Complex extension

A clear difference between Wolff's Latin and German books of philosophy is that the more extensive Latin books have also a more detailed structure than their German counterparts. This is also true of Latin ontology. The book began with a section detailing the two basic principles of contradiction and sufficient reason. The second section was then dedicated to explicating the central notion of essence and some related concepts. Finally, the third section dealt with several characteristics common to all entities, such as identity, quantity and truth. Together, these three sections then formed the first part of Wolff's ontology, dealing with things in general.

The second and final part of Wolffian ontology is then about a general classification of things into simple and complex things. The second part contains, quite naturally, one section dedicated to complex entities and another dedicated to simple entities. In addition to these, there's also a section investigating relations between things, probably just because there was no better place for it.

Schematics of Wolff's Latin ontology

Wolff does not add considerable novelties to his account of complex entities in German metaphysics – the important fact is that the essence of a complex or composite entity is based on the essences of its parts and their mutual relations. Parts are then more essential than their combinations, in which they still retain their independence.

Now, when we are conscious of such a combination of several mutually extrinsic things, we see the combination as extended. In fact, we can abstract from all other features of the complex things, but this extension, as we do in geometry. Geometrically we can then define such notions as continuity (when you cannot put anything else between any two parts of a single thing) and contiguity (when you cannot put anything between surfaces of two different things). If two things are not contiguous, one can also define distance as the shortest line between them.

Extension and related notions can then be used to define space. As I've said earlier, Wolff follows Leibniz in accepting the idea of a relational nature of space – space is determined by certain relations between extended objects (distance etc.), so that space wouldn't exist without extended things having those relations. Here Wolff goes even so far to say that absolute space is just a useful fiction that we abstract from the concrete relations of complex things – and same goes for absolute time.

A novelty in Wolff's treatment of space and time in comparison with German metaphysics is that he extends his account to motion. On the one hand, this means just an extension of mathematical treatment of space or extended things to moving things. Lines can be used to describe not just extension, but also motion – Wolff is here expounding basics of vector calculation.

On the other hand, Wolff also suggests that if both absolute space and time are fictions, so must absolute motion be at least partially fictitious. Still, he is not willing to say that motion is completely imaginary. What is imaginary is the idea of motion happening in some absolute coordinate system with fixed places. Instead, motion is just change in the relations of things – a falling ball is, say, coming closer to the ground.

Furthermore, movement is something that is sustained by the moving entity – falling ball has impetus for moving in constant velocity towards the ground. In addition relations to external things can change the status of movement a thing has – a ball is constantly accelerated by something in its fall, and once it has hit the ground, it will stop moving towards the ground.

So much for complex things and their characteristics, next time I'll have something to say about simple things.

Perfectly true order

I can be quite quick with Wolffian notions of order, truth and perfection, since I covered them already while discussing his German metaphysics. Something of a novelty is Wolff's definition of order, which he states to be a similarity in the modes of things either located nearby each other or following one another. Such an order is then an explanation for a certain thing with particular features being in the place it is – for instance, in a well-ordered library, the place of an individual book is explained by the classification system requiring that a book with certain topic is situated in a particular place. In the case of library, the order is contingent or based on the external factor that some librarian has arranged the books in a suitable manner. There is also a possibility that the order is based on nothing but the very essence of the things ordered: this is the case, for instance, in ordered sequences of numbers.

A well-ordered library?

The principle of ordering can be linguistically embodied in a rule or a set of rules, Wolff asserts. The different rules can then be organised into a hierarchy of rules, in which the different subrules are grouped under more general rules – think of an instructional booklet for keeping a library in good order. As anyone with some experience on libraries knows, often librarians have not been able to order all the books perfectly according to the instructions, for instance, due to physical limitations of the library building or insufficient time for organising books. Similarly, there can be defects in all sorts of orderings, which makes it plausible to speak of more and less perfect orders. A complete lack of order or confusion is also a possibility.

