I learned this lesson intellectually some time ago, but it was driven home to me over the last week: philosophers with different paradigms will find no central question, no decisive claim, that will provide an objective ruling in favor of one paradigm or the other.
The lesson was taught most famously by Thomas Kuhn in his Theory of Scientific Revolutions. Kuhn focused on the debate between Ptolemaic and Copernican astronomers, and argued that the Copernican revolution in fact was not triggered by any objective observation or test. The Ptolemaic astronomers could account for everything Copernicus could – indeed, with greater accuracy – and once the Copernican system was revved up to match Ptolemy’s, in predictive accuracy, it was every bit as complicated as the Ptolemaic system. (With one exception: Copernicus needed epicycles and eccentrics, he didn’t need equants; still, small shavings from Occam’s razor.) Why then did the revolution occur? According to Kuhn, the young astronomers were excited by the radicalness of Copernicus’s view, the old astronomers died, and the young ones took their jobs. Hardly a rational way of doing science.
It should be no surprise that the same is true in philosophy. My friend and I were arguing about the biomechanics of life, and whether materialism had all the answers, or whether something Aristotelian is needed (an immaterial form). I kept insisting that “livingness” is a matter of complexity: arrange the parts in the right way and it’s alive, nothing immaterial needed. My friend kept insisting that “the right arrangement” is in fact what Aristotle means by “form,” and so it is required, and obviously an “arrangement” is immaterial. I responded that he was turning an adverb into a noun: a “way” into a “thing.” And we kept going round and round, until we were left just giving one another incredulous stares, wondering how any intelligent and informed person could not agree with what each of us was saying.
“Incommensurable” means “no common measure.” And that’s the situation we were in, and the situation the Copernican and Ptolemaic astronomers were in: there was no question that could be formulated, no decisive test proposed, that would clearly say, “This one is right and that one is wrong.” Each paradigm had its own way of answering each question or interpreting each test or observation. So, if someone does switch sides, it’s not for any genuinely compelling argument: it’s a vague matter of “what fits best” given that individual’s experiences, preferences, and values.
Now not every dispute is incommensurable in this way. Once two people share a paradigm, there’s lots of stuff that can be settled through experiments and arguments. And some paradigms might be subject to practical refutation, if not theoretically pure refutation. (Meaning, the theory gets so cumbersome and wonky that it just appears silly to defend it.) But it seems that on many big, very big questions, incommensurability stops us from getting any clear sight of the truth.
Huenemanniac 
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