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Popper and Carnap again

Anyone who’s even heard of Popper knows that he advanced his falsifiability criterion (of science) in opposition to the Vienna Circle’s verifiability criterion (of meaning). What the Popper fans seem unaware of (yes, I know, they’re no longer as numerous as in the days of Helmut Schmidt’s public endorsement) is that Carnap actually responded to this criticism by pointing out that you can’t distinguish between verification and falsification except in certain special cases, which happen not to include the laws of e.g. physics. That was in “Testability and Meaning” (1936-7), which Popper praised volubly, e.g. in his Schilpp volume. But despite the fatal consequences of Carnap’s argument for Popper’s whole edifice, Popper never responded, nor, as far as I’m aware, has any of his followers.

I found this incredible, given the centrality of Carnap’s point to Popper’s project, so once when on the HOPOS mailing list, as occasionally used to happen, Popper came up and various Popperians complained about misconceptions about Popper, I wrote the following (apologies to the hopoi who may be reading this and are very bored with Popperiana by now):

. . . while we’re on the subject of common misperceptions about Popper: why does no one talk about Carnap’s demonstration, in “Testability and Meaning,” that for sentences of the form “for all x there exists a y such that (. . .x. . .y)” — any sentence using a limit concept, for instance, i.e. most laws of theoretical physics — falsification is essentially equivalent to verification (see Carnap Schilpp volume p. 879 for a brief summary).  As far as I’m aware neither Popper himself nor any Popperian has ever acknowledged this problem or tried to figure out a way around it.  Miller’s 1994 book (Critical Rationalism: A Restatement and Defence), for instance, has a section on the “asymmetry between falsification and verification,” but only rather flimsy challenges to it are acknowledged, not the comprehensive treatment of T&M.  But I haven’t studied this literature thoroughly. . .

The first time I sent this, there was no response. A few months later, Popper came up again, and I re-sent the above paragraph in a slightly different context, and again asked whether anyone knew of a response to Carnap’s point. Joseph Agassi answered this time:


the reason Popper and cohorts failed to respond to Carnap’s problem is that it is a problem for Wittgenstein addicts only. Only they want sentences to be testable. In his Replies Einstein says, no one demands that every sentence in a testable theory is testable. Wittgenstein’s requirement of sentences that they “show” their truth value in order to be meaningful (i.e. to have truth value) is to be rejected, and with it the problem that you insist on.


To which I responded as follows:

No, Popper often acknowledged that it’s his problem: “My proposal is based upon an asymmetry between verifiability and falsifiability; an asymmetry which results from the logical form of universal statements. . .” (LSD p. 41).  And §22 of the Postscript, entitled “The Asymmetry between Falsification and Verification,” takes 8 pages to fend off all sorts of other objections that had been raised against this asymmetry, but never the Carnap issue of nested quantifiers (which, as I remarked earlier, are indispensable to any theory whose statement involves e.g. limit concepts): “Although some of my critics have denied the existence of this asymmetry, their arguments were anticipated and fully answered in my LSD. . . This fundamental asymmetry cannot, I think, be seriously denied: a set of singular observation statements. . . may at times falsify or refute a universal law; but it cannot possibly verify a law. . . This is the fundamental logical situation; and it shows a striking asymmetry.”  And so on.  Popper himself thought (as in the sentence quoted from LSD above) that his entire criterion of demarcation depends on this supposed asymmetry.  But when Carnap showed in T&M that “the fundamental logical situation” is a bit more complicated than that, and that verifiability and falsifiability are only distinguishable in certain special cases, not in general, Popper doesn’t even acknowledge the problem.

Nor does this have anything to do with Einstein’s issue regarding systems of sentences — that not every sentence can be testable in isolation; Popper’s requirement (like the one Carnap considers in T&M) is that some sentences should be testable.  Wittgenstein did not require that sentences “show” their truth value in order to be meaningful, but in any case that has nothing to do with Popper’s acknowledgement that his criterion of demarcation is based on the asymmetry between falsification and verification or with Carnap’s pointing out that this asymmetry holds only in certain simple special cases, not for e.g. the laws of physics as we know them.


I can’t remember whether there were any further substantive responses to this; I think not, as the moderators soon shut down the discussion. That was about a year ago, I think. In any case, there was certainly no response to Carnap’s argument. So I will here repeat my question yet again: does anyone know of a response to Carnap’s argument?

7 thoughts on “Popper and Carnap again

  1. Fascinating issue and question, esp. because I think Popper continues to be the de facto inspiration for most practicing social scientists to this day.

    My suspicion is that the issue gets at central problems in philosophy of language that have been ongoing questions in several branches of philosophy up and through the last several decades.

    1. My impression is that Popper’s influence in the (hard) social sciences, though still perhaps fairly widespread, is declining. He had a strong influence on a number of philosopher/historians of economics, e.g. Mark Blaug, but this was very much resisted within the profession, where “methodology” has become (and remains) a term of abuse; Milton Friedman’s apparent falsificationism in his classic 1953 paper was largely independent of Popper and, as far as I can see, taken more seriously.

      As to the “central problems in philosophy of language,” I guess it depends what you mean by philosophy of language. Perhaps if one adopts Dummett’s notion of philosophy of language as the (Fregean) concern with logic replacing the (Cartesian) concern with epistemology, you may well be right.

