Course Notes: A.J. Ayer, Language, Truth, and Logic

by Daniel A. Kaufman

It’s finals week, which means that the semester is at a close (and that I’m grading my ass off), and I thought it a good opportunity to get another Course Notes in, before summer break begins.  I’ll be talking about the final readings for my Introduction to Philosophy course, three chapters from A.J. Ayer’s Language, Truth, and Logic, which was published in 1936 and responsible for bringing Logical Positivist ideas from the European continent to the English-speaking world.

Because the work is somewhat technical (and certainly is experienced that way by gen ed students) and the last thing they’d read was J.S. Mill’s Utilitarianism (which is quite easy by comparison), I spent an entire lecture just on background and especially on the question of the Positivist’s targeting of metaphysical statements.  Without this background, the apparatus of the Verification Principle looks as if it’s motivated by nothing more than a narrow scientism, so I took some time to explain to my students that the Logical Positivists were concerned about the role the sort of metaphysical and mystical statements coming out of 19th century Romantic nationalism were playing in the fascist politics that was developing across the continent in the early 20th: “Blood moves the wheels of history” and “The folk is rooted in the soil and bound together by the bond of its common blood” were just two of several examples I gave of the sort of thing I wanted them to think about, when engaging with the Verification Principle.  Of course the Positivists were also motivated by a more general, empiricist-inspired anti-metaphysical attitude (in the Anglosphere, the view is called “Logical Empiricism”), much in the spirit of Hume’s famous statement from the Enquiry, which I also discussed with the students:

If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion

The Verification Principle

I explained to my students that the anti-metaphysical strategy employed by the Positivists and by Ayer involves demonstrating that metaphysical statements are literally meaningless.  Now, for those who have studied philosophy for some time, saying this would be a sufficient prelude to introducing the Verification Principle (VP), but I was concerned that students might find the notion of meaninglessness involved obscure, so I spent some time on two different ways in which a sentence might be meaningless: (1) if it is ungrammatical or ill-formed, such as “Uncle purple rains Wednesday to”; (2) if it involves bogus — in the sense of non-existent — words, like Lewis Carroll’s “Twas brillig and the slithy toves did gyre and gimble in the wabe,” from Jabberwocky.

Ayer proposes a third criterion for meaningfulness and that brings us to VP, which says: A sentence is meaningful if and only if one could, in principle, explain how one would go about showing it was true or false.

Notice that even sentences which are not currently verifiable can satisfy this criterion: “There are caves on Pluto” is not a sentence that we currently can verify, but we know how one would verify it.  But sentences like “God is eternal love” and “The folk is rooted in the soil and bound together by the bond of its common blood” are not like this, for not only are we not currently capable of verifying them, we could not even explain how one would go about verifying them.

Mathematical Sentences

It might appear rather obvious that VP is far too narrow a criterion for linguistic meaningfulness, insofar as there seem to be perfectly ordinary sentences that clearly are meaningful, while not being verifiable in the manner described by Ayer.  “Three plus two equals five” is a sentence that is obviously meaningful – I suspect every person reading this both understands and believes it – and yet, it is not empirically verifiable.  One may have learned the truth that the sentence expresses by counting pebbles or blocks, but no amount of such counting could ever confirm or disconfirm it.  As I pointed out to my students, if they counted the pebbles and got “six” as a result, we wouldn’t conclude that “Three plus two equals five” had been disconfirmed.  Rather, we would insist that  they had counted wrong, and I pointed out that we would say exactly the same thing if thirty or even three hundred people had counted them and got “six” as a result.

So what does Ayer do with mathematical sentences?  They clearly aren’t meaningless, and yet they seem to fail the verification test.  Ayer’s answer here is interesting, but is no longer considered viable today, insofar as it depends on a now defunct program.

Ayer argues that mathematical sentences are in fact analytic – logical truths.  ‘Three plus two’ and ‘five’ are alleged to be synonymous.  So, while mathematical sentences may not be empirically verifiable they are, in a sense, linguistically verifiable, which explains their meaningfulness.

Our knowledge that no observation can ever confute the proposition ‘7 + 5 = 12’ depends simply on the fact that the symbolic expression ‘7 + 5’ is synonymous with ‘12’, just as our knowledge that every oculist is an eye-doctor depends on the fact that the symbol ‘eye doctor’ is synonymous with ‘oculist’. And the same explanation holds good for every other a priori truth. (p. 47)

Of course, this depends on being able to demonstrate that mathematical statements are in fact truths of logic, a claim that was made by those pursuing the logicist program in the late 19th and early 20th centuries.  The overwhelming consensus is that this program was a failure, which, if correct, means that Ayer’s way of handling mathematical sentences will not work, and he is left with the problem of their meaningfulness unresolved.

