The intolerant antinomy revisited

“If it’s what I think it is,” said Lenore, “it’s a sort of joke. A what do you call it. An antinomy.”

“An antinomy?”

Lenore nodded. “Gramma really likes antinomies. I think this guy here,” looking down at the drawing on the back of the label, “is the barber who shaves all and only those who do not shave themselves.”

Mr. Bloemker looked at her. “A barber?”

“The big killer question,” Lenore said to the sheet of paper, “is supposed to be whether the barber shaves himself. I think that’s why his head’s exploded, here.”

“Beg pardon?”

“If he does, he doesn’t, and if he doesn’t, he does.”

– David Foster Wallace, The Broom of the System

Sometimes I can’t get the thermos open. This is frustrating because: A) There is coffee in the thermos, and I want coffee; and B) I twisted the thermos lid shut myself, and thus it seems logical to expect that I should also be strong enough to untwist it myself.

This recalls a popular antinomy involving the idea of an omnipotent God. If such a being is all-powerful, it asks, then can this God create a rock so heavy that even He can’t lift it? (The omnipotent deity of this antinomy always seems to be masculine.)

Like Gramma Beadsman’s paradoxical barber, that’s an entertaining little semantic pretzel. If he can, he can’t, and if he can’t he can, etc.

But unfortunately most of the time this antinomy is invoked, the speaker doesn’t seem to realize, as Lenore Beadsman did, that it’s “a sort of joke.” They seem to think they’re saying something — neither I nor they can figure out quite what — about omnipotence or about God. But this little sort-of-joke antinomy is no more about God or omnipotence than Gramma Beadsman’s puzzle is about barbers or shaving. The big killer questions of such antinomies have nothing to do with whatever subjects they latch on to as pretexts. Those pretexts are incidental to their real subject — the inadequacy of language itself.

It’s tempting to try to answer such questions on their own terms. I sort of want to say that the barber shaves himself for the same reason that 1 is a prime number. But the point isn’t to try to answer such questions correctly, the point is that there cannot be a correct answer. These antinomies imitate the form of yes-or-no questions, but they’re actually neither-yes-nor-no questions semantically constructed as to make either, or any, answer impossible.

Such sort-of-jokes can be quite fun and the source of musings both playful and profound (see, for example, Lewis Carroll and Wittgenstein, respectively, and vice versa). But it’s less fun when the artfully deliberate nonsense of such antinomies is conscripted by those who mistakenly believe they are scoring points in some kind of debate.

As in, “Oh yeah, well if you’re so tolerant, how come you can’t tolerate my intolerance. Hah!”

As with the bit about the all-powerful God and the unliftable rock, the people citing the intolerant antinomy seem to have no idea that they’re not really saying anything at all about tolerance or intolerance, but merely providing yet another illustration of the elasticity and limits of language. They’re really just presenting another illustration of Russell’s paradox, the set of all normal sets, which Bertrand Russell himself illustrated with the example of the barber above.

I think the unwitting (or half-witting) invocation of the intolerant antinomy involves a more aggressive form of stupidity than the bit with the unliftable rock because tolerance is a much easier concept to understand than omnipotence. When you encounter someone who boasts of their inability to understand the concept of tolerance it’s difficult to imagine that they’re not just being willfully obtuse. Omnipotence, on the other hand, is the sort of transcendent concept that’s bound to force us up against the limits and inadequacy of language. (That’s what “transcendent” means, after all.)

Like most Christians, I believe that the Almighty is, you know, all-mighty. That means: A) I believe that God is omnipotent; and B) I cannot really comprehend precisely what that might mean. To be honest, I don’t really spend much time trying to comprehend precisely what that might mean. “All-powerful” is not the attribute of God that ought to concern us most since it doesn’t seem to be the attribute of God that concerns God the most. “All-loving” — that’s the attribute that matters most when it comes to what God is actually doing. As handy as omnipotence might be, it’s nearly useless when it comes to redemption and reconciliation.

I try to remember that whenever my patience is tried by the gleeful morons congratulating themselves every time they mistakenly cite the intolerant antinomy as some kind of rebuttal of the virtue of tolerance. Reminding myself that love trumps power helps keep me from wanting to crush them beneath the Almighty’s unliftable rock.

Oh, and as for the thermos, I find running hot water over the lid for a bit usually does the trick.

 

  • Joshua

    You mean, like every experiment in science ever ?

