Einstein was a deeply religious person. That’s what I mean.

  40. Robin Hanson Says:

    Greg, no doubt do tolerate contradictions more than others. But don’t assume it is easy to tell if your group is worse or better than average.

  41. Miguel Says:

    Greg Kuperberg said: I think that what makes science different is the ideal of staying loyal to reason even when there is no personal need to do so.

    There’s no such an ideal in proper science, because science is a practice that rests on the acievements of shared and accumulated knowledge and experience. The personal interests of scientists and weaved in a complex manner with that of science, in as complex a way as science in mixed up with social (and thus political) interests in a grander way, just on a different level.

  42. Greg Kuperberg Says:

    By his own definition, Einstein was a deeply religious person.

    Eventually he was, with qualifications. But the Einstein of 1940 was a very different person from the Einstein of 1905. For one thing, he was doing a lot less research. It’s hard to say what the Einstein of 1905 believed, because he was then a lot closer to Weinberg’s description of scientists.

    In any case, as of 1998, only 7% of NAS members believe in God.

    But don’t assume it is easy to tell if your group is worse or better than average.

    Sometimes it is and sometimes it isn’t. If your church casts out vipers, you don’t have to be Einstein to notice that something is wrong.

  43. Scott Says:

    Tim, I don’t think you can accuse me of criticizing a straw man — he was sitting next to me on the plane, and was definitely flesh-and-blood. And he’s the one who started the conversation. Would it have been more respectful of his beliefs not to engage them?

    I’ll readily concede that nothing I said in the post (including my theory of fundamentalist psychology) was terribly original. Then again, nothing you said in your comment was terribly original either. This is an argument that’s been going on for 3000 years… :-)

  44. Ryan Boughter Says:

    Thank you for a truly refreshing read. After the weeks upon weeks of Reddit/Digg submissions saying the same old, tired argument (ATHEISTS are RIGHT, CHRISTIANS are WRONG and if you think otherwise I’m gonna call you names like uneducated, stupid, childish, blind, incompetent, etc.), it was nice to read a well written, heartwarming exchange of ideas that still got the message across. Thanks for being respectful, even if we do believe in different things. Why can’t this be the tone for the Atheist/Religious dialogue in the future – if only more people (from both sides) had the compassion and understanding that you showed here.

  45. Dmitry Says:

    Scott, sorry, but why are the comments not enumerated here? You are using WordPress, and it’s a standart feauture there… Can be very useful, when discussing this thread with my friend over icq to have a possibility to say: “but look at number 21, dude!”
    Just a suggestion.

  46. Scott Says:

    Dmitry, not only was nothing I said even vaguely critical of Einsteinian religion, but I’ve always been happy to call myself religious in an Einsteinian sense.

    Certainly it’s possible to be a religious person without believing in young-earth creationism and all the other indefensible things. But does that entitle us to ignore the fact that, in the year 2007, billions of people do believe the indefensible things?

  47. Scott Says:

    Oh, and good suggestion, Dmitry! I just looked through the WordPress Dashboard and didn’t see any option for numbered comments — anyone know how to do that?

  48. viulian Says:

    When using logical thinking, a statement cannot be both true and false at the same time.
    However, you can both love and hate a person at the same time and feel really frustrated about it.

    Logic has some limits when explaining how people feel.

    While I admire logic and use it intensively (engineer) however, using any logical arguments will only prove that Kurt’s definition of God is not valid. But you won’t disprove God’s existence.
    Can someone prove that we are not living in a computer simulation ? That the fine tuned laws of physics aren’t some final static constants in a computer program ?
    Whatever answer you choose is the right answer – it’s mysticism from where the logic ends.

  49. Scott Says:

    Thanks so much, Ryan! I’m really glad there’s at least one believer who liked my post.

  50. Tim Says:

    Fair enough. I wasn’t there and can’t speak to the degree of accuracy with which you represent his views or his own culpability in inciting the argument.

    My major point is that there is a more charitable way of understanding what he was saying than to assume he can only make three inferential steps and gives up. Instead, you played to the crowd (and one has gathered here) by simply insulting him and others by implication. That’s your prerogative – its your blog after all - but it was not deserving of much credit (unlike your other technical writings).

    I think the reason that some Christians have such a suspicion of science is because they’ve been demonized by scientists (or similar types) on poor grounds and they (unfortunately) return that skepticism in kind. After all, “if he thinks like this in one area of life, how can I trust what he claims in other areas?” This is a little early-Augustine in terms of an approach to truth, but thats the sentiment. It only divides us further.

    It is not any measure of “fundamentalist psychology” anymore than sufficient peer reviewed citations would be a “scientistic psychology” in terms of accepting some things on authority. That notion is vacuous. It is all about what authority you accept for answering certain questions and that definition would include a definition of conditions and qualities of that authority. My 2 cents.

  51. Scott Says:

    Whatever answer you choose is the right answer – it’s mysticism from where the logic ends.

    I find that comment both insightful and uninsightful. ;-)

  52. Dmitry Says:

    Scott, [after some investigations I realised that] all you need to do is to delete “list-style: none” string in the “.commentlist li” style in your CSS file.

  53. frd Says:

    John Faughnan – I’d rather have them whimpering in the corner scared out of their wits at the randomness and scary reality of the universe than polluting other people’s (including their and other people’s kids) with a practice that in effect says “we are too mentally weak to face reality so you must believe in some fantasy that will give you a mental crutch to make you feel better”. Idiotic fantasists deserve to be devastated – then possibly they may be in a position to be helped to become real functioning people. Existential crises are to be encouraged, looked at squarely and just plain got over!

  54. Tim Says:

    Thanks so much, Ryan! I’m really glad there’s at least one believer who liked my post.

    Yes.. thats a first – a Christian who takes the point of intellectual laziness being an accidental enhancement of fitness (in the Darwinian sense) as a compliment. Ryan, you may want to reread the post.

  55. Scott Says:

    Dmitry: Done!

    (I found a different way to do it, by editing comments.php.)

  56. viulian Says:

    :)

    About the premise: “Fundamentalists use a system of logical inference wherein you only have to apply the inference rules two or three times before you stop.”

    I think it is true if let’s say this one is true: “Any person uses a system of logical inference wherein you only have to apply the inference rules two or three times before he/she stops given a situation where the person has no desire to know more that it already knows.”

    If someone already admitted (mystically) the that God exists and Bible is God’s word, why waste energy to justify owns belief in a logical way for scientists to examine thoroughly ?

  57. Dmitry Says:

    Great! Though I think that my solution gives a nicer result :) You can give it a try.

    Returning to the point: I absolutely agree with you. What I basically wanted to say is that one has to be very careful when fighting with incredible religious superstitions. Religion in the wide sense is something completely different.
    By the way, I’m still curious about if you really appreciate Russell’s writings on religion (and actually not only on religion).

  58. fl Says:

    “the scientists, mathematicians, and other nerdly folk — who insist on a bizzarre, unnatural system of inference”

    I have lately been thinking something similar. If “turning the logical crank” were important to our species in its evolution, we’d all be doing it. But what we see around us is a world where a profound analysis is not necessary to people. What ~does~ work for people is to “keep doing what they are doing” — and even defend it — until something compels them to do otherwise. And logic will not be that compulsion for most folks.

  59. Osias Says:

    Hmmm, I don’t think the guy himself have a bounded chain of inferences of 2 or 3. I think the people he use to preach or even better the people he is being trained to preach to have the “short horizon”. He was “practising” to preach with Scott. Only this time Scott had no short horizon, but most people most times have.

    The guy himself probably doesn’t botter to reason at all, he have faith.

  60. Scott Says:

    Dmitry: Yes, I’ve learned a great deal from reading Russell — but probably more about the construction of English sentences than about his ostensible topics! In my opinion, the only reason Russell isn’t venerated the way that (say) Heidegger or Wittgenstein are is that Russell made the tremendous mistake of being clear.

  61. Joseph Hertzlinger Says:

    You can think of religious traditions as the accumulated experience of a community. Sometimes part of an early version of that experience didn’t work out and a tradition is abandoned but still remains in the holy books. In that case, it makes sense for the community to ignore the tradition. It still makes sense for the community to adhere to a “fundamentalist” attitude towards those traditions that did turn out to be important.

    The really odd part of the conversation on the plane is that Kurt regarded slavery as something to be explained away instead of as part of the justification for fundamentalism. The story of the Exodus is obviously about the rescue of a people from the horribly unjust system of slavery. For millennia, it was reinterpreted in Judaism and Christianity to be about a special case with no lessons for any other situation. (After all, everybody knew that slavery was a necessary part of the economy.) Since the reinterpretation started before the Bible was closed, the justification of slavery got into it.

    A few centuries ago, a handful of evangelical Protestants (which is embarrassing to those of us in other religions) went for a more literal approach and declared that slavery could not be tolerated. This actually worked. Slavery turned out not to be necessary after all.

  62. Michael Brazier Says:

    From your account of Kurt, Scott, I don’t see any evidence that his powers of inference were defective; he never said anything (that you reported) which is inconsistent. The trouble was, rather, that in his social world the authority of the Bible is automatically granted by everybody, so any appeal to that authority wins an argument. Kurt simply forgot that you don’t regard the Bible as an authority. You yourself are not free of this fault — I have seen you appeal to “a consensus of scientists” as an authority, to shut off an argument you didn’t want to deal with. How many things do you believe, not because you have tested the inferences leading to them, but because everyone you respect assures you they are true?

    (For the evolutionary pyschologists here, trusting the judgement of your neighbors, on a question you can’t answer for yourself, will usually give good results — which is why we humans are prone to do so.)

    Also, “preventing suffering is good” is true, but it doesn’t work as the sole basis of a system of morals. For it’s clear that anything which is dead does not suffer, and therefore the easiest way to keep a thing from suffering is to kill it. If preventing suffering is good, and the only good, we are obliged to kill all living things to ensure they cannot suffer … a conclusion that most people would reject.

  63. Tim Says:

    Yes, I’ve learned a great deal from reading Russell — but probably more about the construction of English sentences than about his ostensible topics! In my opinion, the only reason Russell isn’t venerated the way that (say) Heidegger or Wittgenstein are is that Russell made the tremendous mistake of being clear.

    Also, Russell was consistently inconsistent and out of his league relative to Wittgenstein (even basically admitted to this at certain times). Heidegger. I’m not even going to go there.

    Wittgenstein understood core components of Godel’s Incompleteness theorem long before it was written. Russell was still trying to establish a system of types with so many qualifications that it danced around Frege’s issues, but at the expense of leaving the logicist enterprise completely hollow. In the end, Russell was a failure in his mission and rounded out his career as far more polemicist than intellectual. The esteem we give him in the Comp Sci world is far more applicable to Frege than Russell. It should be asked with conviction, “Why do we need to even go through Principia when we have Frege and Wittgenstein to get to Godel, Church and Turing?”

    Russell – enamored with structure at the expense of meaning.

  64. Scott Says:

    Michael: The trouble is that, before Kurt invoked the Bible as an argument-ending authority, he had previously conceded that it can’t be so invoked — in particular, with regard to the passages about slavery. That’s the inconsistency that I was talking about.

    Yes, if we’re going to take the prevention of suffering as a basis for morality, then clearly we need to define our “suffering function” carefully — for example, by defining dying when you wanted to live to be a form of “suffering.” My point was just that “because God said so” doesn’t work any better than that as a moral theory, even if we assume God really did say so. For we then have to ask the questions that would occur to any 10-year-old: “Why is it moral to do something just because God told us to? What if God had told us to do the opposite; would that make it moral?”

  65. g Says:

    I don’t think there’s anything specific to fundamentalism, or to religion, in Kurt’s cognitive limitation. It’s just that most people who are neither exceptionally bright nor trained in heavy thinking have shallower mental stacks than you have. I expect the phenomenon is more common among fundamentalists than among non-fundamentalists, because fundamentalists are a bit less often exceptionally bright or trained in heavy thinking, but that’s equally true of lots of other groups besides fundamentalists.

