In Which Zach Philositates

I was listening to science Friday’s discussion with Sam Harris. For those who don’t know, Sam Harris is currently pushing the idea that science can determine ethics. I suspect this is not the case, but more importantly, I found his arguments problematic. I haven’t read his book, so I won’t make a critique of it here.

I did however make a critique on twitter. Interestingly, I got a few comments bringing up the Problem of Induction. The basic idea is this: there is no proof that the future will be like the past. This might seem innocuous until you realize that it includes the view that all science stands on an uncertain foundation.


I confess that, although I’m a strong believer in science, I would normally concede the problem of induction. That is, I’d have to agree that science is based on the assumption that the past will be like the present. Today, I changed my mind a bit on this, and I’ll tell you the line of reasoning.

First, let me define “science.”

My philosophy of science (as a theory) is this: Science is the assumption that facts are knowable by repeated observation (1) and that logic is real (2).

My notion of science the method is this: Using 1 and 2, perform experiments to determine facts.

There’s obviously a bit more to it, but I think everything else can be built on the above. For example, the idea of a scientific “theory” is essentially a logical framework you use to suggest experiments. So, even though I don’t reference it directly, it’s in there.

My basic view as of this morning was that in order to do science, you assume 1 and 2. They *seem* to be true and to produce results, but they can’t be proven. This is probably true, but leaves out an import fact: they also can’t be disproved.

Why? Well, let’s look at 1 and 2.

I’ll start with 2, since it’s the easier one to explain.

If you wanted to disprove the realness of logic, you are obligated by the nature of the task to use logic. That is, in order to “disprove” logic, you must use logic. If you disproved logic, you’d then have disproved the logic you used to disprove logic. So, your conclusion that logic was non-logical would be wrong. You see how you quickly end up going in a loop, somewhat like the “This statement is a lie” paradox. Or, to put it more succinctly, the demand to “prove logic is real,” is tantamount to saying “create a paradox.”

From here, it’s easy to see how 1 also breaks down. In order to make an experiment that falsifies 1, I’d have to make observations. In other words, I’d have to make observations that disprove the idea that making observations is meaningful. Again, you get a paradox.

Lest you think this sort of argument could be made against any assumption, let me provide an illustrative example: Say someone says “the sky is blue.” Well, I can easily make observations that suggest it’s blue and do experiments to prove it. For example, I could say “If the sky is blue, I should be able to detect a lot of blue wavelength light if I point a detector at the sky.”

So, you see there is a qualitative difference between these types of assumptions. I put it to you that there are not simply “assumptions,” but rather there are certain cases of assumptions:

A) Normal assumptions – assumptions that can be proved or disproved. (E.g. the sky is blue, 2+2 = 4)

B) Unprovable assumptions – assumptions that can neither be proved or disproved. (E.g. polygamy is bad, Santa Claus exists, etc.)

C) Weird assumptions – assumptions that cannot strictly speaking be proved from earlier assumptions, but whose disproving implies a contradiction (E.g. Logic is logical, observations can be observed).

The assumptions that underlie daily life are in A. The assumptions that underlie theology and some philosophy are in B. The assumptions of science, I believe, are entirely in C.

Science indeed does rest on assumptions, but they are not assumptions in the typical sense. They’re a bit stronger than that.

Additionally, the problem of induction as stated “we can’t assume the future will be like the past” contains logical problems as well. Let’s parse out what this statement means.

We can safely say the simple case of this is not a problem. Of course we know there will be some differences between past and present. The universe will expand and the stuff in it will move around. Few have seriously argued against this, unless you believe that Zeno’s paradoxes imply that motion is an illusion. Science, of course, can exist despite these changes.

The next case would be the physical laws. But here too, science requires no changes to accommodate a universe in which physical laws change. Consider, for example, a universe in which the “fundamental constant” G changes over time. This would seem weird to us, but could certainly be understood in scientific terms. Hell, we might even be able to quantify its rate of change, leading to a “deeper” constant. If that one cycled as well, we could go yet deeper. Even if this recursion continued infinitely, science could still grasp it. It is, for example, not a problem for science that there are infinite digits of pi.

Or, to get even weirder, we could imagine a situation in which the law itself changes. Gravity obeys the inverse square law. But, what if it turned out distance squared was just a little off. What if it was actually distance^(2 + (2^-googol)). And, what if it changed by 2^-googol every 10 billion years? This would certainly seem strange, but there’s no reason science couldn’t accommodate it. In fact, the change would be quite easy. We would just insert a time factor into the equation. This would cause plenty of mathematical headaches, but would be no means expel gravity from the realm of science.

So, exactly what is meant by “the future will be like the past?” Or, to put it more illustratively, “what sort of past-future difference would invalidate science as we know it.”

I don’t have an answer to that question, but I tried to think of something. The best I could do was to imagine a universe in which logic doesn’t work how we think it does. Like, perhaps 2+2=4 was right yesterday, but will have a slight rounding around tomorrow. But, this doesn’t work because if 2+2=4.0000000000000000000000000000000000000001, it’s simple algebra to prove weird things like “0=1/0.” Of course, we could then say “well, maybe in this universe algebra works differently too.” But, this is essentially arguing something to the effect of “well, what if I use illogic?” As mentioned above, I believe this sort of thinking fails because it is self contradictory. Using an “if-then” statement to prove illogic results in an internal contradiction.

What if we try assailing assumption 1 this way? I believe we encounter the same problem. You might propose a universe in which the more you observe something the less likely it is to be true. But here again we have internal contradiction. If observation of this rule is made, it makes the rule less likely, which makes observation more valid, which makes it less valid.

After thinking about this for a while, it seemed to me that I’m no longer certain the problem of induction is real.

I admit that it is perhaps disconcerting to think that logic isn’t self proving. But, it is comforting to think that (at least) logic cannot self-disprove.