Moral Sentences

The other great challenge to VP lies in the area of moral discourse.  Sentences like “Snatching that guy’s wallet is wrong” are clearly meaningful – again, I think it safe to assume that everyone reading this both understands it and will agree with it – but they are not verifiable, either empirically or linguistically.  There are no observations that are going to confirm or disconfirm the wrongness of the wallet-snatching, and the truth or falsity of the sentence cannot be determined just by examining the meanings of the words.

Ayer takes this objection seriously and makes a serious effort in responding to it, one that has had legs far beyond the Verification Principle itself, in the form of ethical Emotivism. What he says is that moral terms are actually performatives: they don’t refer, but rather do various things – approve, condemn, command, plead, and the like.  Thus, when we say, “Snatching that guy’s wallet is wrong,” what we really are saying is something like “Don’t snatch that guy’s wallet!” or “Snatching that guy’s wallet, BOO!”  The verificationist can thus avoid being saddled with the view that moral statements are meaningless, because he doesn’t think they are actually statements, but rather expressions of feeling, commands, etc, whose meaningfulness is not a function of their verification conditions.

The main difficulty with this move is that if correct, it should follow that there can be no moral disputes, as only statements – sentences that express propositions – are disputable.  If I like vanilla ice cream and you can’t stand it, we don’t have a dispute, as evinced by the fact that the difference between us cannot be settled by appeals to evidence or arguments.  Consequently, if moral sentences are not in fact statements but expressions of feeling or commands, they too cannot be matters of dispute.  The trouble of course is that they are.  More than that, they are some of the most heavily and hotly disputed of all the things we say.

Ayer’s take on this is ingenious and persuasive, but only to a point.  Often, a conflict in attitudes or feelings is grounded in disagreement over relevant facts.  Years ago, when the issue of gay marriage was being debated, those on the pro- and anti-sides certainly had conflicting attitudes, but they also disagreed substantially on the facts: specifically, as to whether allowing gays and lesbians to marry would do damage to the institution of marriage.  It seems reasonable to think, moreover, that had there not been these sorts of factual disagreements, there likely would have been less conflicts in attitudes.  Of people growing up, living, and working in the same society it seems reasonable to expect similar attitudes in reaction to similar facts.

When someone disagrees with us about the moral value of a certain action or type of action, we do admittedly resort to argument in order to win him over to our way of thinking. But we do not attempt to show by our arguments that he has the ‘wrong’ ethical feeling towards a situation whose nature he has correctly apprehended. What we attempt to show is that he is mistaken about the facts of the case. We argue that he has misconceived the agent’s motive: or that he has misjudged the effects of the action, or its probable effects in view of the agent’s knowledge; or that he has failed to take into account the special circumstances in which the agent was placed. Or else we employ more general arguments about the effects which actions of a certain type tend to produce, or the qualities which are usually manifested in their performance. We do this in the hope that we have only to get our opponent to agree with us about the nature of the empirical facts for him to adopt the same moral attitude towards them as we do. And as the people with whom we argue have generally received the same moral education as ourselves, and live in the same social order, our expectation is usually justified.  (p. 70)

The difficulty, of course, is that it’s not at all clear that every moral conflict sits astride a dispute over facts, and for another, we’ve all had experiences in which no amount of agreement on the facts eases a conflict in values, even with people who are from our own communities or even our own families.  And so while of all the elements of Language, Truth, and Logic, Ayer’s Emotivism has remained relevant the longest, there are a number of problems that strongly tell against its being a satisfactory treatment of moral language and discourse.


  1. Dan,
    Well, you incite me to read Ryle over at PF, and now I have to review LTL! And I was hoping to spend the week-end reading Perry Mason novels.

    Actually, I read LTL back in 1989; didn’t like it, as you might have guessed. Led me to a considerable appreciation of JL Austin.

    Browsing before this initial post, I find it less offensive and more amusing than when I first read it – so many tiny little glitches! But the sense of Ayre’s class-based arrogance – which permeated most of the writings of the British Positivists – is till annoying…. Sometimes it’s not so much that he’s wrong, but surely he could have phrased it more charitably (esp. concerning Bradley). However, i admit mild surprise that Ayers is more Kantian than I remember….

    Anyway, more to come if I have time this week-end.


  2. Is the difference between a sentence whose truth value we could in principle explain how to justify and a sentence whose truth value we could not a difference in kind or degree? Take, for example, the sentence, “If gays and lesbians are allowed to marry, the institution of marriage would be damaged,” which you imply is an example of a factual (but false!) sentence. Showing that an institution is (or is not) damaged seems more slippery than showing that there are (or are not) three caves on Pluto. What does a damaged institution look like? How would the damage manifest itself? Is there a publicly acknowledgeable or acceptable answer to the question, “Is /this/ damage to the institution of marriage?” in the same way that there is to the questions, “Is /this/ a cave?” or “Are there three of /these/?” I’m not saying the damaged-institution sentence isn’t meaningful; I’m just saying it seems to lie between sentences like “God is eternal love” and “There are three caves on Pluto” on a we-could-explain-how-to-show-it’s-true-or-false spectrum.


