A defense of logical positivism (yes, really)

As far as I know, there’s nothing everyone in philosophy agrees is right. But there are a few things that everyone in philosophy agrees are wrong. Right now I can think of two of them – Rene Descartes, and logical positivism.

Er, well, one of them. Because I kind of like logical positivism.

And before everyone yells at me, I understand this is sort of sketchy. I’m not saying that they were entirely right about anything, or that their criteria work exactly as stated. But it’s like – well, take those ancient philosophers who said everything was made out of atoms. In fact, they’re wrong. Light isn’t made out of atoms, mathematics isn’t made out of atoms, quarks aren’t made out of atoms, et cetera. But they were sure on to something, and I give them much more credit than philosophers who didn’t say everything was made out of atoms.

I am an inexact person, and I tend to think inexactly, and the fact that the logical positivists were working in an area that vaguely points to a cluster of correct things is good enough for me. Let me explain what I mean by “a cluster of correct things”.

In the 1700s, David Hume came up with an idea now called “Hume’s fork”, which Wikipedia describes like so:

Hume’s fork is an explanation of David Hume’s aggressive division between “relations of ideas” versus “matters of fact and real existence”. By Hume’s fork, relations among ideas are strictly divided from states of actuality.

(and before you ask, yes, Hume’s Fork is also a legendary artifact in Dungeons and Discourse)

Then in the 1900s the logical positivists came around; they get described as saying “that the truths of science are verifiable empirical claims and that the truths of logic and mathematics are tautologies. These two constitute the entire universe of meaningful judgements; anything else is nonsense.”

And in the 2010s, the latest Less Wrong Sequence, Highly Advanced Epistemology 101 for Beginners tried to reduce meaningful statements to “two kinds of meaningfulness and two ways that sentences can refer; a way of comparing to physical things found by following pinned-down causal links, and logical validity by comparison to models pinned-down by axioms” as well as combinations between them. This is a really good sequence and I especially recommend Mixed Reference which says a lot of the stuff below only better (I did avoid re-reading it until I was done writing this, so as to keep my brain at least a little in original-idea-mode).

These three claims are somewhat different, but they all seem to have kind of the same idea. They all seem to be saying that we can divide meaningful things into something-kinda-like-science, and something-kinda-like-logic, and that everything else is meaningless. Their differences seem to be mostly how “something kinda-like-science” gets cashed out.

And while acknowledging the importance of figuring out exactly what “something kinda-like science” means, right now to me it seems less important than the overall observation that having even this vague sort of poorly-specified system is a whole lot better than not having any system of this sort at all.

More importantly, this idea is productive. I admit my assertion of its productivity is highly biased, in that by “productive” I mean “things I want to hear fall out of it”, but I do find this happening with gratifying frequency. Usually when this system red-flags a statement as “probably not meaningful”, on further investigation it very often does turn out to be something bad that needs to be thrown out. And when this isn’t the case, I usually gain a much more solid understanding of the statement by trying to see exactly how it reduces to one of these two kinds of meaning or a combination thereof.

It may be that there are some kinds of statements that are meaningful but just plain don’t work this way. I am having trouble thinking of them, but it’s normal to have trouble coming up with statements that disprove a theory you like, and I’m sure I will hear many attempts at them in the comments. But even if they exist, they seem to me much like the “light is not made of atoms” example above – correct, but irrelevant to the fact that atomic theory is really awesome and that if someone goes around saying “That particular horse there is not made of atoms, and no one can force me to say that it is,” they’re probably making a mistake.

As an example of “things that I do think yield to this positivist technique”, let me give some classic examples of things that people say don’t.

Start with mathematics. This one is easy. Mathematical systems are systems of axioms and theorems. These are logical tautologies. Some of these systems seem to describe our world pretty well. This is an empirical observation.

Move onto morality. A little harder. The definition of any moral system is a logical tautology; if I define “utilitarianism” as “act for the greatest good of the greatest number”, I have defined what is…not quite a formal system, but could probably be turned into one if someone were rigorous enough. My brain seems to exist in such a way that it reflectively endorses this system rather than another one. That’s an empirical observation. This isn’t quite what most people want out of morality, but I consider that a feature, not a bug; morality the way most people want it is probably meaningless.

An even harder one: “If Lincoln had kept McClellan as general, the South would have won the US Civil War.” Maybe this describes the output of the logical formal system corresponding to the universe (!) with certain inputs empirically determined by the state of Civil War-era America.(I bet there’s a better way to rescue this one, but I can’t think of it.)