    So it’s not about “religion’s rules of inference”, it’s about “average people’s rules of inference”.

  66. Michael Says:

    I’m not sure we ought to be surprised or bemused when religious fundamentalists fail to think in a rigorous or systematic way. Their minds are conditioned by a profoundly different culture. I think the fact that their speech and outward mannerisms are similar to ours tricks into thinking they’re more like us culturally than they actually are. Their style of thinking is “poetic” rather than rational, I’ve observed.

  67. Scott Says:

    Wittgenstein understood core components of Godel’s Incompleteness theorem long before it was written.

    Tim: It’s ironic that you should say that; my reading is that Wittgenstein failed to understand Gödel’s theorem even at the most basic technical level. (In particular, he doesn’t seem to have understood how the Gödel sentence has a purely syntactic definition, separate from its semantic interpretation of “This sentence is unprovable.”)

    Incidentally, Wittgenstein also denounced Cantorian set theory as a “cancerous growth” in mathematics with no possible applications to anything. From today’s perspective, all he succeeded in showing here was his limited imagination. (2Aleph_0 cheers for diagonalization!)

    Russell never really understood Gödel’s theorem either, but at least he understood Cantor’s work, and (along with Frege, Peano, Whitehead, etc.) provided the launching pad for Gödel.

  68. Ghaith Says:

    My point was just that “because God said so” doesn’t work any better than that as a moral theory, even if we assume God really did say so. For we then have to ask the questions that would occur to any 10-year-old: “Why is it moral to do something just because God told us to? What if God had told us to do the opposite; would that make it moral?”

    But isn’t that part of the definition of God. Under the assumption that God exists, then he knows all possible paths and can easily infer which path (moral theory) yields the best for the largest number of people. The fact that a God (again by definition) has an infinite amount of computational power gives him the right (/ability) to define the best or the correct solution for any given problem.

  69. Chui Says:

    Religions are dime-a-dozen. There are always people who claim to be the new prophets. Scott’s nailed it on the head when he wrote: “In strict Darwinian terms, he’s clearly been more successful than I’ve been”. After all, there’s a good chance Kurt’s achieved stable replacement numbers for Christians.

    Fundamentally, successful religions are memes which propagate well. A religion’s success has nothing to do with Truth, but how well it adapts to thrive in the human society.

    Inclusiveness is a great meme. Christianity was a form of Judaism where one can go to heaven – even if one is not born a Jew. Mahayana Buddhism flourished over Theravada Buddhism, because it opens up salvation to many. Rewarding procreation is another good meme … examples in the old testament, Muslim men being allowed 4 wives. Evangelism is another. Memes with the idea of holy war – Jihad, Crusades spread well.

  70. Scott Says:

    Ghaith, if we defined God to be the hypothetical suffering-minimization-übercomputer of the universe, then I’d certainly agree with you: doing something “because God said so” would be equivalent to doing it because it minimized suffering. But I don’t know if even many religious believers would assent to that definition of God.

    If we’re instead talking about the biblical God, then I’d make the following three points:
    (1) Whether the biblical precepts come from God — as opposed to being cobbled together by King Josiah’s scribes 2600 years ago — is (to put it mildly) the very question at issue.
    (2) From today’s standpoint, the bible’s moral precepts do in fact leave an enormous amount to be desired — I trust you can come up with your own examples here.
    (3) If disagreeing with the Divine Will was good enough for Moses and Abraham, then it’s good enough for me. :-)

  71. Joseph Hertzlinger Says:

    Inclusiveness is a great meme. Christianity was a form of Judaism where one can go to heaven – even if one is not born a Jew.

    I didn’t know that differed from Judaism.

  72. Tim Says:

    It’s ironic that you should say that; my reading is that Wittgenstein failed to understand Gödel’s theorem even at the most basic technical level. (In particular, he doesn’t seem to have understood how the Gödel sentence has a purely syntactic definition, separate from its semantic interpretation of “This sentence is unprovable.”)

    Yes – it is ironic that he would have such an aversion to some of it when the implications (at least in the “New Wittgenstein” school that I would sponsor) overlap. His Intuitionist leanings do create some difficulties in this area. The true outstrips the provable in a formal proof – and this makes nonsense so valuable. I think he resisted the implication that this could be shown in a formal system – as Rebecca Goldstein suggests – and that is a source of his tension. To show it takes the riddle and makes it an inference.

    In any case, it wasn’t my intention to move too much into a tangent on Wittgenstein (though I welcome the opportunity). My core issues remain unaddressed. Though I suppose that is intentional at this point…

  73. Sam Says:

    Tim, of all the great things that have been said about Wittgenstein, why on earth would you choose his understanding of Godel’s theorems as the example of his brilliance? Wittgenstein’s understanding of Godel’s theorems was pathetic, as was indeed all his understanding of any logic post-Russell. You can read Monk’s excellent biography for examples of prominent logicians, some of them old students of Wittgenstein, who can attest to this fact.

    Apart from the mundane fact that Wittgenstein failed to understand what Godel had proved, there’s an additional irony in trying to heap praise on him through that route: Godel’s theorems are antithetical to everything Wittgenstein ever wrote. Both his early and late philosophy ends in the conviction that syntax is semantics, precisely the idea that Godel set out to demolish (indeed indirectly motivated to do so by Wittgenstein’s early writings, which were taken as gospel by the Vienna circle Godel disagreed with so vehemently.)

    Someone ought to propose a variant of Goodwin’s law for Godel’s theorem. It always pops up eventually, though rarely (a mild understatement) used correctly.

    PS. Godel believed in God.

  74. Scott Says:

    The true outstrips the provable in a formal proof – and this makes nonsense so valuable.

    Tim, the above sentence captures the essence of our disagreement so well that I don’t know if there’s anything more for me to say. :-)

  75. Greg Kuperberg Says:

    All right, Tim, since you want someone to address your core issue:

    My major point is that there is a more charitable way of understanding what he was saying than to assume he can only make three inferential steps and gives up.

    The actual claim is not that he can only make three inferential steps, but that he is only interested in three inferential steps (if that many) in questions of religious doctrine. I can’t think of a particularly charitable explanation. I’m skeptical that he shuns extended logic because scientists have dissed his beliefs. Even if that were the explanation, it wouldn’t be all that charitable.

    On the other hand I do see two even less charitable explanations of Scott’s main example. One is that he is prejudiced against homosexuals and doesn’t much care if his defense of his prejudice is either learned or logical. The other is that he is an example of the peculiar American fusion of Christianity and Republican politics, as documented in the movie Jesus Camp.

  76. Scott Says:

    Christianity was a form of Judaism where one can go to heaven – even if one is not born a Jew.
    I didn’t know that differed from Judaism.

    Right, the usual teaching is that “the righteous of all nations have a place in the world to come.” Furthermore, you don’t have to convert to Judaism to be considered “righteous” (though you’re allowed to if you want); you just have to obey the seven “Noahide Laws”:

    (1) No idolatry.
    (2) No murder.
    (3) No theft.
    (4) No adultery.
    (5) No blasphemy.
    (6) No eating the flesh of a living animal.
    (7) Set up a government to enforce the above six laws.

    So, Gentile readers: I know the leg of that living sheep looks mighty tasty, but is slicing it off really worth your immortal soul? :-)

  77. Ze Says:

    The true outstrips the provable in a formal proof – and this makes nonsense so valuable.

    Tim, the above sentence captures the essence of our disagreement so well that I don’t know if there’s anything more for me to say.
    Just because we can’t prove something is true (or we haven’t proved that it is true) doesn’t make it useless , we use statements that we believe to be true all the time, as long as we make reasonable assumptions it isn’t a problem. I’m sure I don’t need point out all the complexity results in CS (purely because you are so much better in this area than I) that we don’t believe to be true because they imply P=NP or some other we find unlikely.

    I’m not defending relgion though , I’m actually an agnostic. I admit I don’t know (however I find it unlikely that currrent religions have got it right).

    It’s all in the assumptions you make and how reasonable the argument it is for them. Science would progress much more slowly if we had to prove things absolutely rather than build a web of evidence around it. In some areas it would stagnate.

  78. Scott Says:

    Err, there’s a big difference between nonsense and things we believe are true but can’t prove!

  79. Michael Brazier Says:

    Scott: “The trouble is that, before Kurt invoked the Bible as an argument-ending authority, he had previously conceded that it can’t be so invoked”

    No, not as you reported it. What Kurt conceded was that correctly interpreting what the Bible actually means requires knowledge of the context in which it was written; so, for instance, the rules about treatment of slaves are in the Bible because when those passages were written slavery existed and nobody could imagine how society would work without it, and not because God requires us to keep slaves. (For a Christian, at least, this principle is licenced by Jesus’ statement that the Jews were permitted divorce, not because God wishes us to divorce, but because the Jews were not ready to obey the ideal law of marriage. I hope the parallel is clear.) Once the meaning of a passage has been discovered, Kurt would say (be logically bound to say) that it is authoritative. (And if you did look into the context in which the Bible’s passages against homosexuality were written, you wouldn’t find the parallel with divorce or slavery that would make your argument to Kurt go through.)

    Kurt would, in short, be quite consistent to admit that, in general, the prima facie meaning of any passage in the Bible may not be the true one, while maintaining that the specific passages condemning sodomy do genuinely mean what they appear to mean. It doesn’t follow that, because the meaning of a command is obscure, we’re not obliged to obey it.

    “Yes, if we’re going to take the prevention of suffering as a basis for morality, then clearly we need to define our “suffering function” carefully — for example, by defining dying when you wanted to live to be a form of “suffering.” ”

    And if you do that the word “suffering” merely becomes a synonym for “evil”, and the statement “preventing suffering is good” means nothing more than “not-not-good is good”. The real content in your moral system would start with listing the forms of evil/suffering, and all you’d gain by the initial “axiom” is an opportunity to confuse yourself or your audience with an ill-chosen jargon.

    “My point was just that “because God said so” doesn’t work any better than that as a moral theory, even if we assume God really did say so. For we then have to ask the questions that would occur to any 10-year-old: “Why is it moral to do something just because God told us to? What if God had told us to do the opposite; would that make it moral?””

    The answer to that is, the “because” in “We are to do X because God says so” is not causal, but epistemic. As a parallel, if I say “P != NP because Scott Aaronson says so”, I don’t mean you have chosen to make P != NP and I must submit to your will. I mean, rather, that you know more about P and NP than I do, and your saying P != NP is good evidence that it’s true. God tells us to do something because it is right, and would be right even if He hadn’t said it; but, because He has said so, we know it’s true.

  80. Greg Kuperberg Says:

    And I thought that noahide was a kind of synthetic leather! (Oh wait, that’s naugahyde.)

  81. Sam Says:

    Tim, I didn’t read your reply to Scott before posting. Sorry about that. Nevertheless, I will maintain that to say that Wittgenstein understood anything profound about Godel’s theorems, before or after having read them, is wildly misleading.

    Godel’s theorems are formal results, applicable to formal systems. If you find it helpful to invoke them in order to describe something vaguely analogous that you read into Wittgenstein’s writings, fine, but don’t claim that this entails an understanding of Godel’s theorems. Especially not when such an analogy is dubious at best (I haven’t heard anyone else describe the implications of Godel’s theorems as “making nonsense valuable”).

    And please forgive me, but much of the “new Wittgenstein” school is just bullshit, an obvious example of academics with too much time on their hands. Wittgenstein even states plainly in FI that he wrote the damn thing because it had become obvious to him that the Tractatus was wrong. New Wittgensteinians are, in my not very humble opinion, simply those who cannot accept that Wittgenstein’s writings are just plain contradictory, and don’t always make sense. Wittgenstein didn’t shy away from contradictions, but to modern analytic philosophers contradictions are embarrassments that must be explained away (except perhaps to proponents of paraconsistent logics, like Graham Priest, but I think we can safely ignore such fringe elements), even if it means assuming that everything Wittgenstein ever wrote was “ironic”, a descriptin he most likely would have loathed.

