This ontological argument of Duhring is as flawed as the ontological argument for the existence of God.
“How do we get from the oneness of being to its unity? By the very act of conceiving it. In so far as we spread our undivided thought around being like a frame, individual being becomes undivided, a unity of thought; for the essence of all thinking consists in bringing together the elements of consciousness into a unity.” (p 52)
It can also be seen, here, why this approach is loved by the bourgeoisie, and its liberal and social-democratic ideologists. The “nation” is a being comprising such unity, and stands separate from all other such nations. The very fact of its “being”, tautologically united, i.e. in the form of “nation”, “society”, “people”, as concepts in the mind, excludes any fundamental disunity within it, any contradiction or antagonistic interests between capital and labour, for example.
But, that is quite clearly untrue, as wholes are frequently comprised of parts which are contradictory and antagonistic in their relation to each other. Indeed, it is such antagonism and contradiction that provides the dynamic of change within them. It is only in wholes that are dead, and unchanging that there is no such antagonism and contradiction between the parts. Even then, death is not the end, but merely the start of a further process of change and decomposition. An analysis of such wholes requires an analysis of these parts, and the contradictory relations between them, which is what Marx does in Capital.
But, its not just in the real world that wholes are constituted of these parts. In the mind, there can be no unity of the whole, comprising these parts, without also, dividing the whole into these parts, as part of the process of categorisation. If we take the whole of the category “animals”, it also requires us to divide this unity into its parts, so that we distinguish mammals from birds, fish, reptiles, and so on, just as we also distinguish cats from dogs.
“... thinking consists just as much in the splitting up of objects of consciousness into their elements as in the union of related elements into a unity. Without analysis, no synthesis.” (p 52)
But, again, although these categories are ones that the mind establishes for the purpose of analysis, these categories are not ones that the mind simply creates, or plucks from the ether, where they exist as some kind of absolute principle, waiting to be discovered. The differences between cats and dogs, mammals and reptiles do not arise because of the mind's creation of such categories, as mental concepts. The differences between them exist independently from these mental concepts.
“... without committing blunders thinking can bring together into a unity only those elements of consciousness in which or in whose real prototypes this unity already existed before. If I include a shoe-brush in the unity mammals, this does not help it to get mammary glands. The unity of being, or rather, the legitimacy of its conception as a unity, is therefore precisely what was to be proved; and when Herr Dühring assures us that he conceives being as undivided and not perchance as a duality, he tells us nothing more than his own humble opinion.” (p 52)
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