    Well, no, if cause and consequences weren’t valid, then you would be unable to take your experimental data and arrive at any conclusion, whether about your experiment, the scientific method, or logic. Therefore, to do an experiment and expect to be informed thereby implies you’ve accepted cause and consequences. You can’t examine your axioms with a method that assumes them. At least, if the assumption being false would lead to no predictable outcome.

    I said in my previous post I agree with you there.

    You did? OK, cool. I can’t find it.

    The only point of difference I see is that you think logic is a property of God, and I think logic is a property of reality. But I’m not sure that difference is relevant to the discussion.

    Um, if the only difference between us is one you don’t think is relevant, I’m not sure what we are talking about. Still, it’s been fun.

     I mean, no matter how hard I study maths I’ll never be able to visualise four-dimensional objects.

    I did, once. I visualised the shape of the graphs of sin and cos (log as well? I forget, it was a long time ago) in complex numbers, C -> C. I was writing a program in Commodore128 basic to draw them as animated 3D graphs and I wanted to know if I’d gotten it right. High school, fun times.Yes, I am a massive nerd.

  • Sgt. Pepper’s Bleeding Heart

    If the answer, for right now, is “I don’t know how you reconcile an
    all-loving god with evil in the world, but I do” I will try to accept
    that is the answer for most people.

    I haven’t reconciled anything, I just live with the tension unresolved. It’s more like “I don’t know how you reconcile an all-loving god with evil in the world, and yet…”

    I haven’t been inside anyone else’s head so I don’t know how common it is for a person’s faith to be acceptance of a series of precepts or arguments entirely divorced from experience. I don’t know how I’d deal with that and I certainly won’t fault anyone for ditching such a faith when it runs into the significant stumbling blocks that human existence throws up.

  • http://tobascodagama.com Tobasco da Gama

    Indeed, the smallest prime is also the only even one… that we know about? ;)

  • Rikalous

    Thanks for the clarification. So you’re suggesting that indifference
    from a god would inherently undermine humanism? I rarely hear anyone
    suggest that such indifference might have its positive aspects, such as
    not having to try to please the god or endure its criticism.

    I’ve never really thought about all this before, so beware of stream-of-consciousness rambling.

    I wasn’t thinking so much that Indifferent God (hereafter IG) would undermine humanism. It’s more that the principles of humanism make IG scary. IG is a violation of the laws and axioms of humanism. People are supposed to be, by and large, pretty dang nifty. We’ve developed all these arts and sciences and metacognition. Other intelligences are supposed to think we’re nifty or threatening or at least worthy of notice. IG thinking that we’re no more interesting than the next mote of dust breaks the rules. So I guess zie’s scarier for me, and probably for most Christians (and theists of various other stripes), because Evil God fits into the framework in a negative sense, and IG breaks the framework. Hamburgers with e. coli in them will turn people off of fast food for a while, but hamburgers that spontaneously combust when you bite into them are terrifying, because they break the framework of how hamburgers work.

    I don’t think that humanism would necessarily be undermined by the presence of IG. I think people might continue on with it in a spirit of defiance towards the uncaring universe. There’s a scene in The Silver Chair, a Narnia book, where the heroes are being mind-whammied by the villain into thinking that they’ve never been to Narnia, and the whole world consists of her underground realm. One of the heroes makes a speech about how he’s going to stand for Narnia even if it doesn’t exist, because it’s better than the villain’s reality. I figure a lot of people would do the same thing, except with Narnia replaced by humanism/Jesus/Mom’s apple pie. It’d be similar to the reaction to EG, except that I don’t think defiance towards indifference is as easy to make forceful as defiance towards hate.

    I’m not sure how to respond to your suggestion about positive aspects, because I’m not sure what you’re comparing IG to. The options I can think of are the Benevolent God most theists seem to worship, where everything would be hunky-dory in the human-divine relationship, and EG, where you’re screwed regardless (and with something less “criticism” and more I Have No Mouth and I Must Scream) but at least you’ve got something to oppose. I guess there’s also Flawed God, but if god isn’t automatically morally better or worse than any given human, there exists the possibility that zie can learn moral behavior from humanity, which sounds pretty cool.

  • Caravelle

    Well, no, if cause and consequences weren’t valid, then you would be
    unable to take your experimental data and arrive at any conclusion,
    whether about your experiment, the scientific method, or logic.