  82. Greg Kuperberg Says:

    No, not as you reported it.

    Yes, as Scott reported it. His fellow traveller first said that he didn’t need the Bible to tell him that homosexuality is immoral. But then he invoked the Bible to distinguish between homosexuality and infertile marriage.

    At least he didn’t say, “God made Adam and Eve, not Adam and Steve!” I’m not completely sure why, but that common phrasing of the real position is even more obnoxious, even though it is technically logical.

  83. Greg Kuperberg Says:

    Wittgenstein didn’t shy away from contradictions

    But it seems that most mathematicians shy away from Wittgenstein. In all of the math that I have learned, taught, or discovered, I have frequently invoked Cantor and Dedekind; Godel is important too. But I have never needed Wittgenstein. Wittgenstein isn’t even important enough to refute.

  84. Scott Says:

    At least he didn’t say, “God made Adam and Eve, not Adam and Steve!”

    Predictably, googling “Adam and Steve” brings up a gay dating service, gay comic book, gay movie…

  85. Sam Says:

    Greg, Wittgenstein was not a mathematician and never proved any theorems, so I’m not sure how mathematicians would come in contact with him, unless they had a side interest in philosophy. I’m also not sure how you refute a mathematician.

    Why do I suddenly feel like I’m defending Wittgenstein when I’ve just spent two long posts attacking him?

  86. John Sidles Says:

    Greg Kuperberg says: But it seems that most mathematicians shy away from Wittgenstein. In all of the math that I have learned, taught, or discovered, I have frequently invoked Cantor and Dedekind; Godel is important too. But I have never needed Wittgenstein. Wittgenstein isn’t even important enough to refute.

    Remarkable, Greg … you must one of the few mathematicians who has used the word “tautology”, or written out a “truth table” — both were invented by Wittgenstein. :)

    (And just to remark, Wittgenstein occupies a prominent place upon my list of intellectually notable engineers … his training was in mechanical and aeronautical engineering). :):)

  87. Greg Kuperberg Says:

    You must one of the few mathematicians who has used the word “tautology”, or written out a “truth table” — both were invented by Wittgenstein.

    Well, he invented the words. I did not know this and I will give him credit for that much. That is not the same as inventing the ideas, however.

    Wittgenstein was not a mathematician

    Sure, that was sort-of my point. He did however do philosophy of mathematics, which some people confuse with actual mathematics.

    Predictably, googling “Adam and Steve” brings up a gay dating service

    Not to stereotype gays, but I think that their community as a whole has been admirably adept at detoxifying vile slogans and symbols. Their use of “Adam and Steve” is actually a pretty small victory compared to the pink triangles. You have made the point that Jews can even laugh at the Nazis; the gay community has been even better at this game than the Jews.

  88. anonymous Says:

    Wow, this post has a lot of comments. Knowing the way comment threads usually work, I’d say Greg Kuperberg’s last comment about gayness and nazis is just the sort of change of subject that can double the length of a thread even if it’s starting to fade… maybe this thread will be a record-breaker for this blog.

  89. Frank Says:

    Have any of you read C. S. Lewis on Christianity? If so, do you consider his perspective interesting in a thought provoking way?

  90. Scott Says:

    anonymous: Nah, I doubt this comment thread is going to break any records — at least not without arguments about Israel, global warming, D-Wave, NP⊄BQP, abolishing STOC and FOCS, or Notepad as world’s best text editor….

  91. Scott Says:

    Frank: I loved the Narnia books as a kid (knowing full well what they were getting at); I think they brought me closer than anything else to understanding the Christian worldview. I also read Mere Christianity, but found it somewhat less interesting.

  92. Gaal Yahas Says:

    You might enjoy a wonderful essay by Peter Suber called “Logical Rudeness” that explores an interesting aspect of how people render themselves impervious to argument.

  93. Michael Brazier Says:

    Greg, I know of three distinct ways to prove the Earth is spherical. I only need one of them; but if I gave you one and you weren’t convinced, would I contradict myself by giving you the other two as well? That’s what Kurt did.

  94. Jonathan Shewchuk Says:

    I can’t let this thread end without pointing out that Ken Wilber wrote a book called Quantum Questions about the “fact that virtually every one of the great pioneers of modern physics—men like Einstein and Schrödinger and Heisenberg—were spiritual mystics of one sort or another, an altogether extraordinary situation.” [Wilber's words.] He also cites and quotes de Broglie, Planck, Bohr, Pauli, and Eddington.

    Mind you, I don’t think many of these gentlemen believed in an anthropomorphic God, fond of city-smiting and locust plagues. Rather, I think most of them believed in an all-pervading Spirit, which Einstein held up against “a kind of optical delusion of…consciousness” that man “experiences himself, his thoughts and feelings as something separated from the rest.”

    I haven’t read the book yet (except excerpts). But I figure Scott might want to know about its existence.

  95. John Sidles Says:

    You must one of the few mathematicians who has [not] used the word “tautology”, or written out a “truth table” — both were invented by Wittgenstein.

    Well, he invented the words. I did not know this and I will give him credit for that much. That is not the same as inventing the ideas, however.

    ——–

    Greg, it is true that the seminal ideas of “tautology” and “truth table” were invented independently by several people (as is common in mathematics and science, and even in art).

    To Wittgenstein also goes the credit for originating a much deeper and far more “modern” idea: the idea of a language game. This powerful concept gave rise to entire branches of mathematics, linguistics, and cognitive science, and it furthermore was extremely influential in the subsequent development of philosophy and the arts.

    For this reason Wittgenstein arguably exerted a greater creative influence than any other modern philosopher on the subsequent development of mathematics and science.

    It is true that Wittgenstein himself did not foresee all the implications of viewing language as a game … even today we are still very far from understanding these implications. :)

  96. Michael Gogins Says:

    Regarding john faughnan Says:
    Comment #2, posted on May 13th, 2007 at 02:52

    >I advise some care in these discussions. If you did cause him to >detect the flaws in his logic chain, he would likely be devastated. >The joy of a crushing victory might would then be balanced by
    >the need to sit next to someone who’s life has just fallen apart.
    >Not to mention that you might feel a bit guilty.

    I think this is highly condescending. The truth is good enough for John, but too good for Kurt. Even if it’s ironic, it’s condescending.

  97. John Sidles Says:

    >I advise some care in these discussions. If you did cause him to >detect the flaws in his logic chain, he would likely be devastated.

    True. Medical students are taught: “Never take away a patient’s illusions unless you can offer them a better illusion.” And it is far from clear that the comforting illusions of mathematical logic are superior to those of organized religion!

    What’s that you say? You believe that “Mathematical logic is devoid of comforting illusions” ? What about the widespread illusion—widespread among graduate students anyway, and also commonly believed by professors who construct problem sets :) —that any true proposition that has a one-page proof, can be proved by a graduate student?

    Pursuing this question leads straight to the intersection of information theory, cognitive science, economics, game theory, strong AI, moral philosophy, and sociology—which is a very interesting intersection, IMHO!

  98. Greg Kuperberg Says:

    The truth is good enough for John, but too good for Kurt.

    If he is a young-Earth creationist, then that does suggest that the truth is too good for him. I’m not sure where you go from there, other than a flat Earth. Speaking of which…

    Greg, I know of three distinct ways to prove the Earth is spherical. I only need one of them; but if I gave you one and you weren’t convinced, would I contradict myself by giving you the other two as well?

    In Scott’s account, after saying that he didn’t need the Bible to know that homosexuality is immoral, “Kurt” instead offered a callous double standard that shouldn’t convince anybody. Namely, the standard argument that homosexuals can’t procreate. Scott pointed out that that argument doesn’t work, which is why “Kurt” backed up and needed the Bible after all. Yes, that is a self-contradiction.

  99. Greg Kuperberg Says:

    Ken Wilber wrote a book called Quantum Questions about the “fact that virtually every one of the great pioneers of modern physics—men like Einstein and Schrödinger and Heisenberg—were spiritual mystics of one sort or another, an altogether extraordinary situation.” [Wilber’s words.] He also cites and quotes de Broglie, Planck, Bohr, Pauli, and Eddington.

    Regardless of who he quotes, his thesis that quantum mechanics is a mystical theory is a misrepresentation. It may have been somewhat fashionable to wax mystical about quantum mechanics in the 1920s and 1930s, but these days most people who really understand it don’t bother.

    And, as you might expect, Wilber’s portrayal of “the great pioneers” is selective. Feynman is an obvious counterexample. If Feynman is outside of the implicit historical window of Wilber’s book, he also skips Dirac, who once said: “I cannot understand why we idle discussing religion. If we are honest – and as scientists honesty is our precise duty – we cannot help but admit that any religion is a pack of false statements, deprived of any real foundation. The very idea of God is a product of human imagination.”

  100. » More on optimal versus equilibrium Says:

    [...] I ran across an example at Shtetl-Optimized In the study of rationality, there’s a well-known party game: the one where everyone throws a number from 0 to 100 into a hat, and that player wins whose number was closest to two-thirds of the average of everyone’s numbers. It’s easy to see that the only Nash equilibrium of this game — that is, the only possible outcome if everyone is rational, knows that everyone is rational, knows everyone knows everyone is rational, etc. — is for everyone to throw in 0. Why? For simplicity, consider the case of two people: one can show that I should throw in 1/2 of what I think your number will be, which is 1/2 of what you think my number will be, and so on ad infinitum until we reason ourselves down to 0.On the other hand, how should you play if you actually want to win this game? The answer, apparently, is that you should throw in about 20. Most people, when faced with a long chain of logical inferences, will follow the chain for one or two steps and then stop. And, here as elsewhere in life, “being rational” is just a question of adjusting yourself to everyone else’s irrationalities. “Two-thirds of 50 is 33, and two-thirds of that is 22, and … OK, good enough for me!” Posted by Gary Carson on Monday, May 14th, 2007 [...]

  101. E. Mouse Says:

    Scott, nice post. Any ideas as to whether or not your proof-theoretic characterization of fundamentalist truth has a corresponding semantic characterization?

  102. wolfgang Says:

    Scott,

    sorry, I am too late and probably somebody has mentioned it already in the 100+ comments above:

    > On the other hand, how should you play if you actually want to win this game? The answer, apparently, is that you should throw in about 20.

    But once it is *common knowledge* that people are irrational and one should choose 20, then it becomes rational to do so!
    And perhaps all the others do not end their chain of thought but just follow your meta-argument…

    And perhaps something similar happened with religion. Once you know that the majority is irrational and that life may be more difficult for an atheist than necessary, it becomes rational to declare yourself as religious too. And Einstein might have just found the perfect solution: “I believe in Spinoza’s God.” This keeps the journalists happy (he believes in God) and it also made sense to his scientist collegues.

  103. Niel Says:

    John Sidles wrote:
    What’s that you say? You believe that “Mathematical logic is devoid of comforting illusions” ? What about the widespread illusion—widespread among graduate students anyway, and also commonly believed by professors who construct problem sets :) —that any true proposition that has a one-page proof, can be proved by a graduate student?

    John, it may have been a while since you were a graduate student, but I find that this attitude is not widespread amoung grad students of my acquaintance. Although I admit the reason for this is perhaps due to ample empirical evidence provided by professors, some of whom may very well believe it.

  104. Scott Says:

    Wolfgang: In the case of the numbers game, if you know everyone else is throwing in 20, then you shouldn’t throw in 20 — you should throw in 13.

    In the case of religion, if you know everyone else believes irrational things and don’t want them to burn you at the stake … well, welcome to the human condition for most of recorded history!

