(btw I probably meant to write "irrefutable") A irrefutable proof in mathematics is no problem - no theoretical possibility of being incorrect exists. But, if

(btw I probably meant to write "irrefutable") A irrefutable proof in mathematics is no problem - no theoretical possibility of being incorrect exists. But, if the phrase "irrefutable proof" in "softer" context is to have any meaning at all, it can't mean the same as in maths, since there will always be a possibility of being incorrect. By using the phrase at all in eg. biology, it must therefore mean "the possibility of being incorrect is vanishingly small", otherwise we're just talking gibberish. Generally, different context give the same phrase different meanings, so taking literal logical paths through a series of different statements is silly and pointless and best left to philosophers. :)