Truth in an ontological or transcendental sense of the word or reality, as we might call it, can then be recognised through its orderly nature. Dreams, Wolff continues, are characterised, on the contrary, by a lack of order of confusion. Wolff goes even so far as to suggest that dreams would be contradictory, which can at most mean that they contradict the rules governing true reality, or indeed, almost all sets of rules. Because all things should have some orderliness in them – at least they have an essence that determines their attributes and possible modes – all things are in some measure true, Wolff concludes.

Finally perfection, which Wolff identifies with the scholastic notion of transcendental goodness, is defined as consensus in variety or unity in multiplicity. Perfection must again have its ground, and this ground is the regularity or orderliness of its constituents. Lack of perfection can then be defined as imperfection or evil. This does not still mean that an exception in the orderliness of some structure would entail its complete imperfection. Indeed, the imperfection might be just apparent, because from a more extensive viewpoint the apparent imperfection might be governed by some rule.

One might reasonably ask whether Wolff is smuggling some normative notions into his ontology with these definitions. Indeed, he appears to suggest by associating the notion of orderliness with words like truth and perfection that order is somehow preferable to a lack of order. Why should we assume that reality is well-ordered, instead of being at least somewhat chaotic? And why should we deem regularity as something perfect and worthy to strive for?

The most plausible defense of Wolff is to assume that the definitions as introduced in ontology should as yet carry no normative weight. Instead, the names hint at future arguments in future parts of philosophy, where the notions are shown to coincide with how we usually understand these words. Thus, we might see e.g. in theology that God has created an orderly world and in ethics that regularity is something we should strive for.

So much for these notions, and indeed, so much for general characteristics of all things. Next time we shall look at some complexities of space-time.

Quantities and qualities

A continuing element in Wolff's ontological studies is his habit of bringing in mathematical examples to substantiate the correctness of his analysis. Indeed, Wolff often ends an investigation of some ontological concept by noting that his conclusions concur with the way how the concept has been used in mathematics. For instance, the analysis of similarity works, because it can be applied to similarity of geometric figures.

All this happens not just for the sake of Wolff's love of mathematics, but it is a part of a larger plan, meant to show that the method of mathematics is useful even in philosophical questions. This argument might have been Wolff's answer to criticism of Rüdigerand Hoffman that philosophy as a study of causal relations exceeds the capacities of mathematics as a study of quantities. We shall see later how Wolff conceived the argument go through, when we look at Wolff's discussion of forces.

For now, it is enough to note how Wolff introduces the very notion of quantity. We have to begin with the idea of unity – idea that things with certain features form an inseparable whole. There is no criterion to say when a thing or entity is such an unity, Wolff says, because all things just are unities, or being equals oneness. Here Wolff is following a tradition beginning from Aristotelian Metaphysics and inscribed in the medieval notion of unity as a transcendental – a property of all things.

What is important in this unity of a things is that we can then collect several of such unities or form a multiplicity. In such multiplicities, we can then abstract from the differences of the entities and concentrate on their common features – we can pick out cows on a field and forget the differences in their colouring. Then this multiplicity forms also a unity or is a whole, of which the original unities were parts. Thus, we can get examples of all the different integers. With integers out of the way, Wolff can then define fractions, and in general, all rational numbers through the notion of ratios of integers and then irrational numbers and generally all numbers geometrically, through the notion of ratios of straight lines – every number has to unit a ratio that a straight line has to another straight line.

Numbers have then, for Wolff, a special connection to quantities, which Wolff defines in a rather peculiar manner as that by which one can discern similar things. Wolff is here thinking about the mathematical notion of similarity, according to which e.g. two figures can be similar, even if their sizes are different. Now, noting what shape a figure has requires only a look on this figure itself. Then again, determining what size it is requires relating the figure to something else, for instance, to say that it is twice the size of that figure. Quantities are then in some sense relational features,because by choosing some quantity of the same type as the unit, we can give a precise numeric expression to that quantity. Quantities can thus be also defined as indeterminate numbers or numbers as determinate quantities.