  105. wolfgang Says:

    > then you shouldn’t throw in 20
    yes indeed. stupid me!
    I guess I should have said, it is *currently* rational to throw in 20 and monitor how this progresses, as more and more people learn that they should throw in 20…
    But my main point remains, that people might chose a number > 0 because they assume that others are irrational.

    The “Spinoza’s God” answer also works well for specified time and place only. It would have backfired e.g. in the Soviet Union.

  106. Scott Says:

    But my main point remains, that people might chose a number > 0 because they assume that others are irrational.

    Right!  That was part of what I wanted to illustrate with this example.

  107. wolfgang Says:

    By the way (inspired by the title of your blog) here is an optimization problem for your readers who know more about theology than I do:
    i) we know that there is more than one religion, with different believes and practises.
    ii) Obviously it would be dangerous to believe in one, if it turns out that the other is correct.
    iii) but it seems to me that there is a lot of compatibility: e.g. catholic believe is probably compatible with praying three times per day in the direction of Mecca and also the rules of kosher food. Also I do not think it is a sin to be buried with a coin on your tongue and it should be ok to build a pyramid in your garden, while practizing your daily Zen meditation.
    iv) so the question would be: what is the optimal combination of rituals and believes to maximize the probablility of a comfortable life after death and at the same time minimize the number of rebirths, before reaching Nirvana…

  108. John Sidles Says:

    John Sidles wrote: What’s that you say? You believe that “Mathematical logic is devoid of comforting illusions” ? What about the widespread illusion—widespread among graduate students anyway, and also commonly believed by professors who construct problem sets :) —that any true proposition that has a one-page proof, can be proved by a graduate student?

    Niel responds: John, it may have been a while since you were a graduate student, but I find that this attitude is not widespread among grad students of my acquaintance. Although I admit the reason for this is perhaps due to ample empirical evidence provided by professors, some of whom may very well believe it.:)

    Sincerely, that is very interesting, Neil. My experience is that engineering graduate students believe that the problems that arise “naturally” in engineering can be solved in almost all cases, even though formally they are NP-hard.

    Perhaps this heuristic principle is also true in mathematics?

  109. Joe Fitzsimons Says:

    John: I think students tend to assume they would only be set problems that a reasonably diligent student could answer.

  110. Tyler DiPietro Says:

    “Are those of us who can live with A→B or B→C or C→not(A) but not all of them at once simply evolutionary oddities, like people who have twelve fingers or can’t stand sunlight?”

    I don’t know if I would call it an evolutionary oddity in the genetic sense, but in the memetic/cultural evolutionary sense it certainly is an oddity. In that sense it’s much like meticulously ridding our food of harmful microbes (by cooking it thoroughly). Not natural, but we’ve collectively decided despite the apparent natural propensity against it that it is a better idea.

  111. Scott Says:

    so the question would be: what is the optimal combination of rituals and believes to maximize the probablility of a comfortable life after death

    Wolfgang: Alas, there’s more than one religion (Catholicism, Islam…) that demands exclusive acceptance of its claims to get to heaven, so you won’t be able to get around making a choice at some point.

    I think your idea would work better with Buddhism, Hinduism, Jainism, Shinto, and Confucianism, which seem to go better in combination with each other than the Western monotheisms.

  112. cody Says:

    “It doesn’t follow that, because the meaning of a command is obscure, we’re not obliged to obey it.” -Michael Brazier
    whoa, really? so if we just had one law that said, ‘dont do wrong’, and then we went around and arrested anyone we deemed to be ‘wrong’, itd be their fault for not obeying? isnt the clarity of the command integral to our ability to follow it?
    really i dont think these lesser arguments over Wittgenstein and whether or not engineering students understand what ‘intractable’ means are all that worrisome compared to the number of people who think that some supernatural mind is the only reason not to pillage thy neighbor. the pope didnt forgive Galileo for more than 350 years. they cut out Giordano Bruno’s tongue as a sign of mercy when they burned him at the stake. why are these offenses so quickly forgotten?

    also, all these arguments about religious scientists are misrepresentative of the problems with fundamentalists. of the spectrum of religious beliefs, it is not common to find a young earth creationist in any advanced field of science. so the definitions of ‘religion’ and ‘god’ that antitheists like myself are often concerned with are the personal god and the religions that follow ‘him’, not the more abstract ideas which (in my view) are less severely damaging to the wellbeing of humankind.

  113. wolfgang Says:

    Scott,

    > exclusive acceptance of its claims
    I did not say it would be easy 8-)

    But it seems that one can be a Jesuit priest and Zen teacher and I dont see why a follower of the Jesuit Zen combination cannot face Mecca while praying and be buried with a coin on his tongue etc.
    This should improve the odds. I am not claiming that one can easily find the global maximum…

    This would also be interesting for the evolutionary perspective: A religion which can be easily combined with another one, should have higher probability to survive???

  114. Tim Says:

    Especially not when such an analogy is dubious at best (I haven’t heard anyone else describe the implications of Godel’s theorems as “making nonsense valuable”).

    And please forgive me, but much of the “new Wittgenstein” school is just bullshit, an obvious example of academics with too much time on their hands. Wittgenstein even states plainly in FI that he wrote the damn thing because it had become obvious to him that the Tractatus was wrong. New Wittgensteinians are, in my not very humble opinion, simply those who cannot accept that Wittgenstein’s writings are just plain contradictory, and don’t always make sense.

    Well, I think this is the root of the disagreement on Wittgenstein. I’m not saying anything about what Wittgenstein thought of Godel or his theorem – you’ve outlined that just fine. My point was about the difference between those things that can be made meaningful by symbol manipulation (i.e. nothing) and those things that can be “discovered” through it. If you have read Wittgenstein’s notebooks, you can see the shift away from any notion of syntactic manipulation yielding truth/meaning (instead this comes from “outside” – but that is a paradox given the system of the Tractatus). This was the logicist project of Frege, Russell and others and once he ran through it and hit a wall, a FINAL wall, he saw it as pointless and walked away to find it elsewhere.

    The only read that I can get out of it is that it was a deliberate “riddle” that ends up on similar ground as Godel – but not showing it through a formal proof but through a more informal Reductio. I can’t take credit for anything here (the Godel part is something I see, but the rest is what I came to agree with the New Wittgensteinians about). I didn’t come to it lightly. I had a traditional Wittgensteinian teacher (with all of the Hacking, Kripke, and Kenny, etc.) but also had the privilege of doing some work with Cora Diamond. Her views seemed a lot more convincing and lined up with the biographical elements in the Notebooks and “Culture and Value” that seemed to be overlooked. In addition, the “nonsense” reference is quite specific and ties back into what Frege’s influence passed to Wittgenstein and some of the New Wittgensteinians have written on (Cora in particular). Taking it as literal nonsense (as some did on the thread) was amusing.

    I can appreciate your differences, but having worked with the people, I can say they are far more rigorous than you have given them credit for.

    The difference between Godel and Wittgenstein is most fundamentally a difference between Platonic and a quasi-pheonological basis of meaning. In important ways, they were both realists and objective about meaning. So, yes, Godel believed in God, but to my knowledge I think he also believed in the reality of the Forms (of sorts). I’m not taking Wittgenstein’s side in this – that whole area is a tangent that you all got on. I’m somewhat sympathetic to Godel on a lot of this more so than Wittgenstein – accepting his naturalistic approach to derive meaning vs. Godel’s formal method.

    My real point was about how both ran into the problem of formal manipulation not yielding a complete notion of truth. With the idolization of inferential procedure as some badge of honor – the very point of the original post – I wanted to point out that two very different and respectable parties agreed on the notion that no amount of symbol manipulation would yield sufficient meaning or truth to justify the true statements of the system.

    To put it much more bluntly – it is more important to consider the coherence of the steps toward things that seem obviously true (preconditions of intelligibility) than it is to build longer and longer chains. If someone walks into a contradiction or into complete arbitrariness, then the coherence is degraded and the web of belief screams of inconsistency.

    For a Christian, once that web is well grounded in something like the interpretation of Scripture – which is not as trivial as to take small, disjoint sections and play “quiz master” about – it counts with presumption against alternative theories.

    For it to be dislodged, something with greater explanative power must be proposed and found sufficient in the most key areas of testing. In many ways, this is the Correspondence Theory for world views. “Kurt” is grounded in his and little Scott stated to him (or in these posts) would shake that. It’s not a mark of irrationality or stupidity. It could just be that he is looking for consistency in far more dimensions than Scott or many of the commenters here.

    This just a way of stating ideas like those that Plantiga and other Reformed Epistomologist thinkers would claim – a point that is rather sound in my opinion. More aggressive postures (Presuppositionalists) would actually put the onus on the nonbeliever. In either case, there are effective epistemologies that do not originate from human autonomy and observational limits. Since Godel and Wittgenstein helped us see the wall of those limits, I used them to make this point for some measure of defense of Kurt – in absentia. He may only need three steps to show enough gaps to make him uninterested in the alternative world view alluded to in the post. That speaks nothing to his ability any more than dropping a hot iron after holding it 3 seconds instead of 20 seconds doesn’t speak to the tolerance of pain. Sometimes it doesn’t take that much to figure out: “Don’t do that.”

    PS- I’ve got the Monk book. Though I don’t think I’ve reread it in 8-9 years. It might account for me being a little rusty. :-)

    PPS – H/T to John Sidles for solid counters to the LW slights. I particularly liked the citation of Language Games- a highly overlooked area outside of Philosophy. Indeed, quite a seminal idea for linguistics, belief revision, agent systems, and numerous other areas. It has a special place in my heart given what my company does. :-)

  115. Anonymous Says:

    This thread finishes at Comment #87 by Godwin’s law.

  116. Chui Says:

    I didn’t know about the “Noahide Laws”. I stand corrected.

    However, I contend that the idea of the chosen people itself is exclusive rather than inclusive, and Judaism is not the blockbuster meme that is of Christianity, as Christianity is more inclusive (i.e. no second class people).

    As always, some exclusion is necessary for a meme to propagate. The idea of an “inherited virtue” gilds a meme so well that parents loath the idea of interracial marriage, because it dilutes their language, way of life, culture, religion et. c.

  117. Scott Says:

    However, I contend that the idea of the chosen people itself is exclusive rather than inclusive, and Judaism is not the blockbuster meme that is of Christianity

    Yeah, it’s only sold 14 million tickets, compared to Christianity’s 2.1 billion. :-) I’ve heard it argued that one can classify religious memes into (a) the ones like Hinduism and Judaism, which historically said “go do your thing and leave us alone to do ours,” and (b) the ones like Christianity and Islam, which historically said “do our thing or face the sword.”

  118. milkshake Says:

    there is a special circle of Hell, for those who tempt divinity school students

  119. anonymous Says:

    “I cannot understand why we idle discussing religion. If we are honest – and as scientists honesty is our precise duty – we cannot help but admit that any religion is a pack of false statements, deprived of any real foundation. The very idea of God is a product of human imagination.”

    The irony being that, if we take evolutionary theory at face value, then human brains (mind, reasoning, logic) evolved, strictly speaking, for its survival value, not for its truth value.

    The other irony being that the Western concept and ideology of “truth(s)” took a Judeo-Christian (and Hellenic) ideological and intellectual background(s) to evolve. No other cultures–despite having greater technological, intellectual, and economic power than most of Europe until the Enlightenment–broke the threshold into a scientific worldview as Europe did until long after the success of (read: the survival power of) that kind of worldview.

    The religion of Cultural Imperialism works in mysterious and miraculous ways.

  120. Michael Brazier Says:

    cody: “whoa, really? so if we just had one law that said, ‘dont do wrong’, and then we went around and arrested anyone we deemed to be ‘wrong’, itd be their fault for not obeying?”

    The statement “don’t do what is wrong” is not obscure — it’s so general that it carries very little meaning, but what it means is quite obvious. In the other direction, the works of Wittgenstein are obscure, but they aren’t meaningless on that account. Indeed, the density of meaning in them is one of the reasons they are difficult to understand.

