The verification principle is too narrow...

In its simplest form, the principle goes like this : The meaning of a proposition is its method of verification, with the important corollary that a proposition without a method of verification is meaningless. This is one of the basic tenets of Logical Positivism and, most famously, the one marshalled into the service of the movements goal to eliminate metaphysics (metaphysical statements, having no method of verification, are meaningless).

One of the most common technical attack against Logical Positivism is to show that this principle is too narrow, i.e. that it eliminates as meaningless a number of sentences that the Logical Positivists would admit themselves to being meaningful. One such sentence is 'all men are mortal' and in fact, many other statements with an universal quantifier ranging over a potentially infinite set of natural objects, could be used to the same effect. The other name of Logical Positivism, and in fact, the one prefered by its members, is Logical Empiricism. So in all cases, what is meant by 'method of verification' is 'empirical method of verification'. That is to say a procedure, or series of steps, that can actually be performed by an individual or group of individuals in a real situation. One of the consquence of this is that the procedure in question must involve no more than a finite number of steps. But how are you going to check that all men are mortal in a finite number of steps ? Should we declare this statement meaningless and, with it, all the familiar ones like 'All C14 nuclei will eventually disintegrate' ?

In the same vein, but even more crucially to science, are statements like 'the laws of nature do not vary arbitrarily'. How is anyone going to engage in doing Physics if he does not believe that the laws of nature are stable over time ? So, presumably, all physicists believe in the statement above. And 'believing in' is even stronger than , and thus entails, 'considering meaningful'. But how are you going to check in a finite number of steps that the laws of nature, or even a single one, is stable over time ?

A last example, from computability theory, that is to say, from logic itself. The statement 'the Turing Machine M terminates' is presumably meaningful: it derives from the very definition of the mathematical object 'Turing Machine'. But it is provably impossible to verify it in a finite number of steps as established by the 'undecidability of the halting problem' theorem.

So, after examination, the verification principle, which was meant as a very precise and clear-cut discrimination tool, seems to be doing a lot of damage in the Logical Positivists own foot soldiery's ranks : the scientists. A case of 'friendly fire', or so it seems.