Leibniz's misunderstanding of Nisolius notion of `multudino'.

Abstract

The Renaissance humanist Nizolius1 is a remarkable exception in the history of philosophy, where the notion of class appears to be extremely rare2. Nizolius substitutes traditional universals by what he calls multitudines and during more than four hundred pages he tries to convince his readers that in the real world there are only individuals and collections of individuals3. It is not perhaps clear whether Nizolius' multitudo comes closer to class or to heap4. General terms in the plural (homines) designate, of course, the corresponding multitudo; in the singular number they designate properly one individual5, and figuratively the multitudo again6. We may understand homo animal as having its two terms used in the figurative sense, but then what does the copula mean? Talking in terms of modern logic we could say that the meaning of the copula should be class-inclusion and not class-membership. In fact Nizolius himself frequently stresses that should be substituted by est in7. Now, it is extremely puzzling that Leibniz seems to have completely missed such a point of Nizolius' theory, because he erroneously thinks that Nizolius' approach leads to such absurdities as {horno}e{animal}8 or to such falsities as {homo}={anima l}9. How or why this could happen, is indeed quite enigmatic10. Leibniz's misunderstanding seems to concern not only a detail, but the very basic conception of the book he was editing for the second time, as is suggested by the fact that Leibniz's account of Nizolius' universals begins with a quite misleading formulation11. Moreover Leibniz assigns to Nizolius' extensionalist view a deduced character12 which it does not have: familiarity with Nizolius' work shows that the insight into universals as collections was something fundamental, a starting-point from which traditional logic and ontology had to be revised. Again, Leibniz suggests that Nizolius has forgotten that there is a totum distributiυum besides individuals and classes13; but Nizolius knows quite well the traditional doctrine de totis 14 and although he does not seem to give explicit rules for translating into his language sentences with quantifiers15 (omnis, etc.), it is obvious that he preserves the notion of the totum