American pragmatism wasn't British empiricism, but nevertheless a cousin of the latter as well as influenced by related positivism. Pragmatists shared the developing Anglophone trend of distaste in metaphysics (IOW, there's ironically little salvaging of transcendent possibilities in pragmatism compared to the former "practical division" of philosophy, corrected by Kant). So any survival of religious beliefs had to be grounded somehow in experience* or the empirical world. Such as indeed converting the value of "religious belief" or a state about its "truth" into merely action or observable events and their consequences. (*Or even restricted to language -- this more applicable, of course, to the emerging analytic philosophy and logical empiricism of the era).
The "distaste in metaphysics" can have many sources.
With James, I have the impression that distaste is due to his sense of
urgency of moral action, rather than anything else.
The difference between the philosopher and the religionist is sometimes sumed up
thus:
"Seriousness is precisely the difference between philosophy and religion. The philosopher deals in expendable theories; the religious man puts his life on the line."
Furthermore, regardless of clinging to contrary beliefs, the individual always has the overhanging threat of her decisions not being her own in the world of experience -- a puppet of either determinism or some heteronomic situation -- making even pragmatic choices simply another illusion that personal decision-making is taking place.
Solipsism, consequent determinism and a few other choice players tend to hold us firmly in their grip, once they catch on.
And in our standard Western view, their threat is real, as we don't believe that a real change in how we experience the world is possible.
The Buddhists aspire to the as-yet-unrealized, the as-yet-unattained, to an altogether different
category of being. This places the above threat into a different context, last but not least, diminishing it.
To put it another way: In the context of the division of philosophy into theoretical and practical, what James refers to would be probably classified as "technically-practical" -- actually on the theoretical rather than practical side (elaboration below). So pragmatism is captured somewhat by Kant's scheme, but not on the practical side of the dichotomy as one might initially feel because of the word-meaning similarity.
I come form a somewhat Eastern perspective, and from there, reading James and others looks different. James' pragmatism doesn't seem shallow or misleading.
The Buddhist would not ask "What exists?" Rather, he would ask "What, when I do it, will be for my long-term welfare and happiness?"
Buddhist empiricism, probably Eastern epiricism in general too, is dramatically different from Western empiricism.
Western empiricism looks without, seeking interpersonal verifiability. Buddhist empiricism looks within, seeking realization, attainment - within.
But everyone, East or West, at least implicitly believes, considers it a mark of maturity, to be able to "look oneself in the face," "to live with oneself," to know that "at the end of the day, one has noone to count on but oneself."
And the Buddhists and Western pragmatists are far more aligned with this basic principle of personal integrity, than the Western empiricists and analytical philosophers.
Watson: It is of the greatest consequence to distinguish clearly between these two spheres.
Why? What will clearly distinguishing between theoretical and practical philosophy accomplish?
Well, again, that tradition in western philosophy was around before Kant. But Kant's scheme, when better understood, is maybe the only satisfactorily one I've found that can assimilate almost any of the other systems without doing any damage to science, while also preserving beliefs not compatible with science. I've tried to abandon it many times but repeatedly found myself returning because it was most equipped to dis-entangle the confusion elsewhere with minimum bias.
But what does Kant's scheme do to help you in your own day-to-day decision-making and pursuit of happiness?
As many people told me in earlier days, "As painful and tedious as it is, you will have to actually read and understand Kant yourself, not try to do it entirely from second-hand sources that are sometimes either clueless or mis-representative." And they were dead-on correct about that.
I admit that although I am fluent in German, I have barely read any Kant.
From what I have read, I doubt that he is a viable alternative to the Buddha.
Influences from either the human's noumenal self or other unconditioned sources would converge with natural causes in the experienced (conditioned) world, and thus be hidden or indiscernible. That is, quite futile to try and verify since there would always be an alternative scientific explanation available. So one might contend that Kant is non-theist from a positive POV in empirical realism, but vacillates between theism and agnosticism in practical reason (where a noumenal POV is viable).
But whence this drive for verification?
What is hoped to be accomplished by interpersonally verifying a hypothesis?