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Positivism asserts that any statement that cannot be empirically tested is meaningless. But obviously, this is a self-refuting statement, because it can't be empirically verified as well.

How do the logical positivists, or the descendants ( modified or not) of logical positivists defend against such an argument?

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    To answer the question would require finding a classical logical positivist. Good luck with that. – virmaior May 27 '14 at 7:35
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    I think that in more "mature" exponents of Logical positivism (e.g.the "late" Carnap) you can find assertions regarding the "positive role" of metaphysical assumptions or concept in the development of scientific knowledge. – Mauro ALLEGRANZA May 27 '14 at 7:40
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    There are some analytic philosophers who are descendants of the logical positivists, but I'm 95% sure the original project with its beliefs about being able to do wholly without a metaphysic and translate all natural language to propositional language is dead. Might still be some really old adherents. – virmaior May 27 '14 at 7:41
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    I'd be curious if historically this did coe up in the debates with logical positivis in the middle of the last century. – Mozibur Ullah May 27 '14 at 10:15
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    Perhaps few if any professional philosophers accept LP, but it is alive and thriving among atheists and skeptics who like to post in online forums and comment on blogs. Therefore, a hearty +1. @firtydank: why don't you write an answer along the lines of your comment? – labreuer May 27 '14 at 16:22
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What you call "Positivism" there is but a crude description of a principle that has been associated with them. Let's consider a more faithful description of the so-called empiricist criterion of meaningfulness:

Criterion. (Hempel 1965b) A sentence makes a cognitively significant assertion, and thus can be said to be either true or false, if and only if either:

  1. it is analytic or contradictory, or

  2. it is capable, at least potentially, of test by experiential evidence.

In the first case, the sentence is said to have a purely logical meaning; in the second case—an empirical meaning or significance. Hempel calls this principle the testability criterion of empirical meaningfulness, and ascribes it not only to empiricism, but also to operationalism and pragmatism (appropriately or not isn't the topic of our discussion here). The criticism as applied to Criterion would be

Criticism. (Graviton) Criterion is self-refuting, because it cannot be empirically verified.

Of course, Hempel's version wasn't the one being criticized. I welcome Graviton to modify the critique to this particular case, if it too suffers from the same flaw. Until then, we should start by noting that the Criterion is of a disjunctive form: either condition (1) is met or (2). It is obvious that Criterion, like the claim "0 ≠ 1", is incapable, even potentially, of being tested. The arithmetical claim is analytic (logically true with respect to Peano's Axioms, say). But so is Criterion:

Defense. Criterion is analytic, and is thus: meaningful according to Criterion.

Neither is capable of being tested. You can reject Peano's Axioms so that you won't have to accept that 0 ≠ 1. You can also reject Criterion so that sentences like "John's aura is powerful" don't become cognitively insignificant. Tolerance (another positivist 'doctrine') is the key here. Consider the definition:

Criterion 2. A binary relation R is called 'symmetric' if and only if for all x, y, xRy implies yRx.

Is Criterion 2 meaningful? Yes. Is it capable of empirical testing? No. Is it analytically true? Yes. It is, of course, possible to say that definitions like Criterion and Criterion 2 are not the sorts of things that can be true or false, but I'm hesitating to commit to that stronger view of definitions to keep things simple.

The topic has spawned a lot of literature over the last (half a) century. It would be good news to some if positivism was dead, for then, there would arise the opportunity to skip reading stuff from Russell, Wittgenstein, Carnap, Ayer, Hempel, Reichenbach, Menger, Hahn, and others on all sorts of interesting topics. But if we're going to bury positivism, the least we can do is shove the right body into the coffin.

                                                                     References

Lewis, D. (1988) "Ayer's First Empiricist Criterion of Meaning: Why Does it Fail?"
Hempel, C.G. (1965a) Scientific Explanation: Essays in the Philosophy of Science.
Hempel, C.G. (1965b) "Empiricist Criteria of Cognitive Significance: Problems and Changes".

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    Is Criterion analytic? An analytic statement is a tautology, right? Then what is equal to what in Criterion? Your answer here makes it seem like Criterion assumes Criterion, which is circular reasoning. – labreuer May 28 '14 at 16:48
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    @labreuer (1) Analytic is logical truth with respect to a set of axioms/postulates. Criterion itself is nothing more than a postulate, so you can say that it is vacuously true with respect to itself. (2) There is no circularity. Criterion is a sentence, and since it's talking about sentences, it is also talking about itself. (3) In retrospect, I think I should have said that Criterion is neither true nor false. Definitions can be inconsistent, etc., but they can't be false. So I'm not sure saying that definitions are true is informative. I need more feedback on this issue. – Hunan Rostomyan May 28 '14 at 16:56
  • Ahh, but if definitions need not satisfy Criterion, I have a few theistic ones to add to the pot... – labreuer May 28 '14 at 17:04
  • @labreuer I don't see the problem with that. You're free to define anything you want. Again, tolerance is the key. – Hunan Rostomyan May 28 '14 at 17:10
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    @labreuer Most people are. What logical empiricists are against is nonsense (like "the absolute is perfect"?). Most, if not all, of today's metaphysics and theology makes a lot of sense. 'Metaphysics', of course, means something different today. Maybe that's part of the problem. – Hunan Rostomyan May 28 '14 at 22:17

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