William James on the conciliation of religion and science; also, mathematics and pragmatism

I'm presently reading William James' Varieties of Religious Experience. Like much of James' writing, some of it can be rather pedestrian and ponderous but then certain sections jump out like great glowing epiphanies. I like this section from the end of lecture 5 on "The religion of healthy-mindedness" in particular:

The experiences which we have been studying during this hour (and a great many other kinds of religious experiences are like them) plainly show the universe to be a more many-sided affair than any sect, even the scientific sect, allows for. What, in the end, are all our verifications but experiences that agree with more or less isolated systems of ideas (conceptual systems) that our minds have framed? But why in the name of common sense need we assume that only one such system of ideas can be true? The obvious outcome of our total experience is that the world can be handled according to many systems of ideas, and is so handled by different men, and will each time give some characteristic kind of profit, for which he cares, to the handler, while at the same time some other kind of profit has to be omitted or postponed. Science gives to all of us telegraphy, electric lighting, and diagnosis, and succeeds in preventing and curing a certain amount of disease. Religion in the shape of mind-cure gives to some of us serenity, moral poise, and happiness, and prevents certain forms of disease as well as science does, or even better in a certain class of persons. Evidently, then, the science and the religion are both of them genuine keys for unlocking the world’s treasure-house to him who can use either of them practically. Just as evidently neither is exhaustive or exclusive of the other’s simultaneous use. And why, after all, may not the world be so complex as to consist of many interpenetrating spheres of reality, which we can thus approach in alternation by using different conceptions and assuming different attitudes, just as mathematicians handle the same numerical and spatial facts by geometry, by analytical geometry, by algebra, by the calculus, or by quaternions, and each time come out right? On this view religion and science, each verified in its own way from hour to hour and from life to life, would be co-eternal. (99-100)

This brief note on mathematics reminds me of Isabelle Stengers' regular insistence on the importance of the fact that A. N. Whitehead was a mathematician. Far from granting transcendent access-authority to a higher realm of ideas, in this understanding mathematics heightens only one's capacity for perspective-shifting—that is, for pragmatism.