    Are you suggesting that if events occurred in completely random and unrelated ways we’d be unable to tell? That world wouldn’t be even a teeny bit different from the one we live in ? (of course we wouldn’t exist in such a world but that’s besides the point)

    But either way… again, I don’t see what assuming one’s axioms has to do with whether logic is part of the universe or not. I’m not examining the axioms; you’re the one making a positive statement about them here (“logic is not a property of this or any other universe”). I’m just asking you to justify that statement, either logically or pragmatically.

    You did? OK, cool. I can’t find it.

    All I said is that our brains have an instinct for logic, which you
    yourself agree with (“We have evolved a degree of ability in logic”).

    Um, if the only difference between us is one you don’t think is
    relevant, I’m not sure what we are talking about. Still, it’s been fun.

    As far as I can tell, we’re talking about whether logic is part of the universe or not. You say it isn’t, I’m saying we don’t know. Whether the logic we experience in the world comes from God or from reality doesn’t tell us whether it could be absent in other universes or not. But if you think it’s relevant then by all means explain how.

    I was writing a program in Commodore128 basic to draw them as animated 3D graphs and I wanted to know if I’d gotten it right.

    You managed to visualise the fourth dimension and you only did it once ? Really ? If I had that ability I’d do it all the time. Sure that wasn’t a nifty projection of a four-dimensional object onto a moving 2.5D image, i.e. what we usually see ?

    Okay, we seem to have completely lost the plot here. I’ll try and reframe the question the way I see it and see if that’s better.

    The idea that the laws of logic are more fundamental than, say, the laws of physics (so that different universes could have different physics but they’d all have the same logic) isn’t alien to me. I can see a few reasons why I’d think it :

    - I’m much more confident of logic than of the laws of physics. Our understanding of the former seems to be pretty much complete and accurate, but we’re still figuring out the latter and all our theories are understood to be approximations of reality.

    - The laws of logic are blindingly obvious. The laws of physics aren’t.

    - I can imagine the laws of physics being different; I can’t imagine logic being absent. Authors who mess up the laws of physics are called SF/F authors. Authors who mess up the laws of logic are called absurdist.

    The first one is merely a statement of my state of knowledge. We don’t know the complete laws of physics, but presumably such true laws do exist otherwise our approximation methods wouldn’t work the way they do. When discussing whether the laws of physics or logic could be different in other universes, it’s those true laws I’m talking about, not our approximations. So the fact we know one field better than the other isn’t really relevant.

    The second one appears more convincing, except that a little digging shows that something’s “obviousness” in our minds has less to do with how true it is, and more to do with whether our palaeolithic ancestors needed to know it. Thanks to evolution those things that seem obvious to us are usually true, but tons of things are just as true and don’t seem obvious at all. See humans confronted with a stats problem formulated as probabilities vs frequencies for a blatant illustration. The problem is identical; the obviousness of the answer isn’t. If “obviousness” had a direct correspondence with “truth” that difference wouldn’t exist.

    So if the obviousness of something has more to do with the brain’s evolution than with something’s level of truth we can’t take logic’s obviousness as a reason why it would be somehow more true than physics.

    As for the third, our ability to imagine things is even more clearly an artifact of our brains than obviousness is. I can picture interventionist time travel resulting in small differences in the timeline quite easily even though AFAICT that’s physically and logically impossible. But to understand quantum wavefunctions or astronomical scales I need to resort to everyday metaphors even though those things are very good approximations of the true state of the universe.

    So my ability to imagine something being different seems even worse a guide to how fundamentally true it is than obviousness was.

    So what other reasons are there to think that logic is more fundamentally true than the universe ?

  • Joshua

    Are you suggesting that if events occurred in completely random and unrelated ways we’d be unable to tell? That world wouldn’t be even a teeny bit different from the one we live in ? (of course we wouldn’t exist in such a world but that’s besides the point)

    As you say, we couldn’t exist, but if we did we’d be unable to tell anything, because we’d be unable to say, “Gosh! Everything is random, therefore no such this as causality exists.” It’s the therefore that would be denied us. You’d be unable to reliably make any inference or deduction, so you’d just have a collection of unrelated facts.

     I’m not examining the axioms; you’re the one making a positive statement about them here

    I’m not saying you are, I’m saying the hypothetical person doing the experiment would necessarily be.

    You managed to visualise the fourth dimension and you only did it once ? Really ? If I had that ability I’d do it all the time. Sure that wasn’t a nifty projection of a four-dimensional object onto a moving 2.5D image, i.e. what we usually see ?

