Intuitive and symbolic cognition

Both Leibniz and Wolff divided cognition into two kinds: intuitive and symbolic. I've had some difficulties clarifying to myself how these two relate to the progression from sensations through imagination and memory to intellectual faculties of understanding and reason, so it feels a bit helpful to see what Bilfinger has to say about the issue.

The basic definitions deriving from Leibniz are pretty straightforward: intuitive cognition is caused by attending the nature of things directly, while symbolic cognition is connected to things only via mediation of signs. Leibniz then had supposed that composite concepts are usually cognized symbolically: after all, analysis of concepts into its constituents happens usually through signs, e.g. if I define square as a rectangle with all sides equal, the definition would be expressed verbally. Primitive concepts, on the other hand, might be cognized either intuitively or symbolically: e.g. point could be defined either by looking at points or by saying what one means when speaking of a point.

Furthermore, all distinct concepts – that is, concepts that can be analysed into clear concepts or into concepts through which we can distinguish objects – must be based on intuitive concepts. In other words, if we had an analysed concept, in which we would know all the constituent concepts only through further linguistic explications, somewhere along the line we would have to use a circular explication, which clearly wouldn't help to distinguish any objects. Thus, an analysis or explication that is successful should at some point meet some cognitions which are directly connected to things. Intuitive cognition is therefore a necessary ingredient of good cognition: if our cognition is not grounded on things, it might well deteriorate into a shamble of contradictions and meaningless expressions.

From the perspective on what Leibniz has to say, intuitive cognition is essential to well-founded science. What good is symbolic cognition then? Bilfinger answers by turning into Wolff's account. While symbolic cognition cannot by itself be a source of true cognition, it can be used in inferring truths from known truths. In particular, symbolic cognition is required whenever we want to move to general truths about classes of objects: we cannot literally be effected by any class of objects, because classes are not real entities. Thus, symbolic cognition makes it also possible that the Leibnizian ideal of an algebraic art of thinking could be one day found. In addition, symbolic cognition is also useful in transmitting cognition from one person to another: we cannot share intuitions, but we can share signs and symbols.

Interesting here is how the division of cognition into intuitive and symbolic kinds corresponds better with Kantian division of sensibility/intuition vs. spontaneity/understanding than Wolff's own division of sensations and concepts. Indeed, Kant's famous statement that intuition without understanding is blind, while understanding without intuition is empty, could be easily translated into the Leibnizian-Wolffian statement that intuitive understanding by itself is blind, because it cannot be generalized, while symbolic understanding by itself is empty, because it fails to connect cognition with actual things. Of course, Kant doesn't call his intuitions and concepts alone cognitions, but reserves this name only for the result of the interplay of the two.

So much for Bilfinger's take on Wolffian psychology, next time I'll discuss his notes on Wolffian natural theology and especially the problem of evil.

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.

Georg Bernhard Bilfinger: The harmony between human soul and body, altogether pre-established, out of the mind of illustrious Leibniz, hypothetically studied (1723)

It is no wonder if you don't remember Bilfinger, because the first work I read from him was short, immemorable and not very original. Although Bilfinger won't get any points for originality this time either, at least the topic is of a more general interest. Like the name says, De harmonia animi et corporis humani, maxime praestabilita, ex mente illustris Leibnitii, commentatio hypothetica aims to examine the theory of the pre-established harmony. Leibniz himself had spoke of harmony between all substances whatsoever, but Bilfinger here concentrates on the particular case of souls and bodies. Bilfinger follows here the example of Wolff, who had