    “This thread finishes at Comment #87 by Godwin’s law.”

    No, no, Godwin’s Law says comparing a poster to the Nazis ends a thread — talking about them is not enough …

  121. BlueNight Says:

    Y’know, as a rationalist fundamentalist Christian with Asperger’s, I get very lonely.

    The only conversations i’m really satisfied by are knock-down intellectual fights, where everything is at stake. My fellow Christians, even the smart ones, aren’t willing to do that. Most atheists, neopagans, and agnostics aren’t, either.

    Nobody else wants to swim in a boundless sea of pure logic. Not the “proving your point to someone” type of logic, either. That’s peeing in the pool — using logic to aid rhetoric. Sheer exploration of derivation and implication, analysis of root principles.

    I’ve discovered why that is. I’ve posted the answer on my blogs. But nobody reads my blogs.

    There are three types of people. Each has a realm of intuition, in which they feel most comfortable.

    For most men, it’s the Physical. For most women, it’s the Emotional.

    The intersection of the two is what I call the Animal. It’s survival-minded, sexual, beastial, gutteral, fearful and angry, waiting to pounce, waiting to be pounced upon. It’s sheer us vs them in a battle to the death.

    For me, it’s the Logical. It has no such concerns. It is only interested in ideas and their interactions.

    And God is the only other person I’ve ever met who’s willing to discuss these things with me.

  122. BlueNight Says:

    BTW, if you define Atheism as a religion (and most don’t), then it’s the most exclusive religion. It says nobody goes to heaven not even us, no matter what you believe.

    Anything multiplied by zero is zero.

  123. Anonymous Says:

    >No, no, Godwin’s Law says comparing a poster to the Nazis ends a thread — talking about them is not enough …

    According to my personal interpretation of Wikipedia’s definition of the law: “As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches one” the preconditions for Godwin law hold unless you call in the “Quirk’s Exception”.

    Of course I always stop reasoning after two syllogism.

  124. Mark Says:

    Tim said:

    “it is more important to consider the coherence of the steps toward things that seem obviously true (preconditions of intelligibility) than it is to build longer and longer chains.”

    I really don’t understand what you mean by ‘coherent’ in this sentence. Clearly, the people advocating “longer and longer chains” have their own requirement of “coherence”, which they would define simply as logical consistency and soundness. Are you using the word to mean that the system of believe should cohere in an intuitive sense?

    Anyway, whatever your definition of coherent, I don’t see how this excuses the young earth creationist with the PhD in paleontology. You’ve made some very interesting points about the limits of rational empiricism. I think you were trying to show why one might choose to use an epistemological framework _other_ than rational empiricism, though your prose is so dense I can hardly tell. After all, we cannot empirically answer the question “Why is there something instead of nothing”, and this question is worth considering.

    But when it comes to people who claim that the earth is 6000 years old while being experts on dinosaurs or petrology, or when it comes to people who have (coincidentally!) come to well-reasoned arguments about why the bible says exactly what the rest of their fundamentalist community expects it to say, I don’t think there is much room for discussions of coherence.

    I think what we have here is people grappling with deep questions (why is there something instead of nothing, what happens when I die, why am I conscious instead of unconscious) and getting fooled into accepting a lot of metaphysically-irrelevant medieval nonsense (gays will burn in hell, the earth is 6000 years old and god put carbon 14 in the rocks to test our faith) along their way to the deep answers.

  125. Jonathan Shewchuk Says:

    Greg, it is not Wilber’s thesis that quantum mechanics is a mystical theory. On the contrary, Wilber spills quite a bit of ink showing that the same physicists who had mystical beliefs were also adamant that modern physics does not support a religious worldview (including their own views). He writes, “They were mystics, not because of physics, but in spite of physics.”

    As an atheist, I appreciate the Dirac quote. But despite my beliefs, I still think it’s interesting that so many of the big early names in quantum physics believed in something inaccessible to physics.

  126. wolfgang Says:

    > God is the only other person I’ve ever met who’s willing to discuss these things with me.

    The next time you talk to her, can you please ask about the Higgs particle, its mass etc.
    And then please let us know what the answer was…

  127. RM Says:

    In reference to #99 (Greg), Wilbur’s thesis is most emphatically *not* “that quantum mechanics is a mystical theory”. He is very explicit in the introduction that neither he nor any of the scientists cited belived that QM is a mystical theory. He rants a bit about New Agers and others who claim it is, but laments that such people are unlikely to read his book anyway, so he is unlikely to be able to change their minds. I checked out the book initially because I have a morbid fascination with books that misrepresent QM for philosophical or spiritual purposes; I bought it because the intro made it clear that Wilbur is aware of this problem and is very upfront about disavowing such conclusions.

    Wilbur’s intrest is in the fact that, nevertheless, each of the scientists included in the collection was a mystic of some sort, for a variety of philosophical reasons having nothing to do with deriving mysticism from QM. From what I remember, he presents this largely as “isn’t this interesting!”. He is certainly not trying to claim that scientists are obligated to be mystics, but perhaps is saying that scientists should be open to the idea that not all flavors of mysticism are incompatible with being a scientist.

  128. The Dark Side « Blogorrhea Says:

    [...] Posted by RubeRad on May 15th, 2007 If you are at all interested in apologetics, you will be interested in reading this post from an atheist, who describes being witnessed to by a seminarian (apparently a presuppositionalist). If you thought that was a good read, you might also want to read this one. [...]

  129. Walt Says:

    Shorter Tim: Thanks to Wittgenstein, we now know that hating gays is a higher truth, one that transcends axiomatic systems.

  130. Greg Kuperberg Says:

    Greg, it is not Wilber’s thesis that quantum mechanics is a mystical theory.

    I concede the point; I had not skimmed Wilber’s book very carefully. I gave it a closer look now and you are right. Whether or not I agree with Wilber, he is at least a fairly sober guy.

    But I still think that his thesis is artificial. I have met a lot of physicists by now (I just went to a great lecture by Seiberg yesterday); and, as a group, they are really the least mystical people that I know. If there is any real mysticism left, Wilber is correct in saying that it is “despite” their physics. In order to have an interesting book, he had to have selection bias. Among the physicists that he picked, some of them (like Einstein, in later years) were genuinely interested in mysticism, while some of them may only have referred to mysticism because they were interested in popular writing. He has a quote from James Jeans, in particular, which reads a lot like Dirac.

  131. Greg Kuperberg Says:

    According to my personal interpretation of Wikipedia’s definition of the law: “As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches one” the preconditions for Godwin law hold unless you call in the “Quirk’s Exception”.

    Except that I didn’t make any direct comparison between anyone and Nazis. I relied on the fact that gays have been persecuted by both Nazis and by American conservatives, which is completely true, but I didn’t make or intend a simile. In fact, a small fraction of American gay-haters are neo-Nazis; but in the main they are more like Scott’s friend “Kurt”. I can only suppose that “Kurt” would be anti-Nazi. Nonetheless, he supports unfair treatment of gays with regard to marriage rights, and probably other rights as well.

    My sole point about the Nazis is that there is a cultural tradition in the American gay community of taking the hate out of hateful slogans and symbols. E.g., the once-notorious pink triangle and the erstwhile-aggravating slogan “Adam and Steve”. (Or at least in part of the gay community, which is of course not a monolith.)

  132. roland Says:

    >Are those of us who can live with A→B or B→C or C→not(A) (…)

    Isn’t A→B or B→C a tautology already ?

    i said this already but i nobody answered.

  133. Scott Says:

    Sheesh, yes, A→B or B→C is obviously a tautology. On the other hand,

    A→B and B→C and C→not(A)

    is a contradiction. What I meant was that I can live with any two of the above clauses but not all three of them.

  134. Anonymous Says:

    xkcd. Mea culpa.

    On the other hand what about this scenario: imagine a parallel universe where God supposedly handed His words to Prophets and Messiahs as a consistent mathematical theory but without a proof for its completeness. I bet that in the other universe the other Scott will debate with the other Kurt on the other Hilbert program. And the other Godwin law will be this: “As an online discussion grows longer, the probability of a comparison involving Poets or Homer approaches one.”

  135. Anonymous Says:

    >Except that I didn’t make any direct comparison between anyone and Nazis.

    Then I have to retract my claim as I was under the bad spell of xkcd. Mea culpa.

    On the other hand what about this scenario: imagine a parallel universe where God supposedly handed His words to Prophets and Messiahs as a consistent mathematical theory but without a proof for its completeness. I bet that in the other universe the other Scott will debate with the other Kurt on the other Hilbert program. And the other Godwin law will be this: “As an online discussion grows longer, the probability of a comparison involving Poets or Homer approaches one.”

  136. anonymous Says:

    nothing wrong with some contradictions

  137. Amory Says:

    Steven Rudich and Alexander Razborov win the Godel Prize

    http://www.eatcs.org/activities/awards.html

  138. anonymous Says:

    Well,

    A->B or B->C

    (not(A) or B) or (not(B) or C)

    (B or not(B)) or (not(A) or C)

    TRUE or (not(A) or C)

    TRUE

    So yes, A->B or B->C is, indeed, a tautology. However, I think what Scott meant was something like “can handle (X and Y) for X, Y

  139. Travis Says:

    I’m going to lay out an argument–not for God–but for the potential importance of faith (with a lower-case “f”, not necessarily faith in a god). I’d be very interested in hearing either of errors in reasoning, or counter-arguments, as I’ve never heard it rebutted before and this seems to be a good place to find people capable of doing so.

    Assumptions:
    1) Rational human thought is (when done perfectly) an “implementation” of some system of logic satisfying the conditions of Godel’s (first) incompleteness theorem. This assumption seems to me to be implicit in the assumption of materialism, if one does not claim some “new physics” is responsible for the operation of the human brain.
    2) The rational human mind is less powerful than a (quantum?) Turing machine in that it is finite.

    Argument:
    1a) Since the rational human mind can only (at best) implement some formal system of logic, there are propositions t in T which are true but not provable by any human.
    1b) Even if 1a were not true, the simple fact that the human mind is finite also implies that there are propositions t in T which are true but not provable by any human.
    2) T, the set of unprovable-but-true propositions (for either 1a or 1b), is infinite. While most of the propositions in T are uninteresting, some are likely to be “important” by whatever reasonable metric of importance you might use. In fact, since the set of propositions we can prove to be true (call it P) is finite whereas T is infinite, it would be rather amazing if more than a fraction of the “really important” propositions were in P, and thus accessible by reason alone.
    3) Since they are not accessible by reason, most of the important truths are accessible only by faith, if at all. This seems kind of depressing for mathematicians and perhaps all natural scientists.

    As a follow-up, an “explanation” of why God would not present humanity with indisputable evidence of his existence. This argument seems vaguely Kierkegaardian, so there are probably counter-arguments out there, but I’m ignorant of them.

    1) God wants us to have free will, and to freely choose to believe in him.
    2) God gave us the capacity for rational thought.
    3) Presenting a sufficiently-clear proof to a rational person necessarily has the effect of forcing him to accept that which is proven.
    4) By giving us such a proof (a la Hitchhiker’s Guide and God’s message to creation), God would be denying us (or at least the rational amongst us) free will in the question of belief.

    These two things together don’t prove the existence of God, but do amount to an argument that there are important things that are true that we cannot prove to be so (i.e., can only come to “know” through faith), and that God’s existence, if he exists, is necessarily one of those things.

    Has anyone ever heard these arguments presented in this manner? Any counter-examples/rebuttals?

  140. Bill Kaminsky Says:

    To answer your question, Travis:

    1) God wants us to have free will, and to freely choose to believe in him.
    2) God gave us the capacity for rational thought.
    3) Presenting a sufficiently-clear proof to a rational person necessarily has the effect of forcing him to accept that which is proven.
    4) By giving us such a proof (a la Hitchhiker’s Guide and God’s message to creation), God would be denying us (or at least the rational amongst us) free will in the question of belief

    … Has anyone ever heard these arguments presented in this manner? Any counter-examples/rebuttals?