[EDIT: Now that I am done writing this I am looking at the Mixed Reference post above, and it does a pretty good job]

Finally, we come to logical positivism itself, which was famously accused of failing its own criteria by Karl Popper. Once again, everyone agrees it’s possible to define logical positivism. And by analogy with math and morals, now we just need to show that this system, as defined, matches some property we want it to have.

And obviously this is going to be sort of subjective, because “property we want it to have” depends on what properties we want of our ontologies. It might even end up circular, because a lot of the properties I want my ontologies to have probably sound a little like “Doesn’t talk about meaningless stuff, with meaningless being defined as [something that uses a lot of the same criteria as logical positivism]”.

But I think it might also correspond closely to that which can be debated. That is, what is there such that, using reason rather than emotion or made-up pseudologic, we can actually change our minds about and correctly judge as having one probability of truth rather than another?

I welcome examples of this being proven totally false.

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34 Responses to A defense of logical positivism (yes, really)

  1. Chris Hendrix says:

    OK I realize this is really late to the game and this is a relatively minor point, but I’m slightly annoyed no one has said this in over a year. Scott your point on atoms is a bit off-base because you’ve confused the word with it’s referent. The original Greek/Indian idea was of indivisible things which make up all stuff. You are correct that the earliest theories didn’t have a separate thing for light, but when physicists found they could split what we call atoms they did not disprove ancient atomist ideas but the ideas of 18th and 19th century chemists. In the 18th and 19th centuries, chemists found elements that they thought were made up of indivisible things, which they figured were ancient Greek atoms. But when we found those “atoms” could be split, we didn’t change the name of the splitable things, but simply gave new names for the stuff they were split into.

    Let’s imagine for a moment that we’ve revived the ancient Greek atomist, Democritus. You go up to him and say “hey your atom idea was really great! I mean it was wrong, but it was close to true!”

    He replies “Oh? How were atoms proven false?”

    “Well,” you say “first we found there are things that can be divided forever like light.”

    To which Democritus concedes “Ah yes that’s a good point. But do at least some things have atoms?”

    “Yeah actually! There’s only one problem, we split atoms into even smaller stuff we call quarks and leptons. Those we can’t divide, but unfortunately for your theory we can tear apart atoms.”

    Democritus looks at you dumbfounded for a moment. When he recovers his composure he says very calmly, “So my basic point that there are indivisible things that make up matter is right, but I only get partial credit because you decided to mislabel things?”

    “We thought we discovered atoms back a couple of centuries ago, so we placed that name on the stuff we found. We just later split that stuff and decided it wasn’t worth it to rename everything we had.”

    “So you use your reluctance to name things correctly as a knock against my theory?! You’re giving me a C when I clearly deserve a B+!”

    “Wait a minute, how do you know how to use the modern American school grading system for analogy purposes?!”

    At this point we leave the dialog before the crack in the fourth wall becomes a major structural issue with catastrophic results.

    But I hope I’ve made my point. This is a mistake akin to the mistake that causes people to think “if a tree falls in the forest and no one is around to hear it, does it make a sound?” is an interesting question.

  2. peterdjones says:

    > Move onto morality. A little harder. The definition of any moral system is a logical tautology; if I define “utilitarianism” as “act for the greatest good of the greatest number”, I have defined what is…not quite a formal system, but could probably be turned into one if someone were rigorous enough.

    So could “the greatest misery…” or “the highest number of paperclips”. Maths is deduction withing a formal that isn’t about anything outside. Physics is deduction within a formal system that *is* about something outside, which is why physical theories can be falsified if they do not match experiment. But at least we know how to match the symbols of the formalism to bits of reality. True formalisms of morality need to be true about soemthing, but about what?

  3. Martin Cohen says:

    A few remarks.
    Firstly, aesthetics and morality have to be separated from things that are tautologically true or verifiably true.
    Regarding morality, the principle of greatest good for greatest number has some serious problems.
    1. There is no agreed upon way of measuring good.
    2. Even if there were, there is no way of knowing for certain what actions would result in the greatest good.
    3. Even if we assume that we can measure and pre-determine goodness, what exactly do we mean by greatest good? Does it mean highest average? What about standard deviation? Do we want to minimize that? How do we compare two situations where one has a higher average but the other has a lower standard deviation?

    As for aesthetics, there is currently no objective way of measuring aesthetic value and unlikely to ever be one.

    For both morality and aesthetics, the best we can do is to offer some general guidelines. These guidelines may be sufficient to characterize certain things as being either unaesthetic or immoral, but as regards others there will be disagreements. The way to reach decisions on such matters is to discuss them freely and allow people, either individually or collectively, to make a knowledgeable choice.

