Marx’s logic in Capital is impeccable, and Marx lets us know how proud he is of it with interminable arithmetic demonstrations of the successive relations. But Marx does his logic differently from Hegel. I’ll give a couple of examples.
In Part I, Hegel would have been content to say that as money is exchangeable for any other commodity it is thereby the universal commodity. But this was not enough for Marx. Marx had to take us through §3 of Chapter 1, tracing the historical genealogy of money beginning from the simple commodity up to money. This was necessary to prove that money was indeed the universal commodity. A mental operation was insufficient.
Another example, this time from Part III. For the worker, the commodity — be that labour power or a product, C, is exchanged for money, M, so as to purchase the means of life. For the capitalist, however, money M, is exchanged for commodities and withdrawn again to realize a profit, M—C—M’. It is easy enough to see how these two transformations are both made possible by the endless chain of M—C—M—C—M... and Hegel would require no more. But with some clever arithmetic, Marx shows that M—C—M’ is impossible until an employer has at least a certain number, maybe 8 labourers before he can implement M—C—M’. “The guilds of the middle ages therefore tried to prevent by force the transformation of the master of a trade into a capitalist, by limiting the number of labourers that could be employed by one master within a very small maximum.” (Capital v. 1, ch 11). Thus the transformation of money into capital had this historical precondition, to overcome the resistance of the guildmasters.
This is the difference between Hegelian Logic and Marx’s logic which, as he says in the Grundrisse, takes place not “as it appears in the head,” but “the real subject retains its autonomous existence outside the head just as before “ It is different also to the normal work of the historian, because Marx is interested in the genealogy of each single relation, not the history of economic systems, for the logic of capital.