After concluding the Latin version of his logic, Wolff moved on to translate his metaphysics. Just like with logic, the latinization added a huge amount of pages to the German version. Thus, Wolff actually divided his metaphysics into five parts, each corresponding to a chapter in the German metaphysics. This series begins with Prima philosophiae, sive ontologia, Wolff's Latin take on ontology.
As a careful reader might notice, there is no book corresponding to the first chapter of German metaphysics, the Cartesian beginning establishing the existence of human consciousness. Instead, Latin ontology begins with a general examination of the nature of ontology. Like the title of the book says, ontology is primary or first philosophy, on which all other philosophical disciplines should be based. This means that even logic or the very methodology of science is based in Wolffian scheme on ontology. What Wolff means is apparently that we couldn't be doing science, or indeed, doing anything, if we, among other things, did not exist.
The description of ontology as a philosophical discipline is also important. Just as we can distinguish natural logic or natural means of cognizing from philosophical or artificial logic, similarly there is a natural ontology, or in other words, we humans have a natural tendency to categorize and conceptualize things that exist. Just like natural logic was not enough for Wolff, he is certain that natural ontology also requires some improvement. This was already attempted in scholastic philosophy, which tried to define ontological concepts more carefully. Yet, scholasticism was sterile, Wolff thinks, and the reason of its sterility was hidden in its lack of scientific form. That is, Wolff explains, scholastics failed to base their ontology on demonstrations starting from evident axioms and reliable experiences.
Wolff's evident attempt is to fix the mistake of scholasticism and to base his ontology on the most certain principle of contradiction. As one might remember, in German metaphysics Wolff wanted to justify the principle through the Cartesian beginning of the whole book: if the principle wouldn't have worked, neither would have the beginning been indubitable. Here Wolff does not have the luxury of assuming the existence of anything. Yet, he also does not just want to accept the principle dogmatically, but tries to give some justification for his position. Wolff's justification is what would later be called psychologistic or it bases theories of what there is on assumptions of what (human) mind can do. Anyone would notice that we cannot think of one thing having two sets of contradictory predicates at the same time, Wolff remarks. The easiest way to explain this is to assume that this repugnant nature of contradiction just follows an ontological truth: things really cannot have and not have some property at the same time.
Indeed, as we already saw when dealing with German metaphysics, the principle of contradiction is an ontological and not merely logical principle for Wolff. What this ontologicity means might be difficult to understand. In German metaphysics it all ultimately led to God, who thought of all possible worlds, but could only will one to existence, because these worlds cancelled one another. Here Wolff is dealing only with ontology and God must still be left out of the equation.
Instead of God, Wolff then bases the principle on what is ontologically primary according to him, that is, individual things – Wolff is a committed nominalist denying the literal existence of e.g. universals. Individual things then cannot have a property (e.g. redness) and at the same time not have it, that is, have a property cancelling the first one (blueness or any other colour beside redness). Possible characteristics, as it were, battle over individual objects and just by their presence exclude other characteristics. It is then redness of this individual that contradicts blueness of the same individual, and the more general contradiction between e.g. redness of all members of a genus and blueness of one member of this genus is just an abstraction out of the concrete relations between individuals.
|Yellow and white battling over the supremacy of the ball surface.|
Although the principle of contradiction should be the highest principle of philosophy, Wolff does not mean that all things could be proved from it – we just have to remember the possibility of using indubitable experiences as further premisses. Yet, he is willing to allow that we can deduce something out of it. For instance, Wolff thinks that the principle of identity, ”what is, is what it is” could be easily derived from the principle of contradiction. Indeed, one would hardly want to deny that the two principles are quite closely related. Well, Kant did deny this, but he was probably reading the principles in a strict logical sense: because negating and affirming are two different activities, there must be different principles governing them. Ontologically, on the other hand, it seems more reasonable that by excluding certain characteristics a thing must presents others.
A more difficult to explain is Wolff's willingness to deduce the principle of excluded middle from the principle of contradiction, especially as we know that the two principles are actually independent of one another. How so, you ask? Think of the principle of contradiction saying that a proposition cannot have both the values 1 or true and 0 or false and the principle of excluded middle saying that its only possible values are 1 and 0: then the first principle does not preclude the possibility of a proposition having a third value (say, ½), while the second principle does not say that it couldn't have two values at the same time.
Judging by Wolff's actual proof of the principle of excluded middle, it appears that there's a hidden ontological presupposition behind it. We are still thinking of individual objects and their possible characteristics. Now, denial of one characteristic of a thing (say, redness) means just insurgence of another characteristic of the same type within this thing (say, blackness). In other words, there are no bare or characterless particulars in Wolffian scheme of things. Then the law of excluded middle becomes a triviality. If you would deny a property A of a thing, this means that another property of the same sort, but incompatible with A arises, and if you deny property non-A, that is, all the properties of the same type than A, but incompatible with it, then A itself must arise. Thus, if you deny both A and non-A, you are actually also letting both A and non-A exist within the same individual thing, which then contradicts the principle of contradiction.
The most famous is undoubtedly Wolff's apparent attempt to deduce the principle of sufficient reason/ground from the principle of contradiction. I myself have already tackled the issue earlier, but I think the topic deserves a second chance. But that's something for the next post.