    Regarding logical positivism, I take verifiability as a definition of meaningfulness. The principle should be self-evident and therefore beyond any need to be shown as itself being meaningful. The only reason why people object is that they want to include as meaningful such foolishness as the accumulation of sin and the cleansing of the soul of said sin.

    Some day, after religion has run its course, we will be able to have meaningful talk about possible ways of acting in the world free of meaningless religious jargon.

  4. 浅草 says:

    “Morality the way most people want it is probably meaningless.”
    I disagree. Just because it does fit the logical positivist ideal, it does not mean that it is meaningless. In a way, logical positivism reminds of religious faith: everything that does not follow from our axioms is meaningless/sinful/heretic.

    “My brain seems to exist in such a way that it reflectively endorses this system rather than another one. That’s an empirical observation.” Really? Is that an empirical observation in the scientific sense of the word? Did you perform that empirical observation?

  5. Doug Spoonwood says:

    I kind of like logical positivism myself. But in several ways it just ends up as shallow.

    In logical positivism, as I understand things, *all* statements come as true or false or MEANINGLESS. That doesn’t even work out for mathematics. The statement “prime numbers are odd” is neither true nor false nor meaningless. It qualifies as undecideable until we have a clarification of what it means. And make no mistake, I intend it here as a statement which I will not clarify.

    Also, what could logical positivism say about truths of human existence or in any way communicate lived experiences between people? Where we the logical positivist books on religion, art, or culture in general? Those books couldn’t get written by the logical positivists, because they all end up as *just* subjective fields. Consequently, not only does everyone have an opinion on them, but all opinions end up as having equal worth in religion, art, and cultural studies. It simply does not usually hold that the opinion of a Da Vinci scholar on the Mona Lisa has the exact same worth as that of a child seeing the Mona Lisa for the very first time. Yes, the child may have an insight that the critic missed. Yes, the child might have a new perspective worthy of more exploration. But, the opinions of the child simply will not have, usually, more value than the critic and the child will know less about the Mona Lisa than the critic. According to logical positivism, since art is *just* subjective all opinions immediately become the same in terms of worth.

    Also, as I understand things, mathematicians will often tell you that mathematics is an art. Or they’ll emphasize the artistic aspect of mathematics. But logical positivism simply comes as horrible at analyzing art, doesn’t it? So logical positivism, if I’ve understood things correctly here, just comes as too shallow to develop a useful perspective to even understand mathematics.

  6. Protagoras says:

    Among academic philosophers, there’s been quite a revival of interest in Carnap over the past couple of decades. Most of the other leading positivists have not attracted the same level of renewed attention, but it has gotten to be a fairly widespread view that the collapse of Logical Positivism was more of a change of fashion than a result of fatal flaws being exposed. So you’re probably not tilting at windmills to the extent that you seem to fear.

  7. Damien says:

    All of some math system might be a tautology, but it takes a fair bit of search and computation to expand a set of axioms into various theorems. I don’t know if traditional LPs dimissed such work as meaningless, but we certainly.

    What about art/aeshetics statements like “I like X”? I guess you could say that falls under “kinda like science”, since I’m reporting the direct empircal experience of what I like. Still, it often seems useful to distinguish between objective measurements (external, repeatable) and subjective preferences.

    Philosophically, I view morality as an aesthetic-like preference regarding the world and how it should be, but one that isn’t compatible with disagreement. We can disagree peacefully about eating avocado, but not about whether you have a right to kill me. If I don’t like anchovies I don’t need a world purged of anchovies.

  8. Alex Theisen says:

    I think for me, personally, the problems with the strictest forms of logical positivism come in largely because logical positivism wants to have it both ways with the word “meaningless.” If you want to take “meaningless” as a term of art, defined to refer to things that are not tautologically true and also do not correspond to verifiable predictions of future sense experience, then that’s fine. When you then start using that term in its broader, non-term of art meaning, such as “things we shouldn’t talk about,” “things we shouldn’t act on,” “things which have no relevance,” etc., then things start getting trickier.

    The logical positivist is still committed to the idea that, if something is a tautology, it is literally adding no new useful information to something. So, if we’re really going with the idea that “meaningless” is tautologically defined as “the category of statements that are not tautologically true and are not verifiable,” then we’re forced to accept that the phrase “Any non-verifiable, non-tautological statement is meaningless” conveys absolutely NO new information. It’s generally accepted that you shouldn’t be able to define your way into winning an argument, and so that sentence above generally shouldn’t be used as a winning card in an argument. Instead, one then has to demonstrate that “meaningless,” as defined by logical positivists, corresponds to “meaningless” as defined by most other people. In order for whatever premises you use to make that case to be true, by logical positivist criteria, they must either be verifiable or tautological. Lather, rinse, repeat.

