Was the Verification Principle Self-referentially Contradictory?

[In the following I'll take the words 'verifiability' and 'testability' as synonyms.]

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It's strange (prima facie strange, at least) that in a philosophical world (circa the 1920s to the late 1940s) in which metalinguistic statements and meta-languages (along with other higher-order techniques) were so popular that the verificationist principle (as well as Popper's falsificationism) came in for so much criticism.

In any case, there are many and various versions of Verification Principle, each of lesser or greater degrees of detail. However, I'll use the following simple expression of it. Thus:

“Every statement must be testable/verifiable or tautological in order to be meaningful.”

Of course we can now ask:

What about this very statement? Is that testable/verifiable or tautological?

It's almost obvious that the verificationist statement was aimed at statements which refer to the world. If that wasn't the case, then why would verificationists have talked about ‘evidence’, ‘testability’ and ‘verification’ in the first place?

Clearly

“Every statement must be testable/verifiable or tautological in order to be meaningful.”

is not itself a reference to the world as such (even if it's taken to be either false or normative). The expression itself can be said to be in the world. (Where else could it be?) Nonetheless, it may have the status of expressing an abstract entity that isn't in the world. In that case, it's an abstract entity (expressed linguistically in space and time) about other entities (i.e., what all other statements refer to). These other entities, on the other hand, purport to refer to the world or are tautological. This isn't the case with the verification/testability statement. Clearly, then, it's not testable or verifiable in the way in which statements about the world are testable or verifiable. It's of a different logical order. That much can be granted. (Though if that much is indeed granted, then so many more statements can be granted – as it were - a special status.)

The testability principle is a statement. Therefore, on first glance, it must refer to itself; primarily because of the quantifier “every” at the beginning. It states that every statement must be verifiable/testable or tautological. Therefore it must also be verifiable/testable or tautological. The statement can, of course, be taken normatively. In that case, it may not be correct to call it a “statement” in the first place (see later).

There’s a simple way out of this. Take this reformulation:

Every statement about the world must be testable/verifiable or tautological if it's to be deemed meaningful.

Now the above can be taken to be a linguistic expression of an abstract content/proposition (i.e., that's not strictly speaking in the world or a reference to the world). It's not, therefore, a reference to things/events/conditions/etc. which are in the world (i.e., the statements themselves).

Thus the verificationist statement doesn't refer to the world; though the statements it refers to do refer to the world.

We can now have another formulation:

The testability statement expresses an abstract entity (i.e., it can be taken propositionally) which refers to entities (i.e., statements) which refer to the world.

It follows that the verificationist statement (at least on the reading so far given) needn't necessarily be verifiable/testable or tautological. We could see it, instead, in various other ways. It could be a normative, stipulative, prescriptive, foundational, axiomatic or simply a higher-order statement. Whether any of these possibilities are workable (or acceptable) is another matter. Nevertheless, the testability statement is certainly of a different logical order than statements which refer to the world.

The Normative and Modal 'Must'

The testability principle states that meaningful statements must either be testable/ verifiable or tautological in nature. This “must” can be taken normatively or modally. If taken normatively, then the word “must” can also be replaced by the word “should”. (This would make its normative character clearer.) If “must” is taken logically, on the other hand, then the testability meta-statement is claiming that all statements about the world are either testable/verifiable or tautological otherwise they're meaningless. It can also be a modal claim about meaningful world-directed statements at all possible worlds.

In a sense, then, the modal and normative character of the testability statement can't be clearly disentangled. That is, if it's the case that all meaningful statements which refer to the world are testable or verifiable, then the verificationist can also say that they should be testable or verifiable (in order to be genuine statements about the world). The normative “must” (or “should”) is therefore born of the modal “must”. Or, more clearly, the normative “must” (or “should”) is born of the modal property must necessarily be the case. Of course what's necessarily the case doesn't depend on what should necessarily be the case (or even on what simply should be the case). However, we're talking about both a normative statement and a statement that also includes a modal claim about world-directed statements in all possible cases or situations.

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Finally, even if the Verification Principle isn't “self-referentially self-refuting” (as it's often put), that doesn't automatically mean that there aren't other things wrong with it.