    Well, I wouldn’t call it an ability as much as something I did once. The equations were fairly simple ones, of two-dimensional surfaces in 4-space, not an actual 4D solid. You could say they were animated 3D curves that move over time – although I did manage to reflect the shapes along an axis in my head and come up with a new shape that, when projected into animated 3D space, looked largely unrelated. And my program agreed with me as to what it should look like.

    So what other reasons are there to think that logic is more fundamentally true than the universe ?

    For me, one is that since logic doesn’t make any assumptions about the universe (as there are only axioms and inference rules, all of which are assumed) and is not contingent on the universe, then it can’t be invalidated by the universe (or our experience of it) in the same way that some idea about physics could be.

    The main reason, however, is that there is a long history in Christian theology, starting in a big way with St John, linking Jesus, the Word of God, with the Greek idea of the logos. Logos literally means word, with connotations of thought and reason rather than physical speech, but in the philosophy of the time the Logos was the ordering or creative principle of the universe. Wikipedia is a good starting point if you haven’t met the Logos before. e.g. Heraclitus, from that page:

    For Heraclitus logos provided the link between rational discourse and the world’s rational structure.

    Also the Stoics on the same page.

    So, John and his followers linked Jesus as Logos to the rational principle of the universe, and to the creation of the universe (slight tangent, more than one early theologian read the personified Wisdom at creation in Proverbs 8:30 to Jesus, also interestingly, she’s female), so I say, the rationality of the universe came from him. Another word for rationality, and one that is cognate to and could translate logos, is logic.

  • Caravelle

    As you say, we couldn’t exist, but if we did we’d be unable to tell anything, because we’d be unable to say, “Gosh! Everything is random, therefore no such this as causality exists.”

    We wouldn’t say such a thing because we probably wouldn’t have a concept of “causality” at all. But I’m not talking about what hypothetical inhabitants of such a world would say, I’m talking about whether such a world would be perceptibly different from ours. And besides, the only options don’t have to be “totally random” and “totally causal”. After all if we’re throwing logic out the window we don’t need consistency even in the inconsistencies… You could have a Lewis Carroll-like world which is mostly causal but contains exceptions. Can you tell the difference between your world and Wonderland ?

    For me, one is that since logic doesn’t make any assumptions about the
    universe (as there are only axioms and inference rules, all of which are
    assumed) and is not contingent on the universe, then it can’t be
    invalidated by the universe (or our experience of it) in the same way
    that some idea about physics could be.

    You still haven’t explained how that isn’t begging the question. You say “logic doesn’t make any assumptions about the universe”, which assumes that logic itself isn’t an assumption about the universe, which is the statement I’m disputing. And what do you mean by “it can’t be invalidated in the same way that some idea about physics could be” ? “Some idea about physics” is invalidated by the universe if and only if it’s incorrect. But how could the true laws of physics be invalidated by the universe ?
    In other words, how do you know the reason our ideas about logic can’t be invalidated while our ideas about physics can isn’t simply because our ideas about logic are correct but our ideas about physics aren’t ?

    And thanks for your overview of the concept’s history, but that doesn’t tell me much as to whether the concept is correct or not. Greek philosophers and Christian theologians said lots of things, and the Wikipedia page gives Heraclitus’ position, not his reasoning.

    EDIT : And reading the Wikipedia page on the Stoics, it sure looks as if they thought logic was part of the universe.

  • Anonymous

    Indeed, the smallest prime is also the only even one… that we know about? ;)

    :p by definition even numbers are divisible by two and some other number, so the only one among them that can possibly be prime is two itself, which is divisible only by itself and one.

  • Anonymous

    “2. The laws of logic are blindingly obvious.”

    Not to Plato they weren’t. The “laws of logic” pretty much start with Aristotle. Which of course isn’t to say that humans were all illogical before that or any such nonsense, but the idea of a formal method of reasoning that could lead unerringly from true premises to true conclusions was not realised before Aristotle (or at least no records from earlier have survived).

    For that matter, there are no universally agreed upon “laws of logic”. There exist paraconsistent logics* (reject the law of non-contradiction*), fuzzy logics (reject the law of the excluded middle), intuitionist logics (reject the laws of the excluded middle, double negation, and De Morgan’s laws), probability theory as logic (extends truth values to any real between 0 and 1, not the same as fuzzy logic). Even within classical logic there are non trivial differences between predicate and propositional logics, and between first, second, and higher order logics. Not to mention philosophers like Quine who famously attacked the very idea of propositions being true independently of matters of fact.