Wolff also uses the idea of quantity to define notions like equality and inequality (respectively, sameness and difference of quantities), greater and less, addition and multiplication. Furthermore, he uses the opportunity to argue for certain basic truths of mathematics, such as the transitivity of equality (that is, the fact that if A equals be B and B equals C, then A equals C). But what is important for now is the definition of the apparent limit of the mathematical cognition, that is, qualities.

I suggested that Wolff takes quantities as relational, but this is only partially true. Certainly the precise numerical expression of quantity is determined by a relation to some given unity. Then again, Wolff is quite sure that a thing has intrinsically the quantity it does have, and only this determination of the quantity requires relating. Then again, we can define another type of intrinsic features, which do not require such relating, but which can be recognised immediately. It is this second type of intrinsic features that defines the class of qualities. At least essential features and attributes of things are qualities, while modes are either qualities or quantities.

At first sight qualities cannot then be expressed numerically, but as we shall see, Wolff attempts to prove otherwise. We shall not consider this topic for a few posts, and indeed, next time I shall look at what Wolff has to say about truth and perfection.

Immutable necessities

Principle of contradiction denies the existence of contradictions, that is, the existence of combinations of contradictories. What then are these contradictories one might ask? Contradictories themselves are a kind of opposites, Wolff answers. Opposites, on the other hand, are such things that cannot exist at the same time, in the same situation (for instance, complete blackness and complete whiteness cannot exist in the same surface). Contradictories are then opposites, one of which must exist in a situation.

It is a well-known fact that when one modal notion (e.g. possibility) is defined, the rest of the modalities can be defined from that beginning. Thus, impossibility is contradictory of possibility: what is not possible, is impossible, and vice versa, and things must be either possible or impossible.

More importantly, when the opposite of something is impossible, this something itself must be necessary. That is, when some situation or thing has no capacity of ever becoming actual, it's opposite must undoubtedly have the power to actualise itself in every situation. For instance, a figure with three sides, but not three angles would be something impossible and could not ever be actualised, thus, if we do have an actual figure with three sides, it must be actualised with three angles. Generally, all such combinations or propositions describing them are necessary, if the predicate could be deduced from the definition of the subject.

Now, there is a special case of necessary propositions, that is, propositions describing the existence of something necessary. Here it is not any feature of the thing that is necessary, but the very entity is supposed to be such that its non-existence would be impossible. In other words, the actualisation of the haecceitas of such an entity would be necessary. Because this haecceitas or individual essence would contain at least implicitly all the predicates of the thing, it could not really have any other predicates. In other words, it could not change into anything else, but would eternally be what it is.

Wolff leaves it open for now, whether there are any concrete necessary individuals – this is a task left for other branches of metaphysics. Then again, Wolff does find examples of more abstract necessary entities. In Wolffian ontological scheme, what is absolutely possible is defined by its non-contradictoriness, and thus, one cannot change what is possible. If something is then possible, it is necessary possible. Then again, essences or coherent combinations of essential predicates correspond to certain possibilities. These abstract combinations or lists of predicates are then necessary, which means merely that it must be possible that some things satisfy these combinations of predicates.

Wolff also points out that there are actually two different concepts of necessity. Firstly, one can speak of necessity plain and simple or absolute necessity – this is essentially what we have considered now. Then again, there is also hypothetical necessity, that is, necessity under some assumption. Wolff's example of hypothetical necessity is the relationship between a feature of a thing determining what other features the thing has: for instance, if a certain figure has three straight lines as its sides, then it is necessary on this condition of its trianglehood that it also has three angles.

This mathematical example is a good point to move to consider how mathematics is presented in Wolff's ontology, which will be the topic of my next post.

Fully determined individuals

In a couples of posts ago, I compared Wolffian things or possibilities with coherent lists of predicates or determinations, as Wolff calls them. Now, he also mentions the possibility that such a thing would be fully or in every possible manner determined. Wolff doesn't really explain what this means, but one might put it like this. Think the aforementioned lists as answers to multiple choice questionnaires, in which one can, with each question, choose one among many possibilities or leave the question unanswered. Clearly, there is the distinct possibility that all the questions of the questionnaire would be answered – then the answers would describe a fully determined entity.