Hope that all makes sense. I’m sure I’ll get plenty of critique (especially from people familiar with Godel and Hofstadter), and I’m looking forward to it!


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43 Responses to In Which Zach Philositates

  1. Telanis says:

    Great post. Was this inspired by the logic-disproving XKCD from a few days ago?

  2. Robert says:

    I think that that does make sense.

    The Problem of Induction, when viewed through the lens you’ve described, becomes a reminder that there may be unexplored elements to the problem under examination; Science needs to remember that it is still hypothetically possible that repeated observation tends to cause the observed phenomenon to be less likely to happen again next time (and, more realistically, other seemingly-bizzarre interactions may be happening that the observer isn’t aware of or is unintentionally ignoring).

    Then again, I like playing with paradox (especially temporal ones), so asking me if a paradoxical explanation makes sense might not make much sense.

  3. WT says:

    I can only accuse you… of awesomeness

  4. Edible says:

    But logic CAN self disprove. You’re saying that using logic to disprove logic is illogical. So? If you disprove it, then nonlogic is the case, so there’s no problem surely?

    • ZachWeiner says:

      Not sure I follow. Could you provide an example that doesn’t result in a paradox?

      • Edible says:

        If illogic is the case, then there’s no problem with paradoxes.
        This whole ‘is logic logical’ thing has been on my head for a while now, interesting seeing it popping up in both xkcd and here.
        I’m finding it hard to bring clarity to what I’m describing, which might be intrinsic in illogic. But by approaching the issue of illogic logically, haven’t you already made the assumption that it is not the case? There is no way to trial for it, empirically or rationally. It either is or it isn’t, and we can’t necessarily say it’d have any effects on reality either way.

        • Chris says:

          Like this. You’re basically just doing a proof by contradiction.

          Also, you could possibly do proofs about one logic using a different logic.

          Although that depends on the precise definition of “logic” we’re using “a logic” vs. “logic”).

        • J-Money says:

          I think I agree with you, but my head ploded there so i might be wrong…
          But my arguement is that you say that to disprove logic, you must use logic, which creates a paradox. Which is a problem. But it’s only a problem according to our logic. In illogic, paradoxes make perfect sense, and could even be the illogic version of what we logicals call a ‘proof’, since paradoxes are sort of un-proofs, but in illogic could almost operate as proofs do in logic.
          tl;dr: screw illogic, it’s to effing illogical.

          In case you didn’t notice, the above was 90% me BSing. BSing well. See if you can identify the 10% that isn’t BS.

        • Zaq says:

          If you can use logic to disprove itself, creating a paradox, this could mean that logic is an ineffective approach all together.

          When working within the realm of logic, you would think that if logic disproves itself, then the method used was faulty. However, the fact that the method can disprove it self is evidence that logic is not the ideal approach.

          To create a better approach, or even a better system of logic, we would need to think up an ideal system with which we can objectively disprove things without being able to disprove our method.

          To do this is actually quite simple, the one key factor that science theory has overlooked in logic is

          (Hello, this is Zachary’s mother, or Zaq, as you knew him. Apparently, my son had a brain aneurysm as he was writing this to you. I hope we wasn’t about to reveal anything of historical and scientific significance. I am truly sorry. Have a great day!)

      • Christian says:

        Surely if logic requires statements to resolve to yield no paradoxes, illlogic must occur when statements don’t meet such criteria, and aren’t required to do so (or not do so)? I suppose if you were able to look at the universe, and observe an unresolvable paradox, then that would disprove logic? I’m not well versed in such things and am just speculating, so I’d be interested to know why I am wrong.

    • Lalsacious T says:

      I’d say [citation needed,] but No.
      A logic can prove insufficient to consistently describe its algebra (i.e. a Mathematics Vade Mecum with cliffhangers is possible,) but there are tells and provisos as you construct the logic, e.g. that you are taking a limit of say, cardinality of real numbers in the algebra, as a working figure.
      Moreover wasn’t this supposed to be a direct follow-on on how Zach needs to be working mad telescreening rather than studying to get tension going on? Neat story anyhow. I sure as hell wouldn’t trust my work fueled by even 70% legumes (as opposed to 18%ish.) Oh well, it’s not like they’re Mars-mission rated webcomics, or rather Revolutionary Guard v. Western Inspector approved Nuclear Enterprise.

      I am of course hanging out for late February when he kills off characters for season sweeps. (Say, the promoter who came of age in the ’70s and is therefore [toxic like a thorium cow.])

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  6. Sigma says:

    What (I think) it all adds up to is that humans reason by induction and logic. If your brain is human, then X happening repeatedly after every time you see Y will make you believe “X happens after Y” is more likely to be true than “X and Y have no relation and every prior observation was coincidence”

    The problem of induction is the problem of arguing with hypothetical non-human brains, and expecting to convince them of something. Imagine you meet a magical entity that implements reverse induction, the more they see something the less likely they expect it to be. You could point out that induction works frequently, and they’ll nod along and say “yes, of course, that’s what makes it so absurdly unlikely!”. To them, that reverse induction works is continuously shown not to work is, by reverse induction, something that confirms it. That might seem ridiculous, but that’s because we are humans and we run on induction. I’m convinced that this is a [i]good[/i] thing, I’d much rather be an inductivist than a reverse inductivist, but it doesn’t change the fact that I have come to that conclusion through my inductivist reasoning.

    Imagine, further, another magical entity whose idea of truth is whatever is written on the mystical stone of truth. You could endlessly argue with them (I shall affectionately refer to them as “stoners”), but it is impossible to convince them of something that contradicts the stone is true. You might be the most skilled orator/mind hacker in the world, but if you don’t change the “stoner” circuitry in the brain, then one look at the stone will convince them you are wrong. Much like humans can mistakenly believe that stabbing yourself doesn’t hurt, but ultimately if you repeatedly stab yourself and it hurts, it will seem false. To a reverse inductivist, it will seem true. A stoner will wonder why you’re stabbing yourself instead of asking the stone.

