WHILE SOME ARISTOTELIAN CATEGORIES ARE LOGICALLY POSSIBLE, THE OBJECTS SUBSUMED ARE IMPOSSIBLE.
If then, considering the constitution of the relative relations as a generic form, it be admitted that it constitutes an unity, it forms a classification; consequently it constitutes an existence and a form in all things. But if the reasons (or, relations) be opposed to each other, if the above-mentioned differences obtain among them, they do not constitute a class, and everything must be reduced to a resemblance, or category. Now, even if we admit that the things of which we have spoken can be reduced to a unity, it does not follow that all the things gathered under the same category by the Aristotelians, could be reduced to a single sort. Indeed, they lump together into the same classification, both objects and mere statements of their absence, as well as the objects which derive their appellation from them; as, for instance, doubleness itself, and the double object. Now how is it possible to reduce to the same classification both a thing and the mere lack of it, as, for instance, doubleness and the non-double, the relative and the non-relative? This is as absurd as it would be to gather into the same classification the living "being," and the non-living "being." Worse yet, how could one assort together duplication and the double object, whiteness and the white object? Such things could not possibly be identical.
3. QUALITIES.[260]
10. We are now to consider quality, on account of which a being is said to be "such." What can be the nature of this quality that it exerts the power of deciding of the phenomena of objects? Is there a same, single quality which is something common to all qualities, and which, by its differences, forms classifications? Or are the qualities so different that they could not constitute one and the same classification? What is there in common between capacity and disposition[261] (that is, the physical power), the affective quality, the figure, and the exterior form?[262]