    But then, I’m with Lakotos’ “Proof and Refutations” in thinking that even mathematical proof is ultimately empirical and contingent*, so I’m not exactly the voice of the mainstream here.

    * Sort of anyway, some types accept as axioms both the law of non contradiction and its negation, but lack an certain rules of inference that lead to the explosion in classical logic. I’ve actually had the good fortune to meet and talk with Graham Priest, one of the most prominent advocates of paraconsistent logics. He’s quite serious about the idea that some contradictions are simply true, like Russell’s Paradox, and that logic should reflect that.

    ** Which actually bothers me a lot more than it should. Platonic forms are to me the most aesthetically pleasing idea in all of philosophy and it drives me up the wall that I find the counter arguments ultimately compelling. I’m an atheist who has never felt the “God shaped hole” people talk about, but I definitely have a “Plato shaped hole”.

  • Caravelle

    “2. The laws of logic are blindingly obvious.”

    Not to
    Plato they weren’t. The “laws of logic” pretty much start with
    Aristotle. Which of course isn’t to say that humans were all illogical
    before that or any such nonsense, but the idea of a formal method of
    reasoning that could lead unerringly from true premises to true
    conclusions was not realised before Aristotle (or at least no records
    from earlier have survived).

    lol, I knew I’d get into trouble over that :)
    I don’t think that affects my argument much, as you point out humans weren’t illogical before formal logic was developed and it’s that basic capacity I’m referring to. Kind of like when I bring up 2+2=4 I’m not referring to number theory, I’m talking of the experience of holding 2 fingers and 2 fingers and the result obviously being 4.

    I don’t know half enough about formal logic to address anything else you’ve said, but it was a very interesting post and I’ll certainly read the links. And given I don’t know that much about formal logic, if I am wrong and it does affect my point I’d be glad to know how.

    Which actually bothers me a lot more than it should. Platonic forms are
    to me the most aesthetically pleasing idea in all of philosophy and it
    drives me up the wall that I find the counter arguments ultimately
    compelling. I’m an atheist who has never felt the “God shaped hole”
    people talk about, but I definitely have a “Plato shaped hole” (or
    perhaps “Plato shaped shadow” would be more appropriate).

    Yeah, I think I have the opposite thing. I always found the idea of Platonic forms to be contradictory and confusing, and it was a great relief when I discovered they can be explained in terms of reality and the way our minds understand it.

  • Joshua

    You say “logic doesn’t make any assumptions about the universe”, which assumes that logic itself isn’t an assumption about the universe, which is the statement I’m disputing.

    But, it isn’t? It isn’t an assumption about anything. A formal system like propositional logic is a set of axioms and rules of inference, for you to take or leave as you see fit. The idea that it is useful in understanding the universe is definitely an assumption, or rather to me a faith statement, but you don’t need to make it in order to do propositional logic. And ditto for other formal systems.

    And what do you mean by “it can’t be invalidated in the same way that some idea about physics could be” ? “Some idea about physics” is invalidated by the universe if and only if it’s incorrect. But how could the true laws of physics be invalidated by the universe ?In other words, how do you know the reason our ideas about logic can’t be invalidated while our ideas about physics can isn’t simply because our ideas about logic are correct but our ideas about physics aren’t ?

    Any theory about physics can be tested, that’s the scientific method. You can devise an experiment that would have a definite outcome if general relativity is false. You can then perform the experiment, assuming technology and funding. General relativity lives or does depending on the actual behaviour of the universe.What possible experiment could test, say, de Morgan’s laws? I have no idea. If you do, please tell. Barring that, it’s a consistent claim that de Morgan’s laws don’t live or die depending on the behaviour of the universe.

    And thanks for your overview of the concept’s history, but that doesn’t tell me much as to whether the concept is correct or not. Greek philosophers and Christian theologians said lots of things, and the Wikipedia page gives Heraclitus’ position, not his reasoning.

    Well, I’m a christian, so I hold that John’s gospel is inspired by God and reveals God, and that the writings of later theologians accurately reflect and explain that revelation, so what he said carries a lot of weight with me. If you or other readers don’t accept John’s gospel, or don’t believe in God at all, I’d hardly expect you to find “John said it” convincing, but you asked my reasons for it.

  • Caravelle

    The idea that it is useful in understanding the universe is definitely
    an assumption, or rather to me a faith statement, but you don’t need to
    make it in order to do propositional logic.