    Yes and yes.

    It’s hard to be wholly original in theology. In this case, there’s a whole literature on “divine hiddenness” or, if you prefer fancy words, the absence of theophany. I was introduced to it via:

    Michael J. Murray “Why Does God Hide His Existence?” in
    Questions About God: Today’s Philosophers Ponder the Divine, Steven M. Cahn and David Shatz, eds. (Oxford University Press 2002) [it's full-text searchable at Amazon.com]

    And as with all provocative questions about God (e.g., “Why does God permit evil / suffering / etc.?”), one of the major explanations is to say that God must do this if he wishes to grant us real free will. This too has a fancy name: the free will theodicy.

    The aforementioned Murray article leans strongly this way, but closes by admitting the main hole in the free will theodicy for divine hiddenness. As Murray writes in his closing paragraph,

    This may make it clear why God does not, say, open the sky and give a world-wide unambiguous proclamation of his existence. However, it does not seem to explain why there is the particular degree of divine hiddenness that there is. An objector may reply here that God may not be able to “open the sky” without the loss of morally significant freedom on the part of humans; yet, must that also mean that merely one more unit of divine manifestation in the world would cause the fabric of significant moral freedom to collapse?

    I’m inclined to argue the same point in the opposite direction. There’s been plenty of supposed revelation of God to humanity as to how we should act. But if God really wanted the maximum exercise of the free will he granted us, why put his big godly thumb on the scale at all with such strong suggestions?

    Other objections off the top of my head:

    1) Who said we had free will?! (And it’s not just godless scientific determinists who would say this. The godly predestination believers would say this too.)

    2) At the opposite extreme, if you got free will, then rebellion for its own sake—rebellion with no hope of success —can nonetheless be compelling. The classic example is Milton’s Lucifer:

    …Here [i.e., Hell] at least
    We shall be free; th’ Almighty hath not built
    Here for his envy, will not drive us hence:
    Here we may reign secure, and in my choyce
    To reign is worth ambition though in Hell:
    Better to reign in Hell, then serve in Heav’n.
    Paradise Lost, Book I, Lines 258-63

  141. John Sidles Says:

    Since we’re going to assert that Wittgenstein foresaw the main ideas of the incompleteness theorems, we might as well assert that Milton foresaw the main ideas of information theory!

    From Milton’s Paradise Lost, Book II:

    … Chaos Umpire sits,
    And by decision more imbroiles the fray
    By which he Reigns: next him high Arbiter
    Chance governs all. Into this wilde Abyss,
    The Womb of nature and perhaps her Grave,
    Of neither Sea, nor Shore, nor Air, nor Fire,
    But all these in thir pregnant causes mixt
    Confus’dly, and which thus must ever fight,
    Unless th’ Almighty Maker them ordain
    His dark materials to create more Worlds,
    Into this wilde Abyss the warie fiend
    Stood on the brink of Hell and look’d a while,
    Pondering his Voyage …

    An immensely harder question is, what future seminal ideas in mathematics and science are presently foreseen in the arts?

    No, I don’t want to hear about Cormac McCarthy, or even about Terminator II.

  142. Chipping the web - ditch -- Chip’s Quips Says:

    [...] Religion’s rules of inference (thanks, Assaf).  I’ve been on both sides of this type of debate at different points in my life, and I don’t think my changes in point of view had anything to do with logic — it’s more a matter of taste.  The discussion in the comments waxes lively and thought-provoking. [...]

  143. Jim Miles Says:

    Hahaha, brilliant entry. More like this and less about difficult Sciency things please. The difficult Sciencey, Quantum Computerey ones only make me feel inadequate as I am myself, in fact, studying a Mathematics degree and feel like I shouldn’t have to work as hard as I do to understand them.

  144. cody Says:

    Travis, i find the idea of applying Gödel’s incompleteness theorems to reality interesting, but it is also the reason i dont really subscribe to your argument.

    right off the bat, we dont know what the ‘axioms of reality’ are, and so we dont know which statements may or may not be independent of these axioms. what we do know is that we can never be certain that our axioms regarding physical reality are complete. at the moment we would like a new set of axioms that explains quantum mechanics and gravity, and produces testable predictions, but even if such a system comes along, we wont be sure it is the system.

    the flaw that i see when applying these arguments however is, if a statement is independent of an axiomatic system, how do you decide whether that statement or its negation is true? just because the statement is independent of the axioms doesnt mean that whatever you feel, or take faith in, is correct.

    i like to think that mathematicians and scientists abhor assumptions about the independent statements, (though i know this isnt the case, and it is difficult when we want to explore areas that we know are independent of the axioms, like CH). the correct response (in my view) is to exploit the areas in which many independent statements exist, in order to further develop the ‘axioms of reality’. investigation of the ill understood is our best hope of expanding our current theories. but along the way, when asserting the truth of a statement, we must stick to those statements which are provable, i.e., the emperical evidence.

  145. Douglas Knight Says:

    (a) the ones like Hinduism and Judaism, which historically said “go do your thing and leave us alone to do ours,” and (b) the ones like Christianity and Islam, which historically said “do our thing or face the sword.”

    This is an important attribute of a religion but it is not historically uniform. Judaism was once a proselytizing religion.

  146. anonymous Says:

    This is an important attribute of a religion but it is not historically uniform. Judaism was once a proselytizing religion.

    as was Hinduism, for that matter (or whatever the Vedic religion was that preceeded the Buddhist/Jainist diaspora, rather)…

  147. matt Says:

    I haven’t read all the comments, so I don’t know if anyone has brought this up, but: in science we don’t just “blindly turn the modus ponens crank”. When reading a paper, we (or at least I) tend to “just get” the motivation of the result from some generalities and only later fill in the logical steps if, and as, needed. Further, I have seen many papers which have some minor error somewhere or other, a factor of 2 off or something. In principle, this means it is all wrong. Of course, though, one can usually quickly see whether this minor error affects anything else, and how much, and so the truth of the result, even if the result is a proof, depends not so much on each individual step, but more on the general strategy embodied in the steps.

    I’m sure also most people writing papers have encountered the converse situation: you know the result is true, it’s pretty clear that something is, say, exponentially small at a certain point in the argument, but for the sake of writing the paper you are forced to go through lots of tiny steps to get there, which in some cases even obscure the argument.

    True, in math/physics one does have to do all this with the attitude that one _could_ fill the steps in if needed, and also a very common situation is to first sketch a proof strategy, and then only later when going through more carefully realize some of the tricky aspects. But I think the point above still stands, that in some ways our inference rules are not as mechanical as they may be claimed to be.

  148. Travis Says:

    Cody, I wasn’t intending my argument to be restricted to the physical universe. The truths I discuss could concern mathematics, or morality, or “metaphysics”–whatever that is. The first part of the argument I posted amounts to a very general claim that most of the “important” truths are likely to be inaccessible via human logic, and thus accessible only by faith, if at all. It is certainly true that we won’t know by logic whether our faith has gotten us the right answers, but that’s the nature of faith. It seems to be a matter of personal preference as to whether one chooses to guess at the important truths and risk being wrong, or to never venture beyond what can be proven with logic.

    Bill, thank you for the reference to Murray–I’ll take a look at that. As for whether we have free will or not, it’s quite true that we may not free will, but, if that’s the case, many things become rather uninteresting. Thus, in such matters, I usually proceed under the assumption that we have free will.

    It seems to me that there may be a simple answer to the question of why we might have the exact degree of “divine hiddenness” that we do. Most of us have had the experience of meeting an indoctrinated-from-birth Christian with an unthinking acceptance of Christian doctrine. Suppose, for the sake of argument, that Christianity is the one true faith. Such unquestioning, unthinking belief does not represent a freely-willed acceptance of God any more than atheism is a freely-willed acceptance of God. If God “turned the dial” of divine hiddenness, he might increase the number of believers, but also increase the percentage of whom were unthinking zealots. For certain weightings of the value of each kind of “soul”, perhaps the current situation is optimal. In any case, this seems to be the kind of argument where “Kurt” would likely smile and claim it was a “divine mystery”.

  149. rrtucci Says:

    If a thread falls to more than 100 posts in the middle of the night, and there is no one there to read it all, does it make a sound?

  150. Len Ornstein Says:

    Faith, belief, commitment, agreement are all of a kind. One or another is required to make communication possible. Either implicitly or explicitly, we must agree to accept a set of unprovable axioms and definitions as a basis for communication. Contrary to the position of most positivists, this puts metaphysics at the roots of language, logic, math…and all other ‘disciplines’ (including religions). In this respect, the main difference between the discipline of religions and the disciplines of science, are, as Scott has suggested, how consistent scientists usually remain.

    Of course there’s another very important difference:

    No empirical induction is certain. As Hume taught, because observation of part of a set of ‘objects’ or ‘events’ is always incomplete, it’s impossible to extrapolate or interpolate, from the part to the whole, with absolute certainty. This parallels Godel’s Incompleteness Theorem. So no observational ‘truths’ can be proved…they remain to some degree uncertain. (Of course science works hard to reduce that degree of uncertainty; like to a few parts in a billion for the fine structure constant.) So the use of empirical extrapolation and interpolation must also be taken ‘on axiomatic faith’; another metaphysical root to the scientific method…(and of course, to all common sense use of observation to comprehend reality).

    Religions generally refuse to let empirical ‘truth’ challenge scriptural truth. By contrast, the scientific enterprise tries to generate consistent theories IN ORDER TO challenge them with empirical observation. Only those theories (models of reality) which survive challenges of experimental science, are allowed the status of tentative (incomplete, provisional) ‘truth’. This distinguishes science from much of math as well as from theology!

    Hope this helps.

  151. cody Says:

    Travis, i suppose i have difficulty understanding these ideas because i am a strict physicalist, and have been for as long as i can remember.

    matters of faith have always baffled me; i struggle to understand why one set of beliefs is or is not chosen over other sets of beliefs, and all of the major religious ideas have always made much more sense to me when viewed as people who were grasping at a superficial explanation of the world around them rather than as truly insightful.

    anyone else thinking of that line in the Way of the Gun when he says “you know what im gonna tell god when i see him? im gonna tell him i was framed.”

    actually, itd probably be more productive for me to ask, Travis, what sort of articles of faith have you ventured to, and why?

  152. Travis Says:

    Cody, as Matt said a few comments back, when most scientists are presented with a scientific concept, they tend to “just get it” before they actually go through all the steps of checking a formal proof, etc. Sometimes this is because the theory or concept has been sufficiently well-proven by informal language, but in some cases it’s that the concept just “feels right”, due to some aesthetic sense of beauty or truth. The reason one might choose to believe via faith in one set of ideas and not another seems to me to be very similar.

    Major religions probably strike you as superficial because of some sort of theological corollary of Sturgeon’s Law–”90% of everything is crap”. It’s easy to assume that last 10% must also be crap because the first 90% is obviously so.

    For most of my life, I was an atheist. As I gradually learned more about Christianity and realized many of my ideas about it were incorrect or oversimplifications, I began to appreciate it more and came to believe in it, or at least the core of it. Sorry, no dramatic story of divine visions or miracles. I fully recognize that my belief in Christianity is not a result of a logical proof but rather of faith. I’m posting on this forum on this topic because I’m interested in truth, and a logical proof of God’s non-existance would convince me to become an atheist again. Believing in something without proof may be faith, but believing in something that is provably false is just stupid.

    Throughout my life and long before I became religious, I’ve believed in the existence of an objective morality (I don’t claim to follow it perfectly or even know all the details, of course). I take certain “moral laws” to be axioms, although you might consider them to be articles of (secular) faith.

