Consider the following quote from Dirac's book, The Principles of Quantum Mechanics (4th ed., p. 36):
When we measure a real dynamical variable ξ, the disturbance involved in the act of measurement causes a jump in the state of the dynamical system. From physical continuity, if we make a second measurement of the same dynamical variable ξ immediately after the first, the result of the second measurement must be the same as that of the first. Thus after the first measurement has been made, there is no indeterminacy in the result of the second. Hence, after the first measurement has been made, the system is in an eigenstate of the dynamical variable ξ, the eigenvalue it belongs to being equal to the result of the first measurement. This conclusion must still hold if the second measurement is not actually made. In this way we see that a measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured, the eigenvalue this eigenstate belongs to being equal to the result of the measurement.
This is usually presented as a postulate in a system of axioms for QM; here Dirac is arguing for them, and not simply asserting them.
What is curious here, given the association of positivism with science, and particularly in physics, is that Dirac's argument, though going through by instrumentalism, relies on 'measurements ... not made'; and in fact it appears that the underlying principle that he relies on is 'physical continuity'; continuity is of course something that Aristotle goes on at great length in his Physics - there is a whole chapter devoted to it.
On the positivistic interpretation of physics, how does one argue for the principle of physical continuity? And is it correct to say, that once this has been shown, then positivistic sense can be made of 'measurements ... not made?'; or is there some further subtlety I've missed?