    I simply don’t understand what you’re saying here. You seem to think that because a given logical statement doesn’t have to apply to the universe that means logic is independent of the universe. But again… How do you know logic doesn’t have to apply to the universe ? Is there any logical property in existence that isn’t reflected in some aspect of reality ? Given our brains, that we use to reason, are part of the universe, and that every single thing we observe is also part of the universe, how can we possibly know that this reason (or the external reality it reflects) are independent of the universe ?

    What possible experiment could test, say, de Morgan’s laws?

    The logical conclusions derived from them could prove to be fundamentally inconsistent. Or I could consider some actual pair of statements and discover that the negation of their conjunction isn’t the disjunction of their negation.
    What, have you never done this ? When you’re given a mathematical or logical property you don’t try and apply it and then go “oh yeah, it is true” ? That’s a test.

    Barring that, it’s a consistent claim that de Morgan’s laws don’t live or die depending on the behaviour of the universe.

    If there is no universe, i.e. no statements or anything for those statements to apply to, do de Morgan’s laws still exist ? And if there are no objects with mass/energy, do the laws of gravity still exist ? If the answer to those two questions is different, why ?

    If you or other readers don’t accept John’s gospel, or don’t believe in
    God at all, I’d hardly expect you to find “John said it” convincing,
    but you asked my reasons for it.

    Fair enough.

  • Joshua

    How do you know logic doesn’t have to apply to the universe ?

    All valid statements in a formal system, such as one of the varieties of logic that have been fully formalised like prepositional or predicate logic, can be found by iteratively applying the formal system’s rules of inference to the axioms and other valid statements found previously. The rules of inference and the set of axioms completely and perfectly define the set of valid statements for that formal system. Nothing outside is needed.

    This would continue to be true no matter how the universe is found to be, or even if none existed at all. Yeah, I’ve got a bit of Plato in me.

     Is there any logical property in existence that isn’t reflected in some aspect of reality ?

    I dunno, but I don’t think my point would fail even if it turned out that every bit of logic turned out to be useful for something.

    The logical conclusions derived from them could prove to be fundamentally inconsistent. Or I could consider some actual pair of statements and discover that the negation of their conjunction isn’t the disjunction of their negation.What, have you never done this ? When you’re given a mathematical or logical property you don’t try and apply it and then go “oh yeah, it is true” ? That’s a test.

    That’s not a test. At least not of de Morgan’s laws. It may be a test of oneself, to see if one has learned the laws correctly. Since they have been proved, in that they are implied by the axioms of propositional logic, testing is both redundant and impossible. (At least in theory – as Donald Knuth aptly pointed out in the first quote listed, we are all too human.)

    Considering actual pairs of statements is a foregone conclusion, unless one makes a mistake and fall short of the Platonic ideal. That’s what distinguishes it from physics, say.

  • Caravelle

    The rules of inference and the set of axioms completely and perfectly
    define the set of valid statements for that formal system. Nothing
    outside is needed.

    Again, why aren’t the rules of inference and the set of axioms and all valid statements themselves part of the universe ? You realize that by basing your argument on the fact that they aren’t you’re assuming your own conclusion right ?

    This would continue to be true no matter how the universe is found to be, or even if none existed at all.

    I’m not talking about how the universe is found to be here. That’s a statement of our own knowledge. I’m talking about how the universe is. How can you know that logic would be necessarily be the same if the universe was different from what it is right now ? Not different from what our current models say it is (we already know it’s different from that), but different from what it actually is.

    … Let alone not existing. I notice you haven’t answered my question about whether either the laws of logic or the laws of physics would exist in the absence of anything to follow them.

    I dunno, but I don’t think my point would fail even if it turned out
    that every bit of logic turned out to be useful for something.

    What would it mean for your point to “fail” ? We’re not trying to prove that logic is a emanation of the universe here; I have no idea one way or the other. You’re the one who asserted that logic isn’t part of the universe and I’m trying to figure out what evidence you have for that assertion. If you mean that “if all logic turned out to describe a bit of the universe it wouldn’t disprove my position”, sure. But if all logic was reflected in the behavior of the universe, what evidence would there be for it being independent ?

    That’s not a test. At least not of de Morgan’s laws.

    And why on Earth not ? Why is looking at the trajectories of planets and saying “yep, they’re at the place they’d be if they followed ellipses all right” a test of Kepler’s laws but looking at statements and seeing that they do follow de Morgan’s laws isn’t a test of them ? Other than one of them being a wrong approximation and the other being true, I mean.