  3. You are an excellent teacher. I am happy you actually include these course notes on here. I am in the middle of Bryan Magee’s memoir in which he really skewers this period of Anglophone philosophy though he was reared in its milieu. I truly think that this material should be part of a basic humanities literacy program rather than a specialized interest. It is important to know what major figures have thought that have come before you.

    Liked by 1 person

  4. It’s interesting how you situate logical-positivism within the context of anti-fascism. I hadn’t realized that previously. I guess that they were specifically concerned about Heidegger’s influence on philosophy.


  5. Interesting essay because you touch on mathematics which is externally verifiable vs the morals that are internally verifiable or shared emotional values. The notion of gay marriage or the emotive value that two people who love each other should be entitled to legally marry regardless of gender or this changed the definition of marriage. Truth is marriage did not legally take root for emotive reasons but evolved to strengthen the ties between extended families and shared property. Case in point the church which essentially was the legal system in old Europe, forbid divorce with all of its messy consequences for property redistribution but allowed for annulment when no rightful heirs to property could be produced. For biological reasons marriage also verifies the partnership between two people who are not directly related along with marriageable girls being virgins also involves the incest taboo in older religious practice. Just like meaningless sentences, ideas like virginity, divorce and adultery float around like meaningless sentences in the modern world.


  6. > No. That’s one of the standard criticisms of it.

    I’m puzzled.

    His theory is based on the idea that some statements are (logically) verifiable, and others are not.
    I don’t feel the urge to make a meta-move here, you got to start somewhere.
    But then he claims that the property of being (logically) verifiable is equivalent with the property of being meaningful.

    That’s basically a definition (perhaps re-definition is a better word).

    No problem with that, definitions are useful. But it’s only a definition. Definitions cannot be “verified”. They are handy conventions to avoid using long expressions like “the property of being (logically) verifiable”.

    I assume Ayer had a solid background in logic. He must have seen that too.
    How did he react to this criticism?


  7. Hi Dan

    Ayer’s idea that the meaning of a sentence is found in knowing what would make it true is attractive and has been very influential, but seems flawed.

    Knowing what would make S true seems neither necessary nor sufficient for knowing the meaning of S. Not sufficient, because machines can be very good at determining the truth of sentences. A calculator can tell us that “9 x 9 x 9 = 729” without it knowing anything about the meaning of that sentence. Not necessary, because I can understand sentences without knowing how to determine their truth. For example, the sentence that “Podocarpus is a genus of conifers” seems meaningful to me, as a botanical statement, yet I have no idea how to identify a tree or shrub as a podocarpus.

    These objections to Ayer are ones derived from Wittgenstein, so I imagine you would agree with them. Spelling out an alternative theory of meaning is a large job. On that, I follow the work of Harrison and Hanna in “Word and World”. On their view, meanings are embedded in practices; understanding the meaning of a sentence is understanding its role in a practice (such as maths or botany).



  8. On second reading I cannot add that much here without a full critique on Ayers, requiring a longer response than would be fair here.

    But a small matter: Ayers: “But we do not attempt to show by our arguments that he has the ‘wrong’ ethical feeling towards a situation whose nature he has correctly apprehended. What we attempt to show is that he is mistaken about the facts of the case.” Outside of the fact that this is flat-out wrong (easily falsified by actually paying attention to ethical arguments in their own language), this is also clearly a surreptitious violation of Hume’s interdiction against confusing the ‘is’ and the ‘ought.’

    This is also what I mean by Ayers’ class-attitude (which is shared by, and hence problematic, in a lot of British philosophy – even Hume himself doesn’t escape it). The reason why Ayers can make a claim like this is because he moves in circles where ‘all would agree, dontcha know?’ In other words, he assumes a fairly homogenous society with participants sharing basic values. But the really interesting ethics questions arise in either heterogeneous cultures with people of differing values, or homogenous cultures that are beginning to fall-apart due to political or economic pressures, or suffering competitive confrontation with cultures of considerably different values (which would include the 20th Century Britain that Ayres would rather not address directly).

    Also, I will say that, as a Pragmatist the notion that there can be any such thing as a purely nonsensical sentence seems to fail to take into consideration the nature of our responses to any sentence when uttered. Even the word-salad of somebody suffering from dissociative schizophrenia has meaning for the people needing to treat the sufferer – at bare minimum, it is a sign that the person is suffering from dissociative schizophrenia.

    To put it more generally: What Ayres seems to rely on is the notion (derivable from Frege, to be sure) that the meaningfulness of language can be determined internally within the language itself. I think, on the contrary that the best evidence is that the meaningfulness of language is determined within a social context. (Why else would we have language if that were not the case?)


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