unnecessary. But this last criterion is evidently a procedure, to remedy the difficulty of judging individual propositions, by having recourse to a system of ideas, whose mutual relevance shall lend to each other clarity, and which hang together so that the verification of some reflects upon the verification of the others. Also if the system has the character of suggesting methodologies of which it is explanatory, it gains the character of generating ideas coherent with itself and receiving continuous verification.
The whole point of the fifth criterion is that the scheme produces a greater understanding of the world, including the better definition of ideas and the more direct analysis of immediate fact. A single proposition rests upon vague apprehensions: whereas a scheme of ideas provides its own measure of definiteness by the mutual relatedness of its own categoreal notions.
It is by their emphasis on schemes of thought that the Greeks founded the various branches of science, which have remade civilization. A proposition which falls within a scientific scheme is accepted with surprisingly slight direct verification. For example, at the present time we all accept the famous doctrine of the shift of the spectral lines. But so far as direct evidence is concerned, there are some experiments on rays from the sun, with very dubious interpretations, and the clear-cut instance of the light from the dark companion of Sirius. There are millions of untested stars, apart from the question as to