    Considering actual pairs of statements is a foregone conclusion, unless
    one makes a mistake and fall short of the Platonic ideal. That’s what
    distinguishes it from physics, say.

    Yeah, it’s a foregone conclusion BECAUSE DE MORGAN’S LAWS ARE TRUE. Unlike all scientific theories, which are approximations.

    By that standard, if we ever discovered the true fundamental laws of physics you’d call them untestable because every test would confirm them.

    Actually you probably wouldn’t, because the true fundamental laws of physics would be so weird and counter-intuitive that no human would imagine them to be true without exhaustive testing, unlike de Morgan’s laws which we apprehend pretty well. But that’s an artifact of our brain and the kind of things it needed to know in its evolutionary history, not a statement about how relatively true the real laws of physics and de Morgan’s laws are.

  • Joshua

    I’m finding myself tempted to repeat myself, so I think I’ll just say that we can agree to disagree. I expect everyone else has left. However, just to clear up something:

     You’re the one who asserted that logic isn’t part of the universe

    That would seem to imply that I felt the universe wasn’t logical, which isn’t the case. My position is not that the universe lacks rationality, but that the Platonic ideal of logic comes from God, and that the rationality of the universe comes ultimately from God, not itself, as a reflection of his character as the creator.

  • Caravelle

    I’m finding myself tempted to repeat myself, so I think I’ll just say that we can agree to disagree.

    Looks like. Do you understand what I meant when I said your justifications were begging the question, though ? What I think happened is that you’re assuming that logic isn’t a property of the universe. Which is fine. But don’t confuse assumption with established fact.

    That would seem to imply that I felt the universe wasn’t logical, which isn’t the case.

    It wasn’t meant to imply any such thing, and I can’t imagine what I could have said to make you think I intended it to. Surely this whole discussion has been premised on the universe being logical. It’s just a rephrasing of what you actually said, which is “logic isn’t a property of this or any other possible universe”.

  • http://twitter.com/FearlessSon FearlessSon

    Thanks for the clarification. So you’re suggesting that indifference from a god would inherently undermine humanism? I rarely hear anyone suggest that such indifference might have its positive aspects, such as not having to try to please the god or endure its criticism.

    Sorry for the long delay in reply, I had not been keeping up with the thread.  

    The horror that Lovecraft evokes is the feeling of being small, powerless, and insignificant in the face of forces far larger and inscrutable than oneself.  Now, you could say that this already exists in many people.  The belief in God or gods is generally an expression of this, as is a more naturalistic view of the vastness of the material universe.  However, both of those previous models can be understood and manipulated.  An all-powerful God could certainly smite people in an instant, but generally does not, suggesting that either such a god cares about humanity, or can at least be placated with the proper observances.  And just looking at the vast universe with an eye for things like physics and chemistry, certainly its scale is far more vast than humanity can manage, but it also follows its own internally consistent rules which can be understood and exploited.  Such belief systems certainly imply forces beyond what we can control, but they are still forces which we can understand and affect.  Having that gives us an “out”, a source of hope we can cling to.  

    The horror of Lovecraft’s deities is that they cannot be affected or stopped, and do not care what happens to us.  People who are smited and consumed were not done so because they were sinners against the Old Ones, but simply because there were there.  Trying to understand whatever sort of logic they follow is equally futile.  The human brain is so tiny in its ability to conceive compared to these other forces than any attempt to do so will fail, and often result in madness as the mind struggles to accept things that simply cannot fit into it.  It is true that many of these Old Ones have worshipers, cultists who try to hasten their awakening, sorcerers who try to tap them for power with careful sacrifices, etc.  But these too are insignificant.  The cultists are like moths drawn to a flame.  Overwhelmed by the sensation of it, they find themselves drawn to a source of power they do not understand but cannot turn away from, even knowing that they will be burned by a force that does not care one whit about them.  The sorcerers are like the mosquito which has figured out that it can make a larger creature scratch by biting it in the right place.  It just has to be sure that some other insect is in its place when the hand comes down to swat the bug away, turning that swat to its own purposes.  

    A caring god can be trusted to love creation.  A malevolent god takes enough interest in mortals that it can at least be placated or avoided.  But an uncaring god can be trusted to do neither.  It cannot be fought, it cannot be reasoned with, and it cannot be understood. For these reasons, many who confront them end up going mad with despair, knowing that all they do is ultimately meaningless.  Nihilism overcomes any hope or optimism they had.