    By the time this whole process has been carried out, you’ll be in one of three spots:

    A) you’ve redefined a huge chunk of the english language, but haven’t ever actually conveyed new information.

    B) you’ve found some way to verify, with sense experience, whether a sentence is meaningful or not.

    C) you’ve arrived at a meaningless (by logical positivist criteria) statement.

    A) is useless and pointless, B) is very, very unlikely, if not impossible, and C) means that the logical positivist is left with quite a few bullets to bite into.

    • Scott Alexander says:

      I don’t know. Is “221 x 535 = 118235” conveying zero new information? It’s a logical tautology. But it says something we didn’t know before, and something that might even be useful (like if we were trying to figure out how much carpeting to get for a room that’s 221 feet by 535 feet).

      I find this whole field of “math is tautological” deeply confusing and unsettling, but it seems like it establishes a precedent of “logical tautologies can be really interesting and useful and convey new information” that could help positivism’s case.

  9. Romeo Stevens says:

    This reminds me of the way some people over-correct for lack of rigor by holding everything to much too high a standard and throwing out useful things. It’s frustrating when you’re having a hard time pinning down a concept to have the person insist that it therefore doesn’t really exist.

    • Paul Torek says:

      +1 to that. Things would be better if LPs had a way to avoid throwing out babies along with bathwater – i.e., basically a criterion for demarcating science from non-science. Carl Hempel tried and failed to locate that criterion, knocking down some of his colleagues’ favorite candidates along the way. I propose the following explanation for his failure to find that criterion: there isn’t one.

      You can’t put the epistemic cart in front of the physical/metaphysical horse. That’s my 2 cents, and worth every penny.

  10. Berry says:

    I’ve slowly been converting more and more of my fellow Philosophy undergrads into Neo-Logical Empiricists. I honestly don’t get the hate, I mean yeah I guess the Vienna Circle got a bit confused in its later stages, but its central thesis and some of the core members are just fantastic. I have to say, I think Eliezer denial of being a LP in “No Logical Positivist I” is off base, since he seems to have misunderstood how verifiability works (I’ve rarely encountered anywhere that he’s just flat out been mistaken… This might be the only one, actually.) It seems LW should be in love with Logical Empiricism/Positivism, no?

    • Mary says:

      Well, when I read logical positivists in Philosophy 101, I was reading ones who wrote before Karl Popper.

      The hatred is probably at least in part inspired by the numerous ones whose use for Logical Positivism was to hold in contempt anyone whose beliefs were nonsense by Logical Positivist standards. Naturally drawing a good deal of contempt when people realized it was nonsense by its own standards.

      • Berry says:

        It isn’t nonsense by its own standards. The core principle of Logical Positivism/Empiricism doesn’t have to be either a tautology or a hypothesis about reality, because it’s simply a definition of terms.

        • Mary says:

          That is nonsense on anyone’s terms. They were not defining meaningful and meaningless — they were casting anathemas on anyone except themselves who did not fit their own standards.

        • Mary says:

          Because they were using the terms in their ordinary English sense. If they were not, they were talking jabberwocky and should have had the sense to make up a word rather than steal one — except that having read them, I know they were using it in the ordinary English sense.

          • Berry says:

            It seems to me like an excellent formulation of how I use the terms ‘meaningful’ and ‘meaningless’ in ordinary language. I wasn’t suggesting that they had RE-defined anything.

            Casting anathemas on anyone who doesn’t fit the standard certainly sounds like a feature rather than a bug to me…

        • peterdjones says:

          A simple definition doens’t assert aything.

          LP seems to be assertign soemthign that anethatises some fields.

          It may be doing so on the basis of a definition, ie arguetn by tendentious redefinition, which is a fallacy.

          See Theisen’s reply below.

  11. UA says:

    I’m curious as to where you would put phenomenology, if you do not think that phenomenology is just crud. It seems that at least some phenomenologists (i.e., the one that I like and can understand) say thing that are meaningful, and do not fall into either category.

    I would also be curious to hear you try to work out a bit more what you mean by morality as formal system. The hortative aspect of moral statements would be seem to be disturbingly manipulative to me if morality were just a formal system, but I very likely don’t really grasp what you mean by saying it is merely that.

    • Scott Alexander says:

      I think a lot of phenomenology (which I don’t know much about, so take this with caution) could be folded into a sufficiently good version of logical positivism’s “kinda-like-science” criterion.

