Christian August Crusius: Draft of necessary truths of reason, in so far as they are set opposite to contingent ones - One and the same

From the very start of metaphysics, in the book with that name by Aristotle, the concept of one was regarded as an important topic. Thus, it is no wonder that Crusius would consider it. Indeed, he thinks that we have many different notions of one, distinguished by what concepts they are opposed to. First of these is the concept of one thing in contrast to several things. This concept, he insists, cannot really be defined, but can only be exemplified. In essence, a thing, no matter what it is, is always one or a unit, because we can think what it would be like, if it were multiplied into several similar things.

Another concept of one, Crusius continues is that of something unified in contrast to what is disunified. By unification Crusius means a relation where things are so intrinsically related under certain conditions that when one is assumed to exist, the other must be assumed to exist also. Unification can come in many forms, the primary ones of which are unification merely in our thoughts and unification in real existence. Crusius notes that we cannot really know all the subdivisions of unification and mentions only a few examples, such as metaphysical unification of one thing subsisting in another (e.g. property in a substance), existential unification of two perfect things connected so as to become inseparable, such as a hand and a torso, and moral unification where two persons are united by having common goals. In any case, Crusius emphasises, all cases of real existential unification are ultimately based on causal interactions. Thus, he insists that Leibnizian pre-established harmony would be no real unification of body and soul.

A third notion of one is connected with the notion of identity. Crusius defines the concept of identity as the opposite of difference, where two things are different if in one is something that is not in the other - Crusius notes in passing that this notion of “not” or denial is again something simple, which we cannot really define. Identity as the denial of difference can then be just similarity, where things share something, but also identity in a strict sense, where one thing - here is the connection to one - is represented through two concepts, of which one is found to contain nothing that wouldn’t be contained in the other.

Crusius considers the question, when we can know that the objects of two concepts are identical. The criterion he suggests is that one should be able to replace what is thought in one concept with what is thought in the other without any consequence. He also emphasises that mere same essence is no true criterion of identity, since we could have substances that are just numerically different, that is, that would agree in their absolute properties, but would be e.g. in different spaces at the same time.

Although Crusius' definition of identity might seem rather rigid, he does admit that identity can fluctuate according to the viewpoint chosen. For instance, when we are considering whether things at different points of time are the same thing, we might get different results depending on what we focus on: corpse is in a sense different from a living body – they have different essence - but in another sense they can be identical, because they share the same matter. Then again, if an essence of a thing consists of a certain relations of parts, the thing can remain identical, despite its parts being replaced by different, but similar parts.

Crusius chooses at this point to give a list of simplest concepts. This list is a development of a similar one from Hoffmann, and we could consider it to be a precursor of Kant’s list of categories. Crusius' list contains the following concepts:

• Subsistence, that is, the relation between a property and its subject
• Relation of one thing being spatially within or outside of another thing
• Succession
• Causality
• Relation of one thing being figuratively outside of another thing, in the sense of not being its part, property or determination
• Oneness in opposition to plurality
• Relation of things being unified
• Thing’s being somewhere in space.

Crusius also clarifies further the relation of these simple concepts to the seemingly simple concepts of sensation, like colours. Crusius’ idea is that while the above mentioned simple concepts are the ultimate result of analysing more complex concepts for any understanding, it is we humans who are incapable of analysing sensations just because they are caused by unknown activities affecting us in a confused manner, so that we cannot distinguish these causes from one another. Crusius also distinguishes the simple concepts from indeterminate, symbolic concepts, which we cannot really think, but which we can only represent by saying what it is not and what its relations to other things are.

Baumgarten: Metaphysics – Relational predicates

The rest of Baumgarten's ontology is perhaps not as original as the earlier sections, but it is at least interesting, because Baumgarten rearranges topics and includes in general relational predicates some issues that Wolff did not consider under relations. The first of these topics is identity and the related notions of diversity and similarity. Here we find Baumgarten, for instance, endorsing the Leibnizian principle of the identity of indiscirnibles: two different things cannot be completely similar.

Space and time or simultaneity and succession are also dealt by Baumgarten in the chapter on relations. Although Wolff had also endorsed the idea that space and time are nothing but relations, Baumgarten is making this notion even more explicit by this simple choice of how to present the topic.

Just like with Wolff, the central relational notion in Baumgarten's ontology is obviously causality. Cause is for Baumgarten, just like it was for Wolff, a more special modification of ground or reason. For Baumgarten, cause is specifically a ground for the existence of something. Just like Wolff before him, Baumgarten defines several notions important to causal considerations – some causes might coordinate with other causes in producing some effect, while others may be called more proximate, when compared with more immediate causes of something.

The most important type of cause for Baumgarten is probably the efficient cause, which has actively produced some reality or positive characteristics in something else (Baumgarten also invents the notion of deficient cause for those actions, which produce some negative characteristics). A number of other causal notions can then be defined in terms of whether they help an efficient cause to do something or whether they hinder it.

In addition to efficient cause, Baumgarten does also, just like Wolff before him, consider the other three Aristotelian causes: form, matter and final cause. This part of Baumgarten's ontology seems rather quaint, like a remnant of a past long gone.

The final relation Baumgarten considers is that between signs and what the signs express. Although Wolff did briefly consider this topic, Baumgarten somewhat expands Wolff's writing. For instance, he considers several sciences, in which one should either make up more signs (heuristics) or help us recognise past signs (mnemonics), and also tries to explain the genesis of human language.

So much for Baumgarten's ontology. Next time I'll look at his cosmology

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.