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B      opens his discussion of the problem of universals, in his second commentary on Porphyry’s Isagoge, with a destructive dilemma: genera and species either exist or are concepts; but they can neither exist nor be soundly conceived; therefore the enquiry into them should be abandoned (In Isag. maior . ). Boethius’ strategy to get around this dilemma is well known. He follows the lead of Alexander of Aphrodisias, distinguishing several ways in which genera and species can be conceived, and he argues that at least one way involves no falsity. Hence it is possible to conceive genera and species soundly, and Porphyry’s enquiry into them is therefore not futile after all (. ). Boethius thus resolves the second horn of his opening dilemma. Yet he allows the first horn of the dilemma, the claim that genera and species cannot exist, to stand. The implication is that he takes his arguments for this claim to be sound. If so, this would be a philosophically exciting and significant result, well worth exploring in its own right. Yet there is no consensus, either medieval or modern, on precisely what Boethius’ arguments are, or even how many arguments he offers, much less on their soundness. One reason for the lack..
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