This simile undoubtedly hinges on the assumption that all possible predicates in such lists could be ordered in the form of such a questionnaire – in effect, a space of possible predicates a thing can fulfill. Wolff himself just innocently accepts this possibility, and I shall also not pursue the question whether the assumption is as innocuous as it looks. Indeed, there is no need, as the notion of fully determinate list of predicates could be characterised even without the notion of such a questionnaire. Just think what adding a new predicate to a fully determined list would do: either it would contradict some combination of the other predicates in the list or then be deducible from such a combination. One need then only to take this characteristic as the defining feature of a fully determined thing.

Being fully determined is then what defines an individual thing, according to Wolff. In addition, being fully determined is also a necessary characteristic of all actual things, and indeed, one rarely sees e.g. otherwise featureless birds flying around. In effect, Wolff is here showing his nominalist leanings. Then again, Wolff clearly is not committed to the idea that full determination would define actuality, as some of his successors were to do. This leaves open the possibility of merely possible individuals that are not actualised (say, a person just like me, except with red hair).

Now, Wolff notes that one need not list all the predicates of an individual to define him. Just think of a triangle with all angles equal – we do not need to tell anymore that its sides are also equal, because this follows from the equality of its angles. Clearly then we could have a minimal set of predicates defining an individual entity – indeed, we could probably have many of them or it wouldn't be a unique set or list (for instance, in case of the triangle, the implication goes both ways, so we could as well begin with the equality of the sides). Such a minimal list would then define what could be called an individual essence, but which Wolff prefers to call by the medieval name haecceitas.

Just as we can distinguish those questionnaires that are fully completed, we can also talk about incomplete questionnaires or lists of predicates that can still be consistently augmented by truly new predicates. If a complete determination defined individuals, incomplete determination then defines genera and species. Wolff apparently doesn't use the modern idea of genera and species as sets of individuals or extensions of certain concepts. Instead, Wolffian genera might be called ”incomplete individuals”: we add some determinations to our would-be individual, but leave it otherwise hazy and vague. Of course, such a vague entity cannot really exist, just like there's no generic triangle, but it might be actualised in various individuals that have the exact properties this vague object is supposed to have. We might say the generic entities are fictional, but they are useful for bringing out the various groupings of individuals. Such a vague entity then has some essence, just like individual had its haecceitas: essence is similarly a minimal list of predicates for such a generic entity.

The genera and species or universals form then a hierarchy, arranged according to their level of determination. The ultimate bottom of this hierarchy is formed by individuals, the only truly actual aspect of the hierarchy. Furthermore, Wolff suggests that in well-planned hierarchy the genera correspond not just with some accidental combinations of characteristics, but reveal how the things are produced. In other words, individuals corresponding to same generic entity should have a similar genesis, just like two humans share some points as to how they have been generated. Furthermore, belonging to a certain genus should determine not just some determinate characteristics of a thing, but also all the possible manners how the thing can be modified.

So much for individuals, next time we shall consider Wolff's notion of necessity.

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.

Ocean of essences

When blogging about Wolff's German metaphysics, I described his idea of modalities through an analogy of an ocean warmed by sun: possibilities swam like drops of water within the ocean, and occasionally heat of the sun made one such drop rise to the air of actuality. In this text I am going to dive deeper to that ocean and describe in more detail its denizens or possibilities. But before going into possibilities, I must begin with impossibilities.

As should be familiar, Wolff defines impossibility through the notion of contradiction: what is contradictory cannot exist and vice versa. Impossibility is then also identified with what in previous text was called nothing. Possibility is defined as contradictory of impossibility, that is, possibility is something or what is not contradictory.

Now the definition above gives a rather good recipe for recognizing an impossibility – if a contradiction pops up, it cannot be. On the contrary, it is still uncertain how one can recognize something as possible, because it is more difficult to know when something is without contradiction. Wolff himself mentions that we can have a priori proofs that something is possible, which might sound rather preposterous. Yet, one must remember that by a priori Wolff actually means all sorts of demonstrations, which can have empirical premisses. Indeed, Wolff appears to accept only actuality of something as an undemonstrated justification of it's possibility. Thus, we can learn that something is possible only by showing where to find or how to make it actual or by demonstrating it from the actual existence of something else.

