I have until now been silent about the structure Wolff gives to his ontology. We have actually passed already through two sections. First of them showed us the principles governing whatever there can be, while the second then introduced the actual topic of the book, namely, the possibilities or essences. The third section, beginning now, deals then with general affects of the essences – by affects Wolff means all characteristics of a thing, whether they be caused by the internal structure of the thing or by its contacts with other things.
The first type of affect Wolff considers is identity. For the basic definition Wolff uses the so-called principles of the identity of indiscernibles and the indiscernibility of identicals. That is, whenever we can substitute name of one thing with name of an apparently different thing, whatever is predicated of it, the assumedly separate things are actually identical or one thing; and whenever two names refer to same thing, we can substitute one for the other in every context.
Both sides of the principle can be doubted. The identity principle appears at first sight to say that whenever two things have exactly same qualities, they can be identified. The possibility of two exactly similar particles at different points of space seems then a difficulty. We would essentially have to fall back to Leibnizian conclusion that no such exactly similar entities exist. Yet, we can offer a weaker reading of the principle, which manages to circumvent the problem, that is, we can suppose that the predicates in question include relational predicates. Then we can simply point out that of the two particles, one of them, call it A, satisfies the predicate of being identical with A, while the other particle fails to satisfy this predicate – the only fault then being that the whole question becomes rather trivial.
The indiscernibility principle seems even more suspect. We just need to think of a statement like ”Everyone admires Spiderman” and compare it with a statement ”Everyone admires Peter Parker”. Clearly people can admire Spiderman without even knowing that he is Peter Parker. Such problems led the early analytical philosophers to clearly distinguish between extensional and intensional uses of concepts. Words like ”admire” or ”believe” are dependent on the intensions or meanings of concepts – when we admire someone, we actually admire the person as described by our notion of her. Thus, it is more about the case of identity of intensions, for instance, a person thought to be Spiderman is not identical with the same person when he is thought as Peter Parker. In cases where we can instead of intensions speak merely of extensions or the actual things, no matter how they are described, the indiscernibility principle works well.
The problems with confusing intensions and extensions raise the interesting point that identity and indiscerniblity principles are rather poor criteria for recognizing identities – we cannot really go and test with every predicate whether each one of them either fits both names or not. In fact, the whole idea of testing is rather misleading. Before the identity of morning and evening stars was discovered, we would have said that while morning star appears in the morning, evening star never does, making it obvious that the two cannot be identical. It was only after the identity was determined that we could see that certain apparently true predications of morning and evening stars were actually false.
Identities should then be determined through some other, more robust criteria. Problem is whether these criteria are tools to determine independently true identities or whether they actually constitute what is identical. That is, different criteria give different results for certain identities. For instance, one could define the identity of human being from identity of the materials out of which the human body consists, while another person could define it through memories. Now, it could be possible that human body is constantly changing its atoms and that an old person had not a single atom common with a child who had lived earlier, although the old person well remember having lived as the child. Then again, while a blow on the head won't change the atoms of the body in a significant manner, it might purge one's mind of many memories. Thus, there are cases where one criterion will point out an identity, while another doesn't.
In such cases, it might seem natural to ask which one of the identity criteria is correct – and even if neither of them would be correct in every case, we often just assume that there is one completely right criterion of identity. Yet, it also makes sense to question the meaningfulness of such problems – could it be that there are many viable criteria, none of which would be the only truth? Then we could accept one criterion in some cases where it fits quite well and another in other cases: different criteria would be answers to different questions. This would not mean a complete freedom in choosing what to take as identical. Indeed, while it would be in a sense free to specify what one means, when one is looking for identities, this task would usually have an answer clearly independent of us – the concepts would determine only the questions asked, not their answers. Furthermore, even if the notion of one true identification criterion was rejected, this wouldn't cancel the possibility that some criteria might be more natural than others.
Getting back to Wolff, it is difficult to decide which side of the fight he would take. Mainly, he just appears to take his definition of identity granted, which might suggest that he would believe identity to be an independent ontological relation that would hold no matter what our criteria of identity are. Then again, Wolff's main interest appears to lie in finding a definition of identity that works in mathematics. This suggests a certain level of relativity – two mathematical expressions may well be identical, even if what these expressions physically say isn't (say, if the two expressions refer to quantities of different things).
Whatever the case, Wolff clearly admits that identity is a relation not just between (possible or actual) things, because he at once talks of an identity between determinations of different things (for instance, when two different berries have the same shade of red). This identity of determinations clearly differs from the identity of individuals – redness of one berry can occupy different space from redness of another berry.
Now, Wolff continues, if those characteristics of two things are identical that can be used to discern them in themselves (that is, not through relations it has to other things), then the things are similar. Later on, Wolff also explicates that similarity can be defined through identity of essence. The problem lies in deciding what can be taken as the characteristics required in the first definition. Clearly any quantitative characteristics won't do, because we cannot e.g. differentiate a one inch square from a one mile square, unless we can see that one is bigger than the other. Otherwise, the Wolffian requirements of similarity appear to be quite subjective. That is, in different circumstances, different characteristics can serve as marks of similarity, or what is taken as essence depends on what we think as essential. Again, Wolff emphasizes similarity as used in mathematics, for instance, in case of seeing two similar figures we look at their shape (not their size, but also not the material from which they are made).
So much for identities and similarities, next time we shall see what Wolff has to say about universals.