    The problem of induction becomes a real problem if you believe you should be able to justify your beliefs to any possible mind. I just give up and say “no, I cannot ultimately justify induction based on something further, but my brain still runs on induction and I can’t change that nor do I see any reason to. Maybe I’m wrong, but I don’t think so, I cannot think so unless I change my brain circuitry, and I don’t want to change my brain circuitry to adopt a stupid thought pattern, no matter how sensible it will seem afterwards and how stupid my current pattern will seem”

    The deal with logic is the same. Human brains think that “a therefore b” means that if a is true, then b is true. A non-modus-ponens-er might know that “a therefore b”, and “a”, and deduce “not b”. You can’t base modus ponens on something deeper, it just seems true to your brain, true to the extent it’s the kind of thing “truth” should be made of.

    Whether science can show murder is wrong depends ultimately on what you think “wrong” is. I don’t know what Harris’ arguments are on the subject, so I’ll refrain from commenting.

    • Edible says:

      I do believe that logic is something that is in the human brain, just as induction is. It might to philosophers seem like a good retreat, but even tautologies are not safe! Logic is, in my view, the associations between bits of data in the mind, and the way that they are combined together. Now, unless you are a dualist(lol) the braining process happens on a very physical level. Which is prone to error. Sure, the likelihood of getting something such as “a = b”, “b=c”, therefore “a=c” wrong is small, let alone with repetition, but it is still not saved from the realm of hypothetical error. There is no objective status that I would be comparing “wrong logic” to. I’m using my own brain which is not protected from any philosophical doubt of accuracy.

      Now, while I disbelieve logic does not stand against philosophical doubt, as with scepticism of 100% certain knowledge, I think it’s alright against normal doubt. I mean, outside of ourselves, all that we can know is that the universe is “happening,” to put it in as loose a term as I can. Our entire subjective experience seems to me (from my subjective experience) to be a matter of making sense of the universe. Pulling pieces together. Which I find a wonderful thing. But if anyone tries to make an objective claim about anything, I’m just going to say “wrong”.

      My lack of certainty in logic shows in the incoherence in my writing.

  7. Nathan says:

    This was a pretty interesting idea! Though whenever you mentioned disproving logic with illogic I just pictured a guy running around screaming nonsense.

  8. John says:

    Zach, these are great reads. However, I have a problem. This website doesn’t have an icon associated with it when one adds it to one’s bookmarks. I have a rule that I can only put bookmarks on my browser’s toolbar that have icons (I delete the text so it’s just a nice picture).

    I was hoping that maybe one day you could perhaps draw a picture for weinerworks? I would love to bestow it in my “check daily” bookmark bar.


  9. Tony says:

    Very interesting.

    Godel did invent a logical structure that could be used to ask questions about that same logical structure, so I’m somewhat skeptical that more cannot be said of the logical structure behind science. But the arguments of Godel are pretty detailed and subtle, so it’s not at all clear to me how these might translate.

  10. Kevin says:

    I’d make the anthropocentric argument that if the past, present, and future have differing laws and responses to actions, life has likely ceased to exist and us along with it. :)

  11. creid815 says:

    Hope I didn’t miss the boat here.

    You note that all assumptions made by science are of type C above. This is not quite true.

    Science assumes that the universe obeys certain laws. This seems obvious now, but it wasn’t so obvious at the genesis of science. It’s easy to imagine a universe that doesn’t obey any kinds of laws, and cause and effect is non-existant.

    Science must also assume that there is such a thing as an empirical, observable world. All sensation that any of us have happens in our brains. So, on a deeply skeptical level, it’s possible that I am the only real person, and the rest of you are just manipulations of my senses in my brain.

    The problem of induction is one that can not actually be solved. Anything that can be proved beyond any doubt cannot add to our knowledge; it must essentially be a tautology.

    On the other hand, I am a hard empiricist. I would say that the assumptions science makes are pragmatic assumptions. Before we can begin to add to our knowledge, we must make these assumptions; otherwise, we will sit around, cold and hungry, dressed in animal skins discussing whether or not the physical world exists.

    I think that the assumption “Reducing human suffering is morally good” is another of these pragmatic assumptions. Before we can get any work done, we have to get past this whole “But how can we know tortured is *bad*?” thing

    • pascal says:

      And that’s what Harris says in his book basically (I’m just at 50% now but it seems his TED-Talk was basically identical to the preface).

      Science builds on some axioms, and it really wouldn’t be that big a problem to create a new science of morality on the axiom that human suffering should be reduced. A large part of the book is spent explaining why this should be sufficient, i.e. human suffering /can/ be measured, and “why shouldn’t we torture people?” can be answered easily. It’s not total either, so he leaves room for situations in which the moral thing to do is increase some suffering (for some/temporarily) to reduce it in the long run etc.

      Also he’s really, really pissed at moral relativists, the “You can’t really prove that killing is bad!”-folk, and anthropologists.

      • Grae says:

        For the record, most anthropologists use cultural relativism as a tool for research so as to reduce bias as much as possible in description of culture, from things such as female genital mutilation / circumcision to the way that they style their hair, so as to present them in their context. Indeed, a growing population of anthropologists is focused upon activism and change with their research which can be traced back to the axiom of reducing human suffering.

        Just for what it’s worth.

        Of course, my work as an anthropologist currently focuses on monkey skulls, so what do I care?

  12. Arturo says:

    I don’t remember where I heard this, but I seem to remember a hearing a claim that logic was an inseparable part of the human mind. It’s not something that exists in the world to be proved or disproved. It is the lens through which we experience and understand the world. We instinctually default to assume cause-effect relationships about the world. Perhaps a creature exists that understands the world in a different set of rules, but we will never have direct enough access to that understand what it means to see the world in a way that is truly illogical.