  2. My reference on these issues is Pierre Jacob’s book on logical empiricism (in french) that I read 2 years ago. There he remarks, if I remember well, that indeed falsificationism fares no better than verificationism as a criteria of *meaning*, because of issues with existentials, and combinations of existential and universal quantifiers. It seems to be the point you’re addressing.

    However PJ says (perhaps similarly to Joseph Agassi’s answer you mention) that there is a difference between Carnap and Popper, which is that Popper is not trying to find a criteria of *meaning* but a criteria of demarcation between science and non-science (Popper is happy to accept that non refutable sentences have meaning). Popper’s falsificationism can be imported to fix problems with verificationism but it’s not its primary aim. And in any case it doesn’t really help: verificationism and its extensions, as theories of meaning, fail.
    (Although I remember now that Pierre Jacob mentions that existential quantifiers can be refuted if they are limited to a finite region of space-time, which is generally the case in science. So Popper’s criteria could do better after all. Sorry I read the book a long time ago).

    Now the point you address could also apply as an objection against Popper’s demarcation criterion. I don’t know if it’s acknowledged by Popperians but the demarcation criterion itself has problems of its own, such as verification holism etc.

    I don’t know if it’s related but I wonder if structural realists, who typically deny that existential quantifier have ontological significance, would be bothered by this problem. If posited objects are not to be taken seriously, but are only heuristic devices to discover general statements concerning the structure of the world, can’t we bring back Popper’s falsificationism?

    1. I don’t remember Pierre Jacob’s book very well, but I had a favorable impression of it when I looked at it years ago. You’re right that Popper claims that his demarcation criterion demarcates something different (science) than the Vienna Circle’s one (meaningful discourse) — which is why I acknowledged that difference (in parentheses) in the first sentence of this post. But I’m actually sceptical that there’s much of a difference that makes a difference here. What the Vienna Circle meant by “meaning” was basically “empirical content,” and Popper wanted to demarcate empirically viable theories (which do after all consist of sentences) from empirically useless ones. So yes, his take on “empirical content” was somewhat different from the VC’s, but he was still basically interested in the same thing. Carnap himself, by the way, answered this point of Popper’s, in his first reply to Popper in the Schilpp volume (I don’t have it available at the moment, or I’d tell you exactly what it says).

      Simple existentially quantified sentences are irrefutable (as Popper acknowledged) for the same reason that simple universally quantified sentences are unconfirmable (one of Popper’s basic points); in both cases an infinite number of instances would be required to do the job. What Popper neglected was non-simple quantification, i.e. alternating (nested) quantifiers; since nearly all scientific sentences of interest have this more complicated form, though, and since Carnap spelled out the problems this raises very clearly and systematically in “Testability and Meaning” (which Popper claimed to like), Popper should really have responded to this problem. It’s a central problem for him, and as far as I’m aware he never so much as acknowledged it.

      Structural realism is a different kind of issue, one that Ladyman and Ross insist on calling a “metaphysical” one (though I wouldn’t). When you mention “posited objects” not being “taken seriously,” you may be referring to their version of structural realism, which dispenses with fixed “things” or objects; if so, I’m unclear how it would be congenial to Popper’s falsificationism. In fact, if you check their excellent paper “The World in the Data” (in the Scientific Metaphysics volume edited by them), you’ll see that they have some good arguments against the overly simple conception of science advanced by some scientists, who often rely on Popper in the background.

      1. I’m sure I’ve overlooked something significant here, but it seems that the (simple) existentially quantified propositions you mention are the EXACT analogue of the universally quantified propositions. As such, how is there not complete and total symmetry between Popper’s theory and verificationism? It seems to me that Popper merely has an arbitrary preference for universals over particulars, hence his bias towards falsification and away from verification.

        Could you possibly summarise Popper’s rationalisation for this preference?

        1. There is a symmetry, yes, but Popper wasn’t quite as dumb as that. I regret that he didn’t respond to Carnap’s challenge, because I’m convinced that the young, pre-dogmatic Popper probably could have, somehow or another, and possibly kept a debate going. The best way to see Popper, perhaps, is as the attempt to take Hume’s challenge to induction really seriously. Carnap never ignored or denied Hume’s challenge; in fact he acknowledged it fully even in his Physikalische Begriffsbildung of 1926, right up front, long before Popper. At the same time, he saw that induction is clearly central to science, and that what we have to figure out is how we manage to use it despite its obvious logical flaws; that’s the task he devoted the last 25 years of his life to. Popper became established and dogmatic, and no longer tried to engage in debate about this issue, and after “Testability and Meaning” Hempel in effect took over from Popper the role of the skeptic about induction. The best answer to Popper’s skepticism (indeed to the whole tradition of skepticism about science, from Hegel to Duhem to Popper and beyond) is actually to be found not in Carnap but in some of George Smith’s papers, esp. the one in the Howard Stein festschrift Reading Natural Philosophy edited by David Malament and another in the Monist issue (vol. 93, 2010) on Philosophical History of Science, edited by Niccolo Guicciardini. Smith leaves aside the whole history of attempts to model induction using probability that Carnap revived (he doesn’t challenge it, he just leaves it aside) and takes a completely different — historical — approach that seems to me much more promising.

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