Variety of causes

The world we experience is clearly a world of interacting things, and one rarely finds anything that is completely isolated from its environment. Despite this evident importance, relations have often been relegated into a subservient position in traditional ontologies. It is like philosophers were interested only of classifying things into neat categories, but when it comes to explaining their interconnections, they soon loose their interest. It is then no wonder that Wolffian theory of relations is presented almost as an afterthought, attached to the discussion of complex and simple substances.

Wolff begins with the general notion that a thing is related to another thing – this happens when we consider two things together in such a manner that one of them cannot be understood without a reference to another. Thus, when we think of a person as a parent, we must think of some other person who is a child of this parent. Now, many things could be considered without such a reference to something else, just like we can describe George Bush Senior, without ever invoking any reference to other human beings. Still, we might also consider some aspect of Bush Senior that requires an essential reference to another person, for instance, when we see him as a father of Bush Junior.

These aspects then are relations. Note that with Wolff's definition it is natural to single out the subject of relation, thinking of which requires the reference to someone else, just like consideration of a father requires at least implicit reference to someone to whom he is the father. It just now dawns to Wolff that he has already described several relations, such as equality of quantities or similarity of qualities. There is still no indication that he would have felt a need to transfer his general account of relations to an earlier position in the book.

An important relation is the one between that which contains a reason (principle) for something else (principate). Thus, as forces are a reason for changes in substances, they could be called the principle of change. This leads to a new possible definition of substance. Changes of finite simple substances are based on their inner force and changes of composite substances are ultimately based on the inner forces of their constituent substances, thus all finite substances contain in themselves a principle of change. Then again, accidences cannot really change – that is part of their definition – thus, they also cannot have any principle of change. This only leaves infinite substance out of account, as Wolff admits it cannot really change. Still, Wolff can always fall back to the option of saying that an infinite substance has eminently a principle of change in itself (it does some have force, evidently). Thus, substances can be defined as those entities that have a principle of change in themselves.

Wolff also defines species of different principles. Some principles contain reason for possibilities – in this sense essences are principles of things being modified in a certain manner – while others contain reason for something actually occurring – in this sense modes and other things are principles of thing being modified in a certain manner. Beyond these, there are also cognitive principles, which are essentially propositions explaining other propositions.

Probably the most important point in defining the notion of principle lies in explicating the concept of cause. Simply put, cause for Wolff means a principle, on which the existence of something different depends. Wolff's definition of cause extends far beyond what nowadays is usually called cause, because even if Wolffian cause differs from what it causes, it might still be an aspect or part of the caused, as long as it contributes to understanding why this thing exists. Thus, it is no wonder that Wolff mentions Aristotelian notions of formal and material cause, the former being identified with the essence of the caused, the latter with the constituent parts of the caused, if it has any.

The important notion of cause from the modern point of view is then efficient cause, which Wolff defines as a cause, the causality of which consists of actions – that is, which acts and thus explains the existence of something else. As Wolff's notion of activity is essentially connected with the concept of force, his idea of efficient causality is based on the traditional mechanistic scheme of bodies striking one another and transmitting movement (needless to say, there is no indication in Wolff of the Humean problem how we can recognise causal interactions). Wolff also notes that often one efficient cause is not enough, but the existence of something has required action of many causes, and that efficient causes form series, in which more distant causes lead on to more proximate causes.

Finally, final causes Wolff defines as reasons why an efficient cause starts to act. Final causes are thus causes for efficient causes and thus must precede them, which is only possible, Wolff concludes, if there has been some entity which has previously thought these ends and now decides to actualise them. In effect, Wolff denies the existence of ends without any conscious beings that can set ends to things. Thus, although he has borrowed his scheme of four causes from Aristotle, he clearly rejects some essential underpinnings of the scheme – all events might not have intrinsic final cause. Then again, since Wolff also supposes the existence of an infinite entity or God that has created the world because of its perfection, he would have to admit that all things have some extrinsic end.

In addition to cause, the only relation Wolff dedicates a whole chapter on is the relation between sign and signified. We may leave this topic almost completely untouched and just mention that Wolff admits the possibility of natural signs, that is, things which by nature refer to other things.

So much for ontology then. Next time I will start by looking at a new generation of Wolffians.

Simplicity itself

As familiar as was his account of complex entities, as familiar is also Wolff's description of simple entities, which in many cases simply have characteristics opposite to characteristics of complex substances. Previously I characterised Wolffian simple things as units of forces, which is quite correct still in light of Latin ontology, but one must not assume that complex entities could not then be described in terms of forces. Instead, the notion of force is something common to both simple and complex entities.