    In fact when you see failures in logic in people it’s usually the result of an instinctual logical process (relation between cause and effect) being applied improperly (confusing correlation with causation). This reinforces the notion that logic is something we use to perceive as opposed to a pattern we recognize in the universe around us.

    I always thought it was an argument in favor of logic enough that it was a choice between accepting logic as valid and simply giving up the notion of understanding anything. I would imagine if someone truly embraced induction and rejected logic, they would resemble the masked dudes from Xenoclash that did and didn’t do things on random whim. I’m not sure it would necessarily result in cannibalism, tree punching, and pissing ourselves until we die, but when you abandon logic, the sky’s the limit, right?

  13. Jemus42 says:

    I feel the need to swing back to Zach’s original statement on Twitter about the impossibility of proving that something is “bad” (e.g. killing).
    Might be because that’s the only topic I feel I can contribute something, since the whole “logic vs. illogic vs. logic vs. my head explodes”-thing kind of… well, I just don’t quite know what to think about it.

    So, when it comes to ethics, I think my basic statement would simply be that ethics are nothing that can be proved or “un-proved” by whatever science or logic we would apply. Simply because our concept of ethics is based on two main sources (at least according to my understanding so far):

    1) The stuff we got hardwired in our brains, specifically the ventromedial prefrontal cortex. It has been shown to be some kind of center for our natural sense of morality, so when we have to decide whether we hurt somebody for our own personal gain or act against any other “basic” rule of morality, our ventromedial prefrontal cortex lights up and shouts “wait a sec that’s pretty stupid and not that good at all, stop that!” – what’s intersting is that this somehow proves that morality isn’t just a structure in individual societies, the basics are pretty much there in every human (and people with damages in that specific area of the brain tend to turn out as murderers etc very much more likely)

    2) the second thing would be what I now will call “meta-ethics”: it’s mostly that sort of things religion and other concepts human societies have come up with. the give us another, stricter set of rules we are meant to stick to – but they’re not “hardwired” to our brains so I, as a filthy atheist, don’t have a problem to break a rule exclusive to christian society (“don’t swear with god’s name”, for example), but I do indeed have a problem to break a rule religion has picked up from that basic set of rules (“don’t kill”) because it’s much more essential. this is one of the rules that we evolutionarily adapted to, because that people that keep killing each other don’t get to make babies (it’s pretty obvious, I know, I think I’m making a point SOMETIME).

    But well, what to we get out of this? Since it’s all about logic and science and proving ethics scientifically and whatnot, I’d just go back to my original statement: our concept of ethics is pretty blurred, I guess. there are basic rules we are used to stick to, due to… well, we just don’t think it’s a good idea to go all apeshit and kill each other. the basic rules to prevent that are the basis for our concept of morality. what we derived from that were linguistic attributes we attached to those behavioral traits, such as “good” and “bad/evil”, so we can brand everything as “bad” that endangers our survival as a society (or in “ye olde cavemen days” our surival as a species).

    the problem I have with these words is that religion (I like blaming religion, I’m sorry) for example enhanced these basic rules to a whole bunch of other things like “abortion is bad” or “research based on stem-cells are bad” or “don’t you jerk off, it’s BAD!” – those are not fundamental rules. those are rules (christian) religion is forcing on us, messing with our concept of “good” and “bad” – because these words just aren’t sufficient to describe the actual width of the ethical spectrum we would actually be required to differentiate these days (in our ever so rapidly changing world, you know the drill).

    since I got a little lost know, I just throw in this neat little article about the so-called “monkeysphere”:
    why did I to that? to prove a point. The bottom line is: humans are physiological incapable of living in a functioning society that contains more than about 150 people. we simply aren’t smart (for lack of a better word) to live in our globalized society these days where we’re practically required to live in societies of much larger numbers (log on to the internet – BAM – society of a billion freakin people). and that’s where relativism goes to waste.
    At least it did, in my head, some time ago. I’m not sure whether I’m able to reproduce my thoughts now (it’s pretty late in germany right now), buuut…

    …as I might have been able to show you, what we call “ethics” is – at least from my point of view – a overanalyzed cluster**ck of different concept we can’t quite get a hold on seperately, and now we try to go for a scientific approach on that? I honestly don’t think so. You may think that I’m just using the “subjectivity”-bomb to avoid a difficult thought, but honestly, I don’t see the basis for a scientific approach in anything I know about ethics, simply because it’s based on things science could easily call irrational or useless.

    so… let me close with this: as far as I can tell, the laws of nature didn’t intend to bring up monkeys with large brains to crack their freakin heads in an approach to grasp the overall concept of reality and shove some “meaning” in it.
    simply for the sake of argument.
    hope ANYTHING I said tonight qualifies as “not completely bullshit”.
    (and yes, I know it’s kind of off-topic here.)

    sincerely, with a smoking brain from all the tinking,

  14. Grant says:

    I have a problem with your argument, which can kind of be summed up as this: Disprove God. By certain definitions the only one who could truly do this is God. But if he does it, then he must exist because we used him to do it, so he can’t do it. The inability to disprove something =/= proving it.

    Full disclosure: I didn’t even read up to the A) B) C) part; this caught me on my way to bed…I’ll remove my foot from my mouth tomorrow some time if it’s necessary.

