Same as usual

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.

Christian Wolff: Remarks on Reasonable thoughts on God, the world and the human soul, also on all things in general - Fragments of ontology

It's hard to do commentary on another commentary – you are twice removed from the real meat of the problematic, and because the commentary itself has no clear organisation, there usually is no guiding thread to connect the various points. Thus, after reading the chapter on ontology I was left with mere crumbs that by themselves would not have the required length of a blog post. Still, I didn't want to make the time spend with Wolff's commentary go to waste, so I present some of these crumbs in a fragmentary fashion.

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One key point in the atheism dispute has been the notion of modalities: if Wolff says that events in the world are hypothetically necessary, doesn't this make his theory Spinozistic? Wolff's consideration of modalities here reveals his own belief – Wolff has to define modalities in this manner to avoid Spinoza's fatalism. That is, Spinoza could say only that possibility means something that has existed, will exist or does exist, which would make all possibilities become actual someday. Wolff's definition of possibility as non-contradictoriness allows the extension of possibility to be larger than the extension of past, present and future actuality. Thus, the only truly necessary thing for Wolff is God, who has no external cause, while other things require some previous cause for their actualisation. Interestingly, the tide of philosophy was to go backwards. What is true sense of possibility and necessity for Wolff, will be disparaged by Kant as a mere formal notion of modalities, while the mere hypothetical necessity and possibility in a world of Wolff are raised to the status of real or ontologically substantial modalities by Kant.

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Connected with the Wolffian theory of modalities is his notion of essences, which he clarifies in his commentary through a helpful simile: if I want to determine what a triangle is like, I need to only determine its essence, that is, two of its sides and the angle between them, because the rest of the triangle is determined through these measures. Unexpectedly, this very same example occurs in Hegel, when he explains how the sensuous side of a thing (say, a triangle) contains lot of surplus material that could be summarized through a lot simpler structure (in this case, through the three quantities). I suspect that Hegel didn't bother to read that much Wolff, so the coincidence is even more surprising.

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Wolff's nominalism is a feature I did not emphasize the first time around: he explicitly says that universals or genera and species are mere summaries for similarities between things (A and B are both ostriches  because they resemble one another and all the other ostriches . An interesting question is then how the similarity is to be defined, and in general, how things are distinguished from one another. Now, in some places Wolff appears to admit at least the possibility or conceivability that two spatially separated individuals of the same species might be identical in every other respect, thus going against Leibnizian principle of the identity of indiscernibles. Then again, Wolff also subscribes to the definition of individuals as fully determinate in comparison to incompletely determined universals – we noted in case of Thümmig that this definition appears to naturally lead to the Leibnizian principle, because two distinct individuals couldn't on account of this definition be completely similar, because they would then belong to a genus defined by all their characteristics – contradiction, because this genus would then be a completely determinate universal. One possible solution might be that the complete determination of individuals would not consist of mere qualities, but also of quantitative and spatial determinations. Indeed, Wolff says ambiguously that individuals are determined by what we can perceive in them, which might include also their position in space.

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Next time it's on to psychology!

Ludwig Philipp Thümmig: Institutions of the Wolffian philosophy provided for the use of academics - Fully determinate individuals

The difference of individuals and universal properties has been recognized at least since the time of Aristotle. Indeed, it is obvious that the universal genus of horse is not an individual horse, although on some reading Plato had treated the genus just as one individual among others. Despite the familiarity of the distinction, it is quite hard to say what exactly differentiates universals from individuals.

Now, Thümmig suggests the rather curious definition that individuals are fully determinate in every way, while universals are still further determinable. The idea behind the strange definition is actually rather simple. Take some general class of things, such as vertebrates. Now, if we know that an animal is a vertebrate, we know something of it – at least that it has a vertebra. Still, many other characteristics of the said animal are completely undetermined by its being a vertebrate, for instance, whether it flies or not. Universal vertebrate is thus determined through this collection of properties shared by all vertebrates. This collection does still not determine any concrete individual, because a particular vertebrate has still some characteristics not included in the collection.

Similarly, all concrete individuals must be completely determined in respect of all possible characteristics (presumably there's an infinity of such possible characteristics). In other words, we cannot have an individual thing that would neither have a certain characteristic nor not have it: the individual must be determinately one or the other. Furthermore, nothing but a completed determination of possible characteristics could individuate a particular thing. One might object that it could still be possible that an individual is identifiable through some incomplete list of characteristics – for instance, George Washington can be plucked out from the rest of the humanity by him being the first president of United States, even if we didn't knew what he was called. But the objection forgets that in Wolffian philosophy we are allowed to look at other possible worlds. Thus, there could be another possible world where the first president of United States was a man called Thomas Jefferson, and the given description would not distinguish the two possible first presidents. Note that while an individual is determinate in all aspects, we might not be able to determine all its aspects.

Some universals and no individuals are then clearly indeterminate in some respect, but Thümmig's definition suggests also that all completely determinate things are individuals, but never universals. This is a far more uncertain proposition. Suppose for instance that we would know a particular rock and all its characteristics completely. Now, if we could then copy the rock and its exact characteristics, we would have two different individuals with the exactly same characteristics. In fact, the list of these characteristics would be completely determined - this was the presupposition - but it would also define a universal class containing several individuals (the two rocks).

Thümmig's definition thus clearly presupposes the idea that no two individuals could have a matching set of characteristics. This principle of the identity of indiscernibles originates actually from Leibniz, who according to a story once challenged courtiers to look for two exactly similar leaves just to prove the principle. Indeed, the principle might well be empirically sound, but as the thought experiment shows, it shouldn't be really accepted as an incontestable axiom of pure reason – and certainly it should not be hidden within a definition. Still, Thümmig's mistake is small when compared to what Baumgarten later did with the same notions – more on this later.

Next time we shall look on animal psychology.