      That is, if you’re allowing sense-experience, your experience of existing seems to be sort of like sensation in the relevant way, in that it’s information presented to the conscious brain.

      If you’re taking Eliezer’s route and grounding it more in “a network of causes and effects”, then our experience is definitely a cause (it causes us to talk about it, for example) and apparently an effect (for example, taking drugs or going to sleep changes it).

      As for ethics, that would require a lot more detail than I want to go into right now, but the quick and terribly inaccurate summary is I think most ethical exhortations are conditional upon something like “…if you want to follow the set of human moral preferences and desires that most people have and I hope you do too”. Conditional exhortations are totally kosher.

  12. Gareth Rees says:

    I’m also a fan of logical positivism. It contains ideas that are powerful, even if it’s not completely watertight as a system. Certainly the critics were right that the verifiability principle is not itself verifiable (nor a logical tautology), but nonetheless as a practical matter the idea you can analyze the meaning of statements by looking to see whether they give predictions about the natural world is a really useful and productive one. You needn’t throw the verifiability principle out of your analytical toolbox just because it doesn’t form the basis for a totalizing system.

    (Compare with naïve set theory: sure, it’s inconsistent, but in practice you can do nearly all of your day-to-day maths in it, and you can leave the experts in mathematical foundations to sort out the paradoxes. Or with the induction principle: it may not be logically valid, but that seems to be a problem for philosophers, not for its users.)

    • Mary says:

      Except of course that logical positivism is far from the only system that maintains you can verify (some) things by their predictions about the natural world. Indeed, there are very few philosophies that maintain you can’t — if any.

      The heart and core of logical positivism is the anathema it casts on all and every notion that can’t be thus verified and is not tautological. Including itself.

      • gwern says:

        I’ve always wondered why you cannot simply justify logical positivism’s meaningfulness criteria by pointing to the results of logical positivism in discarding certain fields and promoting others. It seems to me that adopting logical positivism would lead to decisions like ‘let’s defund the theologians and spend it on more clinical trials’, which would then deliver real results and thus justify the original principle…

        • Scott Alexander says:

          I think this is much like what I meant when I said that logical positivism gets great results but that I might need to be applying some circular reasoning to support that. Like “great, logical positivism gets rid of theology. And that’s good! Because theology is dumb! Which we know because it fails the meaningfulness criteria of logical positivism!”

        • Paul Torek says:

          I think the philosophical school you’re looking for is called Pragmatism.

        • Mary says:

          Only once you define “real results.” A Buddhist might say that by this earnest pursuit you were cultivating wrong-headed desires and so suffering.

        • peterdjones says:

          a) “It just works” isn’t one of LP’s meaningfulness critera, so it is still not self-supporting.

          b) The philosophy of “it just works” is pargmat(ic)ism, not LP.

          c) “Working” is defined more vaguely than LP-es might wish. Maybe prayer works to get you into heaven…

          • dust bunny says:

            Prayer getting you into heaven is very verifiable for the person who dies. Thus, LP seem like it would say that sort of prayer is very meaningful.

            Experiment structure:
            1. Pray
            2. Die
            3. If you are not in heaven, then hypothesis defeated.

            Of course it is a little difficult to get your new found knowledge back to earth. . .

  13. ari says:

    But it’s like – well, take those ancient philosophers who said everything was made out of atoms. In fact, they’re wrong. Light isn’t made out of atoms, mathematics isn’t made out of atoms, quarks aren’t made out of atoms, et cetera. But they were sure on to something, and I give them much more credit than philosophers who didn’t say everything was made out of atoms.

    Nothing important, but just to point out the confusion in terms, current physics has it that lights is made of atoms as in indivisible units, it’s just not made of atoms as in units of chemical elements that have a nucleus and are surrounded by electrons and etc.. I guess the word not used much elsewhere anymore, but mathematicians and especially computer scientists still stubbornly refer to things that are indivisible as “atom”. Even if the best that they can actually do is to make things seem invisible from a given interface, for instance a database transaction which might consist of arbitrarily many operations but of whose effects either all or none are visible to any other transaction.

    • Charlie says:

      Except that one can have half of a photon by amplitude. Photon number isn’t even conserved, so there doesn’t have to be another half anywhere – you can just have half a photon.

      Clearly the fundamental thing is waves, so Thales was right.

    • Scott Alexander says:

      Yes, good point. Sound, then. That works, right?

  14. Erin says:

    It may please you to know that when I read your LessWrong post about logical positivism, a year or two ago, I had no particular exposure to or attitude toward the theory — so my first impression and judgement was quite a positive one. You’re influencing a new generation of philosophers! Or at least me.