  15. Eikinkloster says:

    “Each of us believes that certain things are wrong, not because we believe they are wrong, but because they really are wrong. And that applies to the moral relativist as well.” -Regis Nicoll

    The moral relativist in me will attempt to explain what we really mean by “believe” and “wrong”, before disputing Regis’ assertion:

    “Belief” means “your best guess as to what is true” (Sam Harris). Whenever you *say* (and mean) certain things are wrong, that *is* your best guess. You say it because you believe it. Hopefully, your best guess is right. But just saying your best guess is right is redundant. You say it is right because it is your best guess.This is a not so a hard concept to grasp. The following is harder:

    “Wrong” in a moral sense means “I feel a strong discomfort when I consider doing this”. In this sense, nothing is intrinsically wrong, but there will be things considered “universally” wrong, and spoiling “the value of life” will be probably the first “universal” manifestation of an “universal” sense of wrong: we all want to protect our physical integrity, else we would end up dead very soon. We *value* the physical integrity of our loved ones even above our own, in this cases we can *trade* our lives for theirs. This is where we will “universally” reach similar social contracts, in which, in essence, we will all agree not to take each other’s lives, so that we might experience a heightened sense of security about our own, and our beloved ones’ own.

    It is interesting that this concept will easy the understanding of the exceptions in which we tend to generally agree it is not wrong to let a human life end. One of them is when a person is dying due to old age. Somehow we know that death, in this case, isn’t “wrong”. Quite the contrary: it comes a time when the concept of going on living is the one “I feel a strong discomfort when I consider doing it”, i.e. is the one I “know” is *wrong*. Living in agony, trapped in a feeble body, with a numbed mind I no longer recognize as my own.

    The guy in the video Regis refer to ( tries to come up with several criteria through which embryos could be differentiated from a human individual in order to lack human rights. He wonders, “is it age? But we all have different ages. It is size? But we all have different sizes…” in attempt to invalidate any criteria, showing how it would extend to ourselves and our beloved ones, showing how each of them would be “wrong”, i.e., unsettling.

    My best guess is that the “right” criteria, the one already in use in everyday life, is somehow related to having a mind we can communicate with. That’s how we’re a lot more in agreement about protecting the lives of our dogs than that of our cows. And why a *natural* abortion is nowhere seen as the same kind of tragedy as the death of a child. Embryos don’t even have brains.

  16. Necandum says:


    Assuming God’s existence is a little different. What you are making is a claim about the observable universe, not a basic axiom.


    What Zach seems to be talking about are fundamental concepts that are necessary for us to understand our world. If we do not make these assumptions, among a few others, then we have no reason to do anything whatsoever. I.e We would be frozen and unmoving ’til death

    Saying that looking at the world helps us understand it is a pretty much a tautology. If, like someone said, there are forces that exist that we can not directly observe, this leaves us two options:

    1) The forces make no observable impact upon our world. I.e they are not part of our realm of existence and we can and should ignore them.

    2) The forces, while themselves unobservable, make an observable impact upon our world. We can then deduce the nature of these forces from their impact and make predictions. We may have noticed that such forces are everywhere (gravity, electricity, quantum mechanics), but we have no problem dealing with them.

    A few objections have been mentioned:

    Making an observation makes the phenomenon less likely.
    First, how the hell does this work? Just because a sentence is grammatically correct, doesn’t mean we should pay serious attention to it.

    But if somehow this were to happen, then the statement itself would be an observation of the nature of the world and we would be able to figure out the rules nonetheless.

    Other beings may reason differently
    Fine and dandy. What matters is the results, not the process itself. If these other beings can accurately predict the phenomenon of our world, lovely. If not, then their system is useless.

    Take revelation, for example. Many theologists claim it is a way of finding truth. I.e it is a system separate from logic and observation by which we can learn about the world.

    Does it work?

    No. So its worthless and we can safely ignore it (though in some places you may need to do it quietly).

    For a system to work, you need to justify it to any mind
    I don’t quite understand this. Just because someone doesn’t believe you, doesn’t mean you’re wrong. What matters is how close your beliefs are to reality. How you get there is irrelevant.

    Proving non-existence
    The fact is one cannot prove the non-existence of anything, so we use probability and the Null-Hypothesis instead. Its worked this far, which is an indicator that we should keep using it.

    As for morality, I agree with view that there is no inherent Good or Evil in the universe and these are purely human creations. Face it, the cosmos cares not a whit for any of us and murderers don’t emit eviltrons.

    Instead of seeking an ‘objective’ morality, we should instead construct one based of a few simple axioms (ones in keeping with our biological morality) and then use science to see how to best achieve the aims implied by those axioms.

    If we come into contact with an alien society that has a different set of morals, then we have a problem.

    The best solution I can see would be to act towards the other so as to uphold whatever morality we share and whatever negative principles (rules that prohibit action, rather than compel it) that the other holds.

    But yes, in that case Good and Evil would be completely in the eye of the beholder.

    • Sigma says:

      “Other beings may reason differently
      Fine and dandy. What matters is the results, not the process itself. If these other beings can accurately predict the phenomenon of our world, lovely. If not, then their system is useless.

      Take revelation, for example. Many theologists claim it is a way of finding truth. I.e it is a system separate from logic and observation by which we can learn about the world.

      Does it work?

      No. So its worthless and we can safely ignore it”

      Problem being, the way to evaluate if a method to know works, is in itself a method to know. Induction works because it produces results that line up with our observations most of the time, but that’s the inductive criteria of evaluation. Reverse-induction doesn’t work by inductive criteria, but it does by reverse-inductive criteria (it very rarely corresponds to observation, which is exactly what a reverse-inductivist calls a success)

      If your only method of knowing is revelation, then your only way to evaluate revelation is revelation. If revelation says revelation works, then it does, by revelation-based evaluation criteria.

      “A way to evaluate whether a system works that doesn’t make any unjustified assumption” is an equally difficult problem as “a way to obtain knowledge about the world that doesn’t make any unjustified assumptions”. Neither is solved (there’s no reason to think either *can* be solved), and you can’t invoke one to demonstrate a solution for the other.

      I think induction is correct. In fact, I’m about as sure as I can be that induction is correct, and see no reason to stop using it. But that is true only because I am an inductivist in the first place.

  17. Rylan Nelson says:

    I don’t understand your definition of assumption C. It seems to be a bit of a tautology argument, that this is true, because it is true. I would liken it to Bruce Lee’s response to a student asking him how to kick faster: “kick faster.”