What then are the possibilities and impossibilities according to Wolff? Simply put, we can think of them as lists of characteristics. Picture a huge paper full of descriptions like ”triangular”, ”round”, ”square”, ”humanoid”, ”animal”, ”mushroom”, ”pouty”, ”frivolous”, ”intelligent”, ”rioting” and infinitely many others. Circle some of these characteristics or determinations: if the set of characteristics is such that all its members can belong to a single entity, the set describes a possibility, if not, an impossibility. Note that we then have more and less detailed lists – a pair ”pyramid” and ”red” can be made more detailed by the inclusion of characteristic ”coppery”.

Now, if you are aiming at possible result, obviously circling some determinations will make it necessary to circle also other determinations. For instance, if we accept Euclidean geometry without further ado – and they did this back at Wolff's time – circling description ”triangular” forces us also to circle the description ”sum of angles equals two right angles”. The first characteristic, as it were, determines the second, or using terminology of the previous text, thing having this characteristic is a sufficient reason for it having that characteristic.

Let us now assume that we have chosen a set of characteristics, which are meant to define certain possible thing. This set forms then the essence of the supposed possibility (say, triangularity forms the essence of triangles). Clearly, changing any characteristics that is part of the essence would change the possibility (e.g. square wouldn't be a triangle anymore). In this sense essence is always constant for the possibility it corresponds to. This doesn't mean that e.g. triangular pieces of matter could not turn to square piece of matter: then this piece of matter just wouldn't correspond to the essence of triangularity anymore. In effect, when we speak of an essence of a thing, we must assume some viewpoint from which to decide what is essential and what not for the thing in question.

Note that just putting together characteristics does not produce an essence, because such a list does not necessarily refer to any possibility. What one must do is also to show the possibility of this set of characteristics. We have just seen that it is only through actuality that such a proof can be effected. In fact, we need what Wolff has called a real definition, that is, an account of how the thing to be defined can be generated.

Now, when we have determined an essence, clearly also those characteristics determined by the essence will be constant – they cannot change, unless the essence changes. Such determined constant characteristics Wolff calls attributes (note that it might be equally contextual what to takes as essence and what as attribute). Some of these attributes are shared by things with other essences – these Wolff calls common attributes – while others are proper only for the things with that essence.

While essences and attributes are constant for thing of a certain sort, there are characteristics that are not, that is, modes. Thus, triangle could continue being triangle, even if its colour would change. Clearly such a distinction between essential and non-essential characteristics depends on the perspective – while colour is not essential to a triangle, it would be to a green triangle. Furthermore, the modes are not completely separate from essential characteristics and attributes. In fact, some sets of possible modes (say, a set of possible colours of a triangle) clearly form an attribute of the thing in question (it is not necessary that a triangle has any particular colour, but it must definitely have some colour).

In addition to essential characteristics, attributes and modes, things also have relations to one another. A peculiar notion of Wolff, derived probably from Leibniz, is the conviction that all relations could be reduced to modes. In effect, this means that one need not discuss other things when dealing with one thing. Thus, while essential characteristics and attributes of a thing can be explained through one another, its modes can be grounded on its other modes, current or past – that is, all causal processes can be regarded as involving only one object at a time.

Wolffian sea of possibilities is then filled with such groupings of characteristics. Characteristics of one thing cannot clash with one another, or otherwise there wouldn't be any such thing. Yet, just by being a possibility, the thing still isn't actual – one must still add something to make it actual. Kant was later to criticize Wolff, because no addition of a new characteristic could make possibility into actuality. Yet, here Kant is clearly too harsh for Wolff, who knew that mere addition of characteristic would no difference, but ”something else” is required – what this something else, is purposefully left unsaid by Wolff at this point of discussion, although later on it becomes evident that it is the spark of God that makes everything actual.

So much for possibilities, next time I shall look at what Wolff has to say about identity.