either what they share is a necessary concomitant of the point on which they differ, or the reverse; or it is an accidental attribute of that point, or the reverse.

We answer him thus: Grant that the element they share, in reality, is inseparable from that by which each of them is distinguished from the other—just as animality is inseparable from humanity, and humanity is inseparable from this particular human being. Yet the element they share never exists outside the mind as an absolutely common thing; rather, it exists (1) only in the intellect and in knowledge as such. Now, if this shared element is a concomitant of the differentiating element (2), no absurdity follows. Even were the necessitant the cause of its concomitant, its determinate existence would be encompassed by the differentiating feature, whereas the common notion that exists in the mind does not constitute a component of the real essence that exists externally. Hence nothing in that external essence would be an effect, still less would its very existence be caused. What is caused is only what exists in the mind, and that, precisely because it is nonexistent outside, forms no part of the thing’s external reality.

Third point: What you yourself have labelled “common element” and “distinguishing element” are, in fact, each a concomitant of the other and necessitated by the other. This is a category you have overlooked. You should have said that the relation must be either concomitant, necessitant, or concomitant-necessitant—like humanity, rationality, and the capacity for laughter, for each of these is both necessitated by and a necessitant of the others. By neglecting this category, your proof is incomplete and fails to accomplish its aim.

Fourth point: You then state, “As for the first of the four possibilities, although it is conceivable in itself, it is inadmissible here, because their difference would lie in both existence and necessity …” and so on to the end of your discourse.