    You argue that one must use logic to disprove logic, and that logic is therefore real. It seems someone could say “Logic is not real, because I just ate three baked potatoes.” I also don’t think that observations must necessarily be observed. One does not have to make an observation to disprove that observations are meaningful. Unless you count metaphysical observations. I feel personally that it could be said “observations are not meaningful, because as Plato’s cave allegory postulates, people do not tend to observe the true nature of things, only metaphorical ‘shadows on a wall.’ If this is the case then we cannot say with any certainty that the sky is blue, or that death is real. Since we only see ‘shadows,’ it is possible that there are colors and shapes we are unable to perceive, or that when a person dies there is a literal soul that escapes into a meta-verse. If we cannot, as humans, see these things, than what we do see cannot be counted as meaningful. For what good is there of geometry if there are shapes that we cannot conceive of? Why would we speak of gravity when it is possible that souls could fly? And furthermore, how could our observations be seen as meaningful when we constantly disprove them? Observations like the medical helpfulness of drilling holes into the brain to relieve headaches?”

    As it stands, I could be completely misunderstanding you, or I, being only a high school junior, could be completely wrong in my statements. I just feel like “Logic is logical because we use logic logically,” is missing something.
    “I’d have to make observations that disprove the idea that making observations is meaningful.”

    • Necandum says:

      Yay for semi-obscure classical reference!
      But seriously, my thinking is that if ours is a world of shadows and we cannot perceive the “real” world, we are left with two options.

      1)The real world interacts with our shadow world.
      2) It doesn’t.

      If the first is true, then we should be able to discern the true nature of things by observing how our shadow world is affected by the real one. Like the prisoner deducing from the drawn out nature of the shadows and the contrast between them and his own flesh, that they are somehow other and perhaps deducing their source by carefully observation.

      If the second is true, then no matter what we do, we cannot deduce the “true nature of things”, though since our two world do not interact, the “true nature of things” has no influence whatsoever upon our own reality and for all intents and purposes, there are then two realms, and whose is to say which one is truer than the other?

      Now logic is a little bit more different and difficult. I think to have a truly informed discussion, one would need to have some training/experience with it.

      However, from my own meagre knowledge I understand that logic is a system of thought that can be used to describe the world, based on a few axioms that seem fundamental to our plain of existence. I think its rather odd to ask the question: can logic be proved?

      Why do you need to prove that it works in all situations, no matter what? Why not keep plodding along, keeping on using it until you run into a problem that you can only solve using something else? It is after all only a tool for understanding the world. As long as it works, use it. When it doesn’t work, discard it. End of story.

      Also, I read the following (paraphrased) somewhere recently, no idea where (maybe even on this blog, my memory is that bad!):

      “No system can be both complete and consistent. Logic is necessary incomplete because it is consistent.”

  18. Captain_Sakonna says:

    I’ll go back to the assertion that the problem of induction might not exist for science.

    You did a good job of showing how science can handle variation in the laws of the physical world over time. But what you didn’t address was the possibility of completely random variation. Even then, if there is some sort of pattern or regularity within the randomness, we can use probability and statistics to understand the universe (as is done in quantum mechanics). But suppose there is no pattern at all, and the universe is essentially chaotic? Then science breaks down, or at the very least becomes non-useful. The usefulness of science lies in its analytical and predictive power, and you can’t analyze or predict anything under such circumstances. You can’t establish cause-and-effect relationships if the effect which is linked to one cause today might end up linked to an entirely different cause at an unknown time in the future (perhaps the next day, or perhaps the next second — you have no way of knowing).

    Basically, science works as long as there is order in the universe, which is precisely what creid815 was saying. It can handle time variation perfectly well, but only as long as said variation follows an orderly pattern.

    Here’s where the problem of induction comes in: based on our observations, the universe appears to us to be orderly. However, it’s entirely possible that we are in the midst of an unusual quiescent period, and the universe is on the cusp of becoming chaotic. We have no way to prove with absolute certainty that the law of gravity won’t change, or even cease to exist entirely, in the next five minutes.

    Does this have any relevance to life as we know it? Not really. If we allow for the possibility that the laws of the universe might go chaotic at any moment, there’s still no reason to change our behavior. We can’t possibly predict how the universe would change, so there’s no reason to plan for the eventuality. Therefore, practically speaking, we might as well go on living like inductivists, even if we acknowledge that induction has problems. I’m curious about how Sigma’s hypothetical reverse-inductivists would manage to survive or accomplish anything. Let’s say they predict that there’s a high probability gravity will be invalid tomorrow, because it’s been valid so many times in the past. Well and good, but they can’t make any prediction about what will take its place. Will the earth start repelling us instead of attracting? Will we just float motionlessly? Will we bounce around randomly, or unaccountably move in circles? In the reverse-inductionist’s mind, all these possibilities are equally likely, since none of them has happened before, ever. Or let’s say they decide that substances typically seen as food will cease to be nourishing soon. What should they eat instead? The best they can do is pick up a random substance and hope it satisfies their hunger. So they can’t do anything except resign themselves to the notion that the future is unpredictable. While their philosophy may be internally consistent, it’s not very practical at all.

    The problem of induction also applies to spatial variation, not just time variation. We naturally assume that the laws we recognize as basic and fundamental — the first and second of thermodynamics, gravity, electromagnetism, etc. — apply everywhere in the universe, because, after years of extensive observation, we haven’t found any place where they don’t apply. So if we found a wormhole and managed to zap ourselves to some part of space that hadn’t even been imaged by telescopes yet, we probably wouldn’t expect any difference in the laws. But that might be a mistake. The fact that we haven’t yet found a place where the laws fail/are different doesn’t mean that such a place doesn’t exist. So unless we become capable of observing the entire universe, we can never prove our scientific laws to be truly universal. Unlike the time problem, though, this doesn’t overthrow science. As long as we have laws that are locally valid, we can retain the usefulness of science within our local sphere. We just have to question its predictive power a little bit more, once we leave our home turf.

    • Necandum says:

      Nicely said.

      A question though, how could a system be truly random? I’m guessing you’re just throwing it out as a hypothetical, but when I consider it, my mind boggles. That would be, wtf, to say the least.

      Dodging missiles by turning them into whales, much?

  19. Elithrion says:

    I’ll keep this short just to be different. Reading this post was slightly painful on the whole – talking about science in terms of classical logic is such a complete waste of time. The only thing for which you should really use classical logic is mathematics, for everything else you should really really go with Bayesian reasoning (/decision theory/rationalism). We don’t use science because the Problem of Induction is real or because it’s not, we don’t use science because some underlying assumptions are true, we use science because it’s a good way for gathering evidence that lets us rationally draw high-probability conclusions about the structure of the world. See also:

  20. Necandum says:

    Hmm, I can see where you’re coming from, but I disagree.

    Problem being, the way to evaluate if a method to know works, is in itself a method to know. Induction works because it produces results that line up with our observations most of the time, but that’s the inductive criteria of evaluation. Reverse-induction doesn’t work by inductive criteria, but it does by reverse-inductive criteria (it very rarely corresponds to observation, which is exactly what a reverse-inductivist calls a success)

    I’ll agree with that sucess may be hard to measure, but it doesn’t mean that all methods are equally valid. There is after all only one truth, and so your system’s success can indeed by objectively evaluated, even if you yourself are unable to do so.

    Example: Person relies only on revelation. Can they build, or find out how to build, a nuclear reactor? No. Can they accurately plot the procession of the stars? No. Can they elucidate the origin of life? No.

    So you see, no matter how successful they think they may be, reality says otherwise. After all, reality is the final measuring-board and the ultimate criteria, not our own opinions. I believe science based on induction works not because of induction, but because we have cool stuff like magnets and jet skiis. It get results, no matter how you look at it.

    Of course, if you’re saying that looking itself determines whether something works, then you’ve completely lost me. Either I’m too dense to understand (not likely), I don’t have the proper background (likely), your explanation is insufficient (perhaps) or the concept is gibberish (I’m leaning this way).

    Btw, apologies if I’m coming off a bit flippant, my current situation doesn’t really allow for seriousness. =).

    • Sigma says:

      I’m not saying all methods are equally valid. Like I said, I’m as sure as can be that induction is correct, and revelation, reverse induction and probably any other method that yields results different from induction are wrong and stupid ways to approach the world.

      What I am saying is that any test of a method of knowing has to be based on a method of knowing. Induction, reverse-induction and revelation all have the distinct feature that they are self-confirming, that is, any one of those “works” if tested by themselves. There might be other similarly self-confirming methods of knowing, but that’s besides the point. The question is, how do you choose a way to test your method of knowing?

      You claim that a revelator cannot build a nuclear reactor, or plot the procession of the stars, and this is true. But how do we know this? Because we have observed it to be so, in other words, used induction. The revelator might simply look at a piece of revelation that says they indeed succeed in building a nuclear reactor, and this will seem as true to them as the fact that they didn’t seems true to us. All our tests of induction assume induction is true, because we don’t have any other way to test it. Saying that induction is true because we observe it to work is equivalent to saying induction is true because induction says so, which is the same kind of reasoning as “Revelation is true because revelation says so”. You wouldn’t trust someone who came to you and said that they hold the Book of Absolute Truth, and as only evidence opened page one, which reads “Everything in this book is Absolute Truth”. It’s circular reasoning, and so is proving induction by observing it to work (and so is proving reverse-induction by observing it not to work)

      That doesn’t mean these methods are equally valid or that we should use them in equal measure. It does mean that it is impossible to prove which one is true. I will continue to use induction as often as ever, because induction seems almost synonymous with truth to my inductivist human brain. But I cannot pretend I am basing that on some deeper principle.

  21. Kevin says:

    I’ve always wondered if this proof of logic is very silly or very deep:


    • Lalsacious T says:

      You elided some steps; you need to end in a tautology, and it doesn’t read like a lemma (having all-caps and no Greek, f’rexample.)

  22. OzoneNerd says:

    This all seems worryingly similar to Objectivist logic.

    I think things get a lot easier if you don’t try to make a set of definitely true laws, but justify everything using the rule of succession. If you observe n trials, and s of them are successful, the best estimate to the odds that the next event will be successful is (s + 1)/(n + 2). This is the best answer to the sunrise problem. If the sun has risen and set for the last 1000 days, we rationally think with 1001/1002 odds that it will tomorrow as well. Bayesian probability can solve a lot of problems for us.

  23. Lalsacious T says:

    That’s a weird outcome for Sam’s claims to say science is tenuous. It’s certainly tenuous to see the Irani Nuclear Wonks cited as Top Scientists (see NYT ca. this date); that’s like saying the (fictional) writer in Misery is at the peak of his career in his Biggest Fan’s care. Velcro has not been the end of zipper checking. What I expect instead of course is for the awesome solutions to iniquity and tossers to be forthcoming (like Feminism cranks out, from time to time.) One hopes Sam thinks he has the Gene Sequencing Speed X Prize, set out in scientific understanding of moral issues’ domain.

    Induction scope usually presents the problem; certainly self-defense and that everybody’s out to get everyone (or do that on others’ behalf) are valid; but you learn early that (when, if you had a feral childhood) the flu’s a more imminent threat than that, even before concerns precluded by distantly defensive killing that might fall into scope, traffic that’s murder, etc, and maybe hubris. The Harvard Law Review often tends to try comically to put a reticle on some of those measures to cover cases where e.g. Unicorns turn out to want to fondle small children. Contrawise Sam might aspire to make a precrime computer, formalize law to be consistent, do for law what computers do for real estate (in settlements, or still wackier congressional committee hearings, at random), etc.