    Those are my only articles of faith, as far as I’m aware. As I mentioned earlier, I believe in free will, but that’s for purely pragmatic reasons; if I believe in free will and I’m right, well then I’m right. If I believe in free will and I’m wrong, I had no choice in being wrong anyway so who cares. The opposite belief–that we have no free will–is much more dangerous if wrong. Someone who seriously believes we have no free will cannot rationally believe in morality (since we would have no capacity to make moral choices), and is thus either irrational or an aspiring sociopath. In a world without free will, that’s neither here nor there, but if we actually have free will, it would be a terrible mistake.

  153. Koray Says:

    Travis, excuse me but did scientists of the previous eras just “get” that the earth was going around the sun? Or theory of relativity? Godel’s incompleteness theorem?

    I don’t know how we develop what is “elegant” about a proposition. I just don’t think that it’s infallible.

    There’s no logical proof of god’s non-existence. God is not said to be an abstract mathematical entity like a prime number between 15 and 17. We don’t have the universe’s axioms nailed down to postulate what may or may not exist “by definition”. I have a pepsi can on my desk, but I can’t verify that this conforms with the universe’s laws by logic alone. (Does the universe even have laws? Is the speed of light constant across the universe?)

    If you think that you are free to choose to accept existence of one god sans evidence just on principle, then should you not be able to believe in a group of gods? Why just one god? Maybe it’s like Greek mythology.

    If it’s something about christianity that compels you, then there are one billion muslims that probably don’t know what you know, yet they are at least as confident that theirs is the right faith.

    Even if you are dead certain that “a” god must exist, you just can’t assume that Jesus didn’t lie. You still have to demonstrate that Jesus (and not Mohammad!) was right.

  154. cody Says:

    Travis, as i understand it, Matt’s comment only really applies to armchair scientists, and scientific hypothesis. ‘feeling right’ is not a criteria upon which we can safely judge scientific hypothesis, though we often take that as assurance that we are moving in the right direction. in the end it is the predictive power of the theory that we use to judge validity. so while Einstein thought quantum mechanics ‘felt wrong’ (in some sense), he seems to have been incorrect. and while string theorists suspect they have a lot going for them, it hasnt gone anywhere yet; intuition tells them its useful, but it hasnt yet become a grand predictor like relativity or quantum mechanics (no disrespect to you string people intended). Occam’s razor is only really invoked in situations where two theories explain the exact same set of phenomena, (such as the geocentric model with epicycles versus the heliocentric model).

    as Feynman put it, “the first principle is that you must not fool yourself, and you are the easiest person to fool.”

    it would be nice to ‘just get it’ when it comes to faith, but i have no reason to think the universe should be one way over another. not in quantum mechanics or any concept of aesthetics. if there were any sort of ‘absolute beauty’ then i dont think fashion and art would vary so dramatically so often.

  155. John Sidles Says:

    For all you folks who enjoy science, history, philosophy, and theology, but have trouble finding a book that is simultaneously strong in all four areas, may I strongly recommend Jonathan Israel’s Radical Enlightenment and Enlightenment Contested?

    These two books together comprise 1,793 pages of exceedingly small type, each of which describes exceedingly fascinating episodes in science, history, philosophy, and theology.

    Haven’t you ever wondered about the reasons Newton really took an interest in alchemy? :)

  156. Michael Brazier Says:

    “Religions generally refuse to let empirical ‘truth’ challenge scriptural truth. By contrast, the scientific enterprise tries to generate consistent theories IN ORDER TO challenge them with empirical observation.”

    This is misstated. Religions generally deal with questions that cannot, even in principle, be settled by empirical observation — for instance, the validity of inductions from sets of empirical observations; for another instance, the whole field of ethics — but which are of interest to everyone who ever lived. Challenging a religion with empirical data is like asking what color an equation is, or refuting a political theory with a painting.

  157. Travis Says:

    Koray and cody–from what I know of the history, Einstein was initially motivated by the aesthetic beauty of relativity. As a physicist, I find the idea that the speed of light is constant everywhere to be beautiful, and I’m sure he did, too. Of course, as a scientist, he couldn’t stop there, and he had to build a solid base out of logic and empirical facts.

    cody–I see your Feynman quote, and I raise you a Feynman example. There was a case where an experiment showed one of Feynman’s theories to be incorrect. Feynman was so sure of the theory (motivated by its aesthetic beauty), that he declared that the experiment must be wrong. The experiment was eventually repeated, and Feynman was right. Obviously, it doesn’t always (or even often) turn out this way, and we can’t base science on aesthetic beauty.

    My point is simply that, in the case of science our aesthetic sense is often a useful guide. In the case of matters of faith, it’s all we have. If Feynman were part of this debate, he’d probably propose an experiment to see if our “aesthetic sense” is more accurate than random chance, which would be an excellent way to move the debate forward.

    Koray–I don’t have to prove that Jesus didn’t lie, or that we don’t have the Greek pantheon of gods, or anything like that. I don’t have to do these things because I’m not trying to logically prove that the Christian God is God. As I argued earlier, there’s good reason to believe it to be impossible to logically prove the existence of God. Before deciding upon a particular religion, it’s worth doing a check that the most obvious ways of disproving it don’t work, but it’s probably impossible to cover all such ways.

    My point is that we should recognize that there are propositions whose truth we cannot ascertain with logic. We can either choose to ignore those propositions, or we can approach them with our aesthetic sense of beauty and truth (i.e., faith). Faith is less clearcut and less reliable than logic, but it’s the only tool we have for this infinite domain of unproveable propositions.

    That’s not to say that I reject the application of logic to all theological matters. It may well be impossible to prove or disprove God in general, but there are many tenants of specific religions that are accessible to logic and science. For instance, central to the idea of Christianity is Jesus’ life and death as a real, historical person. If one could show that Jesus never lived, that would disprove Christianity. In other words, while Christianity is not a scientific theory, it is at least falsifiable. Furthermore, one can easily show that various versions of different religions are incompatible with each other, obtaining results like (A –> ~B) & (B –> ~A).

    Cody said: “it would be nice to ‘just get it’ when it comes to faith, but i have no reason to think the universe should be one way over another. not in quantum mechanics or any concept of aesthetics.”

    Really? You don’t look at quantum mechanics and see the beauty of it? That’s most of the fun of doing it, for me. Since you’re reading this blog, I’m guessing you’re a quantum information scientist of some sort. If not the beauty of quantum mechanics, what motivates you? Is it the money or the power or the groupies? :-)

  158. John Sidles Says:

    Travis says: Since you’re reading this blog, I’m guessing you’re a quantum information scientist of some sort. If not the beauty of quantum mechanics, what motivates you? Is it the money or the power or the groupies?

    Hopefully, there are many individual answers to this question. It would be very bad news if everyone worked on QIT for just one reason!

    For me, QIT in general—and quantum system engineering in particular—is all about tools; tools for creating resources.

    And this means resources in the most basic sense: food, clothing, shelter, meaningful work, and a global society and ecosystem that are not fubar’d.

    Almost all of humanity’s tools press against the mathematical and physical limits of speed, size, sensitivity, power consumption, and informatic complexity. Quantum system engineering is the discipline of pressing against these limits.

    As Donald Knuth famously said: “Science is what we can tell a computer to do, Art is everything else.” In accord with the Knuthian Principle of Science, the emerging science of quantum system engineering can be summarized in two pages (which we distribute to our students as “QSE Page A” and “QSE Page B“).

    These two pages succinctly link the modern axioms of quantum mechanics (as expounded, e.g., in “Mike and Ike”) to modern methods of model order reduction and differential geometry—this turns out not to be too hard.

    Both God and the Devil are in the details … as usual! These saintly and devilish details encompass both the initial challenge of creating new tools that work, and the subsequent difficulty of applying new tools with foresight and compassion.

  159. Len Ornstein Says:

    Michael

    “Religions generally deal with questions that cannot, even in principle, be settled by empirical observation — for instance, the validity of inductions from sets of empirical observations; for another instance, the whole field of ethics”

    It might make life easier if this were true. What about the stories of creation? What about the age of the universe? What about answering prayer? What about promises of an afterlife?

    Even ethics ‘benefits’ from science. When science forecasts risks and rewards with high confidence, action taken now may insure the general good in the future (global warming, depletion of nonrenewable resources, threats to food supplies, risks of pharmaceutical side effects, etc.). Without such forecasts, and with the best of intentions, Golden Rules can be misapplied.

    Shared belief (commitment, agreement, faith) in unprovable metaphysical axioms and definitions are necessary for meaningful communication within all disciplines. Models are built on/with such metaphysical foundations. Models must be tested for consistency to try to assure that they’re consistent, at least within their discipline. Godel warned that such ‘assurance’ is not always possible. Within disciplines like math, as Scott suggested, practitioners do a much better job at checking for consistency than do theologians.

    Science, however, also MUST use reality checks to distinguish simple internal consistency from empirical ‘truth’. And that’s what makes it especially useful.

  160. Greg Kuperberg Says:

    cody–I see your Feynman quote, and I raise you a Feynman example. There was a case where an experiment showed one of Feynman’s theories to be incorrect. Feynman was so sure of the theory (motivated by its aesthetic beauty), that he declared that the experiment must be wrong. The experiment was eventually repeated, and Feynman was right.

    I have heard this story too, and I found the quote “the experiment must be wrong” in an old Usenet posting. However, I don’t think that it was just Feynman’s own theory, rather it was a partial theory of weak interactions that was contradicted by this one experimental result. Moreover, it wasn’t just that the experiment was repeated with a different answer, it was specifically that they found a bug in the set-up and analysis of the stray experiment.

    Above all, Feynman was not primarily motivated by aesthetic beauty. The real foundation for his position was a combination of Occam’s razor and theory supported by prior experiments. Something was wrong somewhere, and Feynman concluded that it was almost certainly a problem with the new experiment, because the experiment just contradicted too much. Aesthetic beauty is related to considerations such as Occam’s razor, self-consistency, and inference from past experiments, but it isn’t exactly the same.

    From time to time, these days, people dismiss a really good theory as merely “elegant” or “beautiful”, as if to suggest that its proponents care more about that than validity. In fact, there is an interesting gray area between theoretical appeal and experimental confirmation. You could imagine a block-headed ancient Greek saying, “To be sure, Eratosthenes, a round Earth is an elegant solution to the problem of the boundary of geography; but I don’t believe you because your evidence just isn’t very good.”

  161. dude Says:

    Scott, dude — your blog is so much better than the complexity weblog! I hope it stays this way after you join MIT/Stanford/Berkeley/Caltech/wherever

  162. Dani Fong Says:

    One must always keep in mind that famous scientists, yes, even Feynman, are still human. If an experiment is sufficiently surprising, people are quite given to saying that it’s flat out wrong. Sometimes in spite of abundant evidence.

    Cosmologists say things regarding the second law of thermodynamics which strike me as incredibly oversold. Nonetheless, the fluctuation theorem has been known for more than a decade, and microscopic (not nanoscopic) measurements of second law violations have been shown back in 2004. “The experiment is wrong!” many exclaim, but it all seems to be damned sensible, and excellent science.

  163. anonymous Says:

    Hmm…. this is the 161st comment so far. I left one earlier (comment 88)… Well Scott, what’s the current record anyway? This post has more comments than I’m used to seeing on any other blog.

  164. Paul Beame Says:

    Evolution, the age of the earth, and the morality of homosexuality are very peripheral issues and not particularly relevant to the core of Christian faith. However, when logic has been applied within Christian denominations to the more fundamental issues of sin and redemption, the conclusions have sometimes been disturbing and it is no wonder some believers are not so happy with logic.

