Importance of Truth in "Insignificant" Arguements

In "What Pragmatism Means," William James shows how ridiculous some arguments truly are because nothing changes with the choice of either option. He claims, "It is astonishing to see how many philosophical disputes collapse into insignificance the moment you subject them to this simple test of tracing a concrete consequence. There can be no difference anywhere that doesn't make a difference elsewhere-no difference in abstract truth that doesn't express itself in different concrete fact and conduct consequence upon that fact, imposed on somebody, somehow, somewhere, and somewhen" (96). This made me think back to the two laws he presents in "The Will to Believe": "Believe truth! Shun error!" (82). What I wonder is how important are these laws if it is a situation when there is no difference in outcome whether you believe truth or error? If, as James says, that arguments only have significance when the effect of choice A or choice B does not result in the same effect, then must we still take the time to determine which option A or B is really the truth?