  24. Jamie says:

    This may have already been stated, I really only read the first half of stuff, so sorry if I repeat trodden ground.

    Logic as I see it is the use of a set of rules in a step-wise manor to categorize and/ or prove nouns of sorts. So I see the use of disproving logic using logic would be a proof for logic, or at least an application of that methodology. To encounter a truly undecipherable paradox would not be the discovery of logic’s undoing, but merely the discovery of a new category, such as imaginary numbers in mathematics (or just bad questions).

    I think in order to actually disprove the validity of the logical and scientific methodologies we need to somehow discover that past observations provide absolutely no new information about future occurrences of the stimulus. An example would be nothing short of the complete rewriting of all fundamental physical laws of the universe randomly at random intervals. Only if these governing rules arbitrarily change in a fashion defined as unpredictable would that case be true.

    (…and that is how Oktoberfest started – D. Tosh)

    Well, that is my current stance I suppose. Probably wake up tonight at 2am with something a little more coherent.

  25. Evan says:

    “Hope that all makes sense. I’m sure I’ll get plenty of critique (especially from people familiar with Godel and Hofstadter), and I’m looking forward to it!”

    I’m a bit disappointed only one person picked up on the issue of completeness here (and even then only peripherally)! Evidently you’re as familiar with the topic as I am (via Hofstadter), so there’s no need for a lecture here. However you seem to refer to ‘logic disproving logic’ as being tantamount to ‘creating a paradox’, which hits the ear wrong.

    You absolutely hit the nail on the head regarding the situation’s parallels with a Godelian statement (of course), but nothing Godel ever did could really be called “disproving logic”, or even attempting to do so in earnest. What he did was to point out the incompleteness of any logical system which surpassed a certain threshold of complexity (a threshold which “logic” most certainly satisfies).

    Therefore it is possible (trivial, really, in the case of “logic”) to construct “paradoxical” statements which point out the incompleteness of logic. For example: “It is not possible to logically demonstrate that this statement is true.” Although gratuitous uses of “this” as a self-referential hardly touch upon the elegance of the proof, but such is the overwhelming complexity of “logic” that it allows that kind of trivial “paradox.”

    But that doesn’t really impact anything of substance that you said. Regarding the past/future difference in the meaning of induction, I don’t believe anyone’s mentioned Boltzmann Brains yet. This response has gone on long enough without trying to get into what they are in any depth, but the idea is that suppose a universe undergoes a heat death wherein entropy has reigned supreme, and all matter and energy are just chaotically and randomly intermingling for an arbitrarily large amount of time.

    Once in a googol millenia (give or take) the random particle fluctuations line up to form your body, mind, the room you’re in, the chair you’re sitting in, everything (for about, say, 1,000 miles around you). This all came out of nowhere, of course, but if we are to consider ourselves physicalists, then it follows that such a fluctuation could result in our exact brainstates (chock full of false memories and the rest of it).

    Now, all of this will only last a fraction of a second, because just 1,000 miles away is a universe of high-energy chaos descending upon your world at something just shy of the speed of light. But for that fraction of a second, the experience would be identical to whatever you’re experiencing right now.

    Now that’s cute and all, but the real kicker is that in positing such a heat death universe (which is not what ours appears to be, if we are to believe we are not currently in a Boltzmann brain) the probability of that once-in-a-kajillion-years-event of randomeness occurring is VASTLY more likely than our experience being genuinely built up slowly over the presumed course of the universe.

    At any rate, I mention it in case someone really needs help to plant a seed of doubt in induction.

    Finally (and I hate myself for allowing myself to write this much), and least interestingly, who says that the laws of physics should change gradually? Why not have everything change tomorrow? Maybe when the energy density of the inflationary vacuum state cools off to a certain point it triggers some radically new behavior, maybe gravity gets a negative sign.

    Hell, maybe time just ceases, tonight’s the end of it all, the universe frozen in place. Of course any of these hypothetical positions are stupid and unreasonable, but you can’t really argue against induction without relying on dumb technicalities like that.

  26. Telmah says:

    There is a great deal of modern literature on the subjects of logic, belief, inference, and the philosophy of science. For instance, Bayesian probability theory teaches us that beliefs correspond to expectations of the physical world, that knowledge of a thing is mutual information between the knower and the thing, that the observation of evidence allows us to update our beliefs away from max-ent ignorance and toward reality, but does not justify absolute proof or perfect assurance / perfect absurdity, and the sense in which coherent beliefs are logically consistent. Judea Pearl’s work on belief networks formalizes both causal inference and the counter-factual reasoning by which we can speak of “possibility” in a deterministic universe. Ray Solomonoff’s theory of universal inductive inference show how a rational agent assigns beliefs to the set of formally specifiable hypotheses which fit its observations and demonstrates that compression is a quite beautiful, and more interestingly, mind-independent procedure for evaluating the simplicity of hypotheses, which is how we form beliefs about the plausibility of a theory prior to our observations, in accordance with the philosophical principle of Occam’s razor.

    A little scholarship can impart a great deal of strength, and by that I do not mean reading Hume.

  27. Travis says:

    Very late to the game here…

    The only thing I had a problem with in the post was your assertion that “polygamy is bad” as an example of un-provable assumptions. I guess if you want to also assert that psychology/psychiatry and statistics are theologies then you’re right that “polygamy is bad” is un-provable. Without further explanation as to your contextual meaning of “is” and “bad” you could do several studies and prove that in some cases polygamy is good and in some cases polygamy is bad based on people’s experiences, stories as well as some empirical data outside of stories and surveys like stress levels and overall health. Also there are gray areas…Polygamy isn’t always bad. I wouldn’t consider ultimatums to be theological in nature either, if that’s what you were going for there. Bottom line: “polygamy is bad” is a bad example of a B) type assumption.

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