Do logically incoherent statements still have meaning?

Question

My reading of Carnap's "The Elimination of Metaphysics Through Logical Analysis of Language" suggests to me that it is possible to form sentences in a language that are grammatically correct but logically meaningless. The consequence of this is that the statement, due to its logical incoherence, cannot be proven to be true or false. And likewise, if a statement cannot be proven, then it is meaningless.

Such sentences, while unfruitful or wrong, are nevertheless meaningful; for, only meaningful sentences can ever divide (theoretically) between the fruitful and unfruitful, the true and false. By contrast, a series of words is meaningless in the strict sense when it forms no sentence within a certain predefined language. It may happen that such a sequence of words at first glance looks as if it were a sentence; in this case we call it a pseudo-statement. Our thesis now claims that the alleged sentences of metaphysics are revealed as pseudo-propositions by logical analysis.

Carnap criticizes Heidegger and others in this essay. And yet, I and many philosophers have read Heidegger and, while they may disagree on the interpretation of the work as a whole, they could probably agree to some extent on the meaning of some of the individual sentences. And further, one could still derive utility from this sentence even if it is not "true" in the logical sense. This argument could apply to many metaphorical statements too. Two people can still understand each other even if the statements are "meaningless" as defined by Carnap.

So the real crux of my question is, how can Carnap (and other logical positivists) prove the axioms of their own theories/systems? For example:

• How does one prove that "something is meaningful if it is logically coherent and resolves to true or false" without resorting to the statement itself or whatever axioms are used to support this statement?
• How does one prove that "the scientific method allows us to investigate knowledge and modify current knowledge" without resorting to the scientific method?
• Carnap sets up axioms in his paper for what constitutes a "meaningful" statement. Can he prove that these axioms are true without resorting to using the definitions he has laid out for what constitutes meaningful statements? What about other statements he makes in the essay? Could these statements be proved or resolve to true/false? How?

So what's going on here? Am I missing the point of what Carnap is arguing entirely?

Answer 1

You need to be careful with the extent to which Logical Positivist statements are analysed metaphysically. It is a common cliché to say that the axioms of the Logical positivist system could not be proven by their own theories, and this is true, what does not follow is the conclusion that their theories themselves are therefore meaningless.

Firstly it's important to recognise that LP's 'Emprical verification' has been improved upon and it might now make more sense to talk about falsifiable theories, I don't see this as a failure of LP as I don't see any reason to conclude that their proposed method of deriving meaningfulness should be expected to remain unaltered. I see the thrust of LP being that some statements can be empirically shown to have justifiably 'more' meaning than others by some objective means. It is not crucial to the process what that means is.

Either statements which cannot be empirically verified have some meaning or they do not. The statement "something is meaningful [only] if it is logically coherent and resolves to true or false" cannot be empirically verified, as Ayer concludes, but if we are to reject Logical Positivists, then the fact that this statement cannot be empirically verified doesn't matter it can still have meaning, and so does not constitute a proof that the system is meaningless. Godel demonstrated how no system can prove it's own axioms, that doesn't cause us to dispose of such systems.

Looked at in this light their analysis of metaphysics is still useful. The crux of the problem is summed up well in your assertion that

Two people can still understand each other even if the statements are "meaningless" as defined by Carnap.

and

one could still derive utility from this sentence even if it is not "true" in the logical sense.

Without empirical verification, we must question these assertions, which is something that metaphysics, prior to the Logical Positivists, failed to do. Do the two people actually understand each other? Have any metaphysical statements had any demonstrable utility? If you're just presuming they do, then the analysis of the statements becomes pointless as you've already decided to simply accept your own intuition as gospel, if you're stating that they do understand each other or have utility because of some empirical evidence that this is the case, then you're still following Logical Positivism.

The point is, vague statements whose meaning can be fuzzily agreed upon by whatever means (Family Resemblance, Baptism of names etc.) can still have this meaning objectively verified by this means. It is still objective to say that by 'unlucky' (to use Alexander's example) we do not mean something pleasant, nor something to do with blame, these are definitely opposites of whatever we mean by 'unlucky' and can be demonstrated to be so by analysis of the use of the term in common language.

What continues to go wrong with much of metaphysics, and where LP I think had it right, is that the metaphysician proceeds to define a term themselves, or hold forth about what a term means to us without feeling the need to forward evidence when such a conclusion is objectively available to the philologist. Having done this, their conclusions are 'meaningless' as they come off the page. We may then take their terms and fuzzily apply meaning to them as we do any other vague term, but then it is us who are doing the philosophy, not the original author, who has simply presented us with something more akin to a Rorschach ink-blot for us to interpret.

Carnap never claimed that his conclusions about metaphysics would be true in perpetuity, just that they followed from the empirical evidence he'd examined thus far.

