A Refutation of Positivism
The positivists maintain that a sentence is meaningful if and only if it is verifiable. Thus a sentence can be said to be both meaningless and unverifiable. Here is a possible counterexample to that claim: “It’s raining”. This sentence is not meaningless, but it is not verifiable–and similarly for all other indexical sentences. Considered out of context, just in virtue of their lexical meaning (what Kaplan calls character), such sentences are not verifiable—they are unverifiable. It will be replied that we need to consider such sentences in a context in order for them to be verifiable—we need to consider the proposition they express in a particular context of use (what Kaplan calls content). That is undoubtedly correct, but now we are talking about propositions (or statements or sentences “under an interpretation”), not sentences per se. Thus we might reformulate the positivist’s principle to read: A sentence is meaningful if it expresses a proposition that can be verified, and it is meaningless if it expresses a proposition that can’t be verified. (The same point goes for falsifiability as a criterion of meaningfulness.) This implies that a sentence can be meaningless and yet express an unverifiable proposition. But how can a sentence be meaningless if it expresses a proposition? Either it expresses no proposition, in which case it cannot be either verifiable or unverifiable; or it does express a proposition, in which case it is meaningful. Meaningfulness (or the lack of it) is a property of a sentence; verifiability (or the lack of it) is a property of a proposition. The positivist’s principle conflates this distinction, which is what enables it to sound like a viable principle.
Some sentences are meaningless in a straightforward way, such as ungrammatical sentences or sentences like “Twas brillig and the slithy toves did gyre and gimble in the wabe”. Into this category falls the positivist’s favorite example of meaningless metaphysics, Heidegger’s “Nothing noths”. The problem here stems not from unverifiability but from other kinds of linguistic defect—and no proposition is accordingly expressed (unless we stipulate a sense for the problematic verb “noths”). Other sentences arguably fail to express verifiable propositions, for example “God exists”; but to call them meaningless appears far-fetched. The only reason “God exists” is unverifiable is that it expresses a proposition that is unverifiable; but then it is meaningful in virtue of expressing that proposition. The problem for the positivist is that no sentences fall between these two possibilities: no sentences are both unverifiable and meaningless—simply because to be unverifiable requires a proposition to have that property. Any sentence that fails to be verifiable because it fails to express a proposition at all will be so for reasons other than its unverifiability, say by being ungrammatical. Such sentences are unverifiable only in the entirely trivial sense that a brick is unverifiable: it is simply not the kind of thing that could be verified. A sentence can be unverifiable in the non-trivial sense only if the question of its verifiability can arise, but that requires an expressed proposition to be a candidate for verifiability. So the sentence must be meaningful after all.
Nor can we say that a proposition is meaningful if and only if it is verifiable (or falsifiable), since it is a category mistake to call a proposition meaningful or meaningless. A proposition has meaningfulness built into it (it is a meaning). Sentences are meaningful in virtue of expressing propositions, and these propositions can be verifiable or unverifiable; but they cannot express propositions without thereby being meaningful—and this is what they need in order to be verifiable or not. Indeed, we should not speak of sentences as verifiable at all, unless this is simply short for “expresses a verifiable proposition”–in which case the problem with the positivist’s principle is evident straight off. Expressing an unverifiable proposition is a way of being meaningful, not meaningless. Intuitively, we can only know that a sentence is unverifiable if we know what it says, but if it says something then it must be meaningful. Positivism thus rests on confusion between sentences and propositions–bearers of meaning and bearers of verification.