  • Anonymous

    Explain the Trinity then, logically.  It can’t be done.  Christian theology has long held three can equal one and one can equal three, where God is concerned.

    One being, three parts.  Like the old clover analogy… there are three leaves, but it’s all part of the same plant.

    In the defense of Dungeons & Dragons theology, their pantheons actually have some consistency and provide believers tangible evidence of their existence.  They usually grant their most devout followers boons for following their principals and furthering their goals, and since there is a pantheon of them, each with different areas and outlooks, it is hard to say someone’s belief in another deity is “wrong”.  If they display those boons, then their deity exists.  There is hardly any room for theological argument.”

    Not neccessarily, you can apparently channel divine energy yourself if you believe hard enough.  It’s… not incredibly consistent.  And, of course, there is in universe debate on what exactly a ‘god’ is…

    I always wondered why the solution to the barber paradox wasn’t “The barber is a woman, who doesn’t need to shave.”

    Because the original paradox specifically states that the barber is a man.

    Basically, I’m just observing, nobody seems to want to bother believing in Cthulhu. I’ve always thought this is interesting and maybe a little suspicious. Why *not* an omnipotent, evil god?

    Cthulu is/was hardly omnipotent.

    To put my reactions into more geeky terms: The ideal character in a campaign where Satan is the main threat is a badass packing holy water and a BFG-9000. The ideal character in a campaign where Cthulhu is the main threat is an illiterate Olympic sprinter.

    The ideal character in a campaign where Cthulu is the main threat is a boat captain.Or an mech/ersatz-Eva pilot.

    Whoops. My comment was more about the horror of indifference to humans in general, not Christians specifically. I don’t think that Christians are necessarily more susceptible (I don’t think Christians are a homogenous enough group to make any broad statement like that), nor do I think the horror comes from selfishness. For instance, I’m agnostic, but I am firm in the opinion that we’re pretty hot stuff as a species. I’ve heard some about some impressive cognition from, say, ravens, but I don’t see any of them landing on the moon. So I see Indifferent God as scarier than Evil God more because of humanism than anything else.

    Huh?  Whether the god cares about humanity or not is irrelevant to our ‘hot stuff’ status.  Besides, it *is* a pretty big universe, so we’re probably not the only awesome dudes around…

    You mean, like every experiment in science ever ? We can test that some events are reliably followed by other events in a predictable manner consistent with the concepts of “cause”, “consequence” and “mechanism”. It’s as testable as anything is in science.

    Yeah… but now try an experiment falsifying that.  And rembember that ‘random’ is a valid cause/consequence/mechanism.  As is Godwillsit.
    “I don’t think that humanism would necessarily be undermined by the presence of IG. I think people might continue on with it in a spirit of defiance towards the uncaring universe.”Considering that secular humanism is basically already this (just skipping the ‘god’ portion of ‘uncaring’, yeah, I’d think so.

    - I can imagine the laws of physics being different; I can’t imagine logic being absent. Authors who mess up the laws of physics are called SF/F authors. Authors who mess up the laws of logic are called absurdist.

    They still follow logic.  It just might not be *earth logic* so to speak, or even logic related to the story, but there’s still a correlation.  The street curves in on itself because it represents the futility of modern life.  The train station suddenly turns into a burger because the author was hungry. 
    “We wouldn’t say such a thing because we probably wouldn’t have a concept of “causality” at all. But I’m not talking about what hypothetical inhabitants of such a world would say, I’m talking about whether such a world would be perceptibly different from ours. And besides, the only options don’t have to be “totally random” and “totally causal”. After all if we’re throwing logic out the window we don’t need consistency even in the inconsistencies… You could have a Lewis Carroll-like world which is mostly causal but contains exceptions. Can you tell the difference between your world and Wonderland ?”Just because events appear unconnected doesn’t mean they really are.  There might be events working behind the scenes, it might be what the local diety finds amusing, it may follow the laws of Narrative Convention, and ‘It happens randomly’ is still a cause.

    Again, why aren’t the rules of inference and the set of axioms and all valid statements themselves part of the universe ?

    Because they’d work for arbitrary axioms and valid statements?

    … Let alone not existing. I notice you haven’t answered my question about whether either the laws of logic or the laws of physics would exist in the absence of anything to follow them.

    Well, the statement that ‘nothing exists to follow them’ is a logical statement…The laws of physics are a property of the universe, the laws of logic are a property of reality.


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