To understand what Wolff means by a force, one must begin with the notion of modes that we know to be characteristics that can be changed without changing the essential identity of a thing. Now, consistent collections of modes define a certain state. Such states, if they happen to be instantiated, belong to some thing, which can then be called the subject of these states, which are then adjunct to the subject. Note that the notion of subject, just like the notion of essence, is context dependent: in geometry we might take certain figure as stable, while in physics this figure could also be mutable.

In some cases, the change of states can be explained through the subject of change – then the change can be called an action of the subject, while in the opposite case it could be called passion. Thus, while if I voluntarily jump from a plane, the subsequent fall is my action, if on the other hand I am thrown from a plane, the fall is my passion. A subject undergoing an action can be called an agent, while a subject undergoing a passion can be called patient.

Furthermore, corresponding to action and passion, a thing has corresponding possibilities for action and passion or active potentiality and passive potentiality, the former of which Wolff also calls faculty. Without these potentialities actions and passions could not occur, but as mere possibilities they still require something in order to be activated.

In case of actions, this activating element is finally called force. What a force is or how it will be generated should not yet be apparent from this nominal definition. Still, it is quite clear from the definition that it makes no sense to speak of a force if there is no action that it activates, unless there is some opposing force resisting this activation.

This is as far as conceptual analysis takes us. From empirical considerations Wolff concludes that we could describe force as consisting of conatus. Conatus is a peculiar notion, common to many early modern thinkers, such as Spinoza, meaning a sort of life force of a thing that aimed at preventing the destruction of the thing. In physical contexts, conatus was often identified with impetus, the habit of bodies to remain in the same state of movement – this tendency was thought to be due to some internal yearning of bodies.

One obvious aim of this talk of conatus or impetus is to introduce the possibility to quantify forces – forces can be connected to the actions they trigger, and we can thus present forces as vectors. Because of their quantitative nature, forces can be combined (basic principle for this possibility is easily seen in a so-called parallelogram of force). Thus, we can regard forces of composite entities as combinations of forces of simple entities.

Parallelogram of forces: when forces F1 and F2 are the only forces affecting a thing the resulting movement is described by their sum

The mathematics of forces is one step in Wolff's project of quantifying philosophy. A final step is taken with the notion of grade, which Wolff defines as a characteristic of qualities that can be used to distinguish different (spatial or temporal) instances of same quality (thus, two apples might have a different tinge of green). Now, Wolff notes that it is possible to create at least a fictitious quantification for the grades (just think of a temperature scale – if a temperature of air rises two grades, this does not happen because of adding two individual grades of warmth to air). Because qualities were originally the only impediment of the quantification program, Wolff thinks he has solved the problem suggested by his critics.

The final piece in separating complex and simple entities is the notion of substance. Here Wolff begins by distinguishing between what is mutable (that which can be changed without it losing its essential identity) and what is only perdurable (that which can exist for a time without losing its essential identity). Now, Wolff's interest lies in perdurable things: cows, shadows, colours, you name it. Some of these perdurable entities are not mutable, some of them are. According to Wolff, this distinction among perdurables captures the traditional distinction between accidences and substances. This might need some explanation. Consider a traditional example of an accidence, such as certain shade of colour. It can definitely exist for a while, say, on some surface, but when you try to change it, it will change into a different shade. Then again, a substance, like a cow, will not be destroyed, if you paint it black – thus, it is not just perdurable, but also mutable.

Wolff's definition clearly is not meant as a strict division, but more as a hierarchy of substantiality – that is, we can speak of what is more accidental or substantial. Thus, we can change e.g. shape of a certain blob of colour, so that it will still remain a blob of this colour. Then again certain modifications of cow, such as tearing it apart, will undoubtedly destroy it. In addition, Wolff suggests we may define as proper substances those perdurables that will endure through any humanly conceivable change – these are essentially the simple substances. Then again, complex substances are in comparison accidental, because all their essential characteristics, such as figure and magnitude, are mere accidents. Thus, they can be only secondary substances.

Wolff ends his account of simple substances with a consideration of infinities. The characterisation of an infinite substance contains no surprises – infinite substance is incomparable with finite substances, but we can say that it has some analogical or eminent characteristics (eminence appears to be just a roundabout way to say that we really do not understand what it is). Then again, Wolff also makes some interesting remarks on mathematical infinities and infinitesimals. To put short, he admits that no mathematical infinities or infinitesimals actually exist, but also suggests that such fictions are useful in e.g. differential calculus.

So much for simple substances, now it is only relations we have to speak of.