Answer 2

My reading of Carnap's "The Elimination of Metaphysics Through Logical Analysis of Language" suggests to me that it is possible to form sentences in a language that are grammatically correct but logically meaningless. The consequence of this is that the statement, due to its logical incoherence, cannot be proven to be true or false. And likewise, if a statement cannot be proven, then it is meaningless. [...] So what's going on here? Am I missing the point of what Carnap is arguing entirely?

You have to be careful about what Carnap and other logical positivists are trying to do. They are not trying to prove a linguistic point about grammar and meaning. They are trying to prove an epistemological point about how language and meaning connect to the world, as expressed in their famous verification principle. The verification principle states that the only statements that are meaningful are those of logic and those that can be verified empirically. Let me illustrate:

Consider 3 statements:

• (a) The green frog caught the matrix because he was dialectic.
• (b) The man caught a disease because he was unlucky.
• (c) The man caught food poisoning because the shrimp he ate was bad.

That (a) is meaningless even though it is grammatically correct is uncontroversial, most people would consider (a) to be meaningless, while both (b) and (c) are meaningful sentences.

This is not what Carnap and the Positivists are saying, their claim is much stronger: They think that (b) is just as meaningless as (a), because the concept "unlucky" cannot be verified empirically. What does it mean for someone to be "unlucky"? Can you measure "unluckiness" or observe it with a microscope? Can you perform an experiment to prove that Sam is unlucky? No, and hence the term unlucky doesn't carry any meaning, and hence (b) is just as much gibberish as (a).

This is why they objected to Hegel, Heidegger, and other who used the same style. Statements about "Geist", "The Owl of Minerva", "Dasein", "Nothingness nothings", etc...fell in the same category as "unlucky" in that there was no way to verify them empirically, and so their philosophy was meaningless. Their goal wasn't the analysis of language for its own sake, but the elimination meaningless statements from philosophy, so that the only statements that remained were similar to those of the sciences - in the process they would get rid of metaphysics, which they thought a pejorative term.

So the real crux of my question is, how can Carnap (and other logical positivists) prove the axioms of their own theories/systems?

Well they couldn't, that's why Carnap and the Logical Positivists' program is considered to have failed (*). It is unique among philosophical school in that it declared dead by its own people after it faced several challenges including the one you allude to which is that the verification principle is itself a statement that cannot be verified empirically. See here and here for details, and this video of here's A.J. Ayer, leading British L.P, admitting it all turned out to be false - starting just before 34:00

And yet, I and many philosophers have read Heidegger and, while they may disagree on the interpretation of the work as a whole, they could probably agree to some extent on the meaning of some of the individual sentences. And further, one could still derive utility from this sentence even if it is not "true" in the logical sense. This argument could apply to many metaphorical statements too. Two people can still understand each other even if the statements are "meaningless" as defined by Carnap.

This is the same conclusion that Wittgenstein and others arrived at. Wittgenstein started out as holding views very similar to Carnap and the Logical Positivists: Logical statements and empirical statements are the only meaningful statements. But then he abandoned those views and in his later philosophy subscribed to the view that meaning is use: Statements derive their meaning not from the way correspond to empirical facts, but from the way we use them. The term "unlucky" is used in a certain way when we communicate and that is enough to give it meaning. See Ordinary Language Philosophy and Pragmatism.

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(*) An additional note: That the logical positivist program is considered to have failed and was abandoned by the 1960s is the most common position, and is frequently mentioned in various introductory articles and courses. As I mentioned earlier, it was notable that several people who were themselves associated with the L.P movement had agreed that it failed, which is why most accept its failure as a fact.

Some philosophers, notably Michal Friedman, have argued that Logical Positivism shouldn't be dismissed, that it hasn't failed as completely as most sources claim, and that too many people dismiss it because it became fashionable to do so, without actually examining the ideas of LP. See Reconsidering Logical Positivism and this post.

Regardless of whether the L.P program failed completely or not, it's influence on philosophy in general and analytical philosophy in particular cannot be denied. One can argue that although the verification principle itself has challenges, the spirit of L.P with its emphasis on clarity and rigor has been passed on to subsequent schools of thought.

Answer 3

Maybe Carnap was trying to recreate the process of thinking represented in the Tractatus - but he does not seem to have recognised the contradiction of dissolving the sense in metaphysical propositions through propositions themselves, as did Wittgenstein with his phrase at the end of the Tractatus, that he hopes that someone, after having used this "ladder" to climb out of the hole, then throws the ladder away. I think you are picking up on a contradiction in what Carnap was attempting to do, which Wittgenstein did pick up on when he was trying to do the same thing in the Tractatus.

Answer 4

Hilary Putnam's lecture at UCD (Univ. College Dublin) on acceptance of the Ulysses Medal brought some "sanity" to this subject in my opinion. Last I checked it was still available online. The lecture is not hard to understand. (Sorry it is no longer available at UCD). It does appear to be available on YouTube: Putnam: The fact/value dichotomy and it's critics.