    For Roman Catholics there was this annoying logical gap: Given axioms: Human -> Original Sin and (Saved -> Baptism in the Church & …), ((Sinned & ~ Saved) -> Damnation) there was the annoying problem of babies who died too young to be baptized: how does one fill the logical gap given the premise (Human & ~ Sinned)? The unsatisfying solution of ‘limbo’ was only repudiated by Roman Catholic Church a month or so ago

    For Calvinists, the problem is predestination: Given axioms of Omniscience, FORALL X (God knows the truth value of X), and Omnipotence, FORALL X (God can make X true) and (Saved(y) Believer(y)) along with “Belief is a gift of God”, i.e. (Believer(y) -> God made Believer(y) true), what happens when one substitutes Believer(y) for X? The conclusion is that God must have made a decision about the truth value of Saved(y) explicitly. Hence the Calvinist Westminster Confession of Faith:
    By the decree of God, for the manifestation of his glory, some men and angels are predestined unto everlasting life, and others foreordained to everlasting death. Raised as a Presbyterian, this logic was something I found particularly disturbing when I was growing up.

  165. Paul Beame Says:

    Argh: I should have used (Saved(y) IFF Believer(y)) instead of a biconditional arrow which of course doesn’t show up in HTML without using & characters

  166. John Sidles Says:

    From Douglas Adams’ Life, the Universe, and Everything:

    He hoped and prayed that there wasn’t an afterlife. Then he realized there was a contradiction involved here and merely hoped that there wasn’t an afterlife.

  167. matt Says:

    My previous comment wasn’t really talking about aesthetics. It was more aimed at the actual rules of inference used in practice. I haven’t ever read any of Scott’s papers (sorry, Scott), but I’d be willing to bet (the stakes would have to be high enough for this exercise to be worth my time) that I could find, in at least one of his papers (including early arxiv versions, etc… anything that was available to the general public) a _minor_ error somewhere. Not something that invalidates the result, maybe a small typo, which meant that while A didn’t actually imply B, and B didn’t actually imply C, it is still true that A implies C, and you can see this by slightly fixing the expression for B (replacing it with some close B’) and then A->B’ and B’->C. So, was he following strict modus ponens? No. Is the whole paper false? I don’t think so in this hypothetical example….

    Another example. The arxiv proof of Poincare seems to be recognized by many as a proof. Perhaps with a lot of details to be filled in, but that’s where the essence of the proof is. On the other hand, the mathematical proof that, for sufficiently strong disorder, solutions of the one-particle Schrodinger equation are localized, follows many of the ideas of Anderson’s original paper on localization, just making the arguments more rigorous. But, despite Anderson’s huge insight, I think no one would credit him with the proof of localization in this case. So, it is a fine line that one learns, between what counts as a proof and what doesn’t!

  168. Johan Richter Says:

    “Evolution, the age of the earth, and the morality of homosexuality are very peripheral issues and not particularly relevant to the core of Christian faith.”

    Really? I agree about the homosexuality stuff, (though certain right-wing christians seam to think it is of major importance). But do you really think the creation story is a peripheral part of Christianity? I don’t buy it, most of the Bible seams to deal with historical stuff (even though a large part of the history happens to be fictional), like the creation of life and earth. Moral issues, and certainly abstract theological issues like predistination seams to play a far smaller role. Indeed, I would argue that few Christians other than theologians have understood or cared about issues such as predestination, or how Jesus human and divine natures could be reconciled.

    Oh, since I want this thread to set a record I am going to end with a provactive statement, NP=BQP=Israel.

  169. cody Says:

    Travis: werent Einstein’s motivations the emperical evidence that a non-inertial reference frame doesnt exist? and didnt Feynman vehemently reject all forms of mysticism?

    no money, power, or groupies in science and mathematics so far, nor have i ever expected those. no, i study science and mathematics because i wish to understand how the world works, i enjoy understanding it, i enjoy learning it, it excites me; problem solving excites me (hence i enjoy the theory side of things, which is entirely dependent on the experimental side of things as well).

    as i have strived for objectivity, i have lost all sense of any absolute concept of beauty; while i find many things around me to be beautiful, i do not count on anyone else agreeing with me, and while quantum mechanics interests me, excites me, and provokes lots of ideas, it does not yet appear ‘beautiful’. it is interesting, but those are not the same thing to me.

    Paul, if “evolution, the age of the earth, and the morality of homosexuality are very peripheral issues and not particularly relevant to the core of christian faith”, why are christians so involved in these issues? why all the hubbub? (i should say, the first two are important to me, as issues of science; issues of morality are not science, and thus of less concern personally).

  170. Jonathan Jones Says:

    cody writes: ‘Paul, if “evolution, the age of the earth, and the morality of homosexuality are very peripheral issues and not particularly relevant to the core of christian faith”, why are christians so involved in these issues? why all the hubbub?’

    The obsession with creationism is a modern aberration. Historically speaking most christian debates are ostensibly about christology and soteriology, and actuallly about political authority.

    Homosexuality, and sexuality in general, is more complex, and it comes and goes as an issue over the centuries. But once again you usually find that apparent concerns with sexual ethics are a cover for something else.

  171. John Sidles Says:

    Jonathan Jones Says: … Historically speaking most christian debates are ostensibly about christology and soteriology, and actually about political authority.

    LOL … that sentence suggests Grouch Marx saying “Soteriology? You said the secret woid!”

    What you say is surely correct, yet a devout Christian would be equally correct in saying “Historically speaking, most scientific debates are ostensibly about truth and evidence, and actually about political authority.”

    What IMHO makes religion and science both worthwhile—and relentlessly evolving—is that politics aside, they both deliver some finite measure of truth and salvation.

  172. Scott Says:

    I haven’t ever read any of Scott’s papers (sorry, Scott), but I’d be willing to bet … that I could find, in at least one of his papers … a _minor_ error somewhere.

    No way, man…

  173. Walt Says:

    Scott’s papers come with a major-error-only guarantee.

  174. RM Says:

    NP=BQP=Israel
    This brings new meaning to the idea of a two state solution.

  175. The P-C-B theory and intolerance « Epistles Says:

    [...] For non-atheists and atheists alike. [...]

  176. John Sidles Says:

    Just to help preserve a fine thread from falling silent … folks have blended math, science, philosophy, and history—but the arts have been neglected so far.

    May I recommend guitarist Ken Hatfield’s CD String Theory (samples are available on Ken’s home page); in particular the composition Averroe’s Search, whose ineffable theme was inspired by Borges’ extraordinary story of the same title.

    I am not sure who Ken Hatfield is, but his command of both music and LaTeX is pretty remarkable.

  177. itistoday Says:

    I dunno… 176 responses?? Geez… it wasn’t that amazing…

  178. Nagesh Adluru Says:

    Geez… it wasn’t that amazing…

    Evidently it’s blogically proven to be amazing enough to gather 178 comments.

  179. Travis Says:

    Cody: as far as Einstein knew, there *was* an absolute reference frame (the ether/center of the universe/Vatican/New York/whatever). He considered the implications of having no absolute frame of reference, and found them compelling, despite having essentially no experimental evidence at the time (the closest he had for general relativity was a “retrodictive” calculation of the precession of the perihelion of mercury, at which point he experienced heart palpitations out of excitement).

    At this point, I’m tired of debating whether aesthetics has a role in the initial consideration of a scientific theory (which ultimately needs to be weighed with logic and experiment, of course). I thus resort to Google as the ultimate arbiter of all human knowledge; a search for “beautiful theory” turns up over 50,000 hits.

    I hope you were able to see the joke in my “money, power, groupies” comment; it would be an even bigger shame if you lost your sense of humor on top of your sense of aesthetics. As far as I know, very few scientists get any of those three, let alone all of them (except perhaps for Feynman, but then Scott is probably the only one here with a shot at being a latter-day Feynman).

  180. mollishka Says:

    I don’t stop by here very often, but it’s posts like this that make me glad when I do. Quite an entertaining read.

  181. cody Says:

    yes, i understood your joke Travis, though i did not respond as if it were a joke since i wanted to provide my motivation. and its not that ive lost my sense of aesthetics, ive just lost all sense of absolute aesthetics; my understanding of beauty is that it is very personal.

    i read once in some sort of time-magazine related publication that Einstein had used a 1500 dollar check as a bookmark, and then lost the book. and his statement, “to punish me for my contempt of authority, fate has made me an authority myself.” sums up his opinion on power, (along with his refusal to be the first leader of isreal). as for groupies, i suppose ive read he was good with the ladies, but his sexual antics seem less well documented than Feynman’s.

    though i dont concede your point, ill drop it if you wish.

  182. Scott Says:

    (along with his refusal to be the first leader of isreal)

    Slight correction: he was offered the presidency of Israel, which is basically just a ceremonial post (the leader is the Prime Minister). Taking that post wouldn’t even have required giving up his research. Even so, Ben-Gurion was said to be greatly relieved when he said no. :-)

  183. cody Says:

    ha, well, then im glad i didnt say prime minister (which was my flawed memory’s suggestion). though even if i had been aware that it was the presidency, i still would not have known it was a cermonial position.

  184. Depth First Search » Blog Archive » Today’s Misc. Says:

    [...] A great post. [...]

  185. Fatwah Friday, Courtesy of PBH | Prose Before Hos Says:

    [...] Other things to check out: World’s greatest flags (bears!!!! axes!!! swastikas!!!), Comcast 911 Fails – 4yr Old Suffers – Comcast Support Hangs Up On Father, deport Kenneth Eng, Religion’s rules of inference, and the Inventor of Mother’s Day Wants You To Stop Wasting Money (consider it done a long time ago). [...]

  186. Jonathan Vos Post Says:

    Scott commented to me in person that I seem always to mentioning Feynman.

    #179:
    “… but then Scott is probably the only one here with a shot at being a latter-day Feynman)…”

    #181:
    “… as for groupies, i suppose ive read he was good with the ladies, but his sexual antics seem less well documented than Feynman’s….”

    Let me suggest two hypotheses, both supported by documented facts [the wonderful many-volumed "Einstein Papers Project" is limited to primary documents; the editors have explained to me exactly how they disdain mere eyewitness reports such as by my mother and my great-uncle's lengthy conversations with him, and oral history], which I omit here for brevity:

    (1) Einstein spent a night with Marilyn Monroe.

    (2) Feynman wanted everyone to think that he was a Byronic Lothario Stud sort of guy, with the ladies. That was, in part, mere public persona. The precise parallel was to Isaac Asimov. The duality is that Feynman was the Asimov of Physics, and Asimov was the Feynman of Science Fiction.

    Both Asimov’s and Feynman’s place is popular culture is due both to their spectacular mentality, personality, and work; and to their own carefully spun autobiographies (several volumes each). The enormous size of Asimov’s printed output (90 words/minute, 10 hours/day, 363 days per year) makes comprehensive analysis impossible until AI assistance is available.

    Feynman had fewer than 40 refereed papers, all amazing. Yet the mythological encrustations on Feynman (Pulitizer-winning “Genius” by James Glieck, at least 2 dramatic films and several film documentaries) make it hard for those who did not know him to tell Real from Reel.

    The working papers, correspondence, manuscripts and related materials of Richard Phillips Feynman (1918-1988) form the collection known as the Feynman Papers in the California Institute of Technology Archives. Feynman was the Richard Chace Tolman Professor of Theoretical Physics at Caltech from 1951 to 1988.

    The Papers were gifted to Caltech by Richard Feynman and Gweneth Feynman in two main installments, beginning in 1968. Caltech has title to the Papers themselves, while the Feynman heirs retain literary and publication rights. The Feynman Lectures on Physics and the Lectures on Gravitation form an exception, in that Caltech is the copyright holder in these publications [and I can ssure you that he was as surprised as anyone by how much money he'd lost by agreeing to that!].

    The first group of papers, now boxes 1-20 of the collection, was donated by Feynman himself in 1968 and added to from time to time during his lifetime. It contains materials dating from circa 1933 to 1970. The second group, comprising just under three-fourths of the whole collection, occupies boxes 21-90. It was given to Caltech by Feynman’s widow Gweneth early in 1989. Group 2 contains papers primarily from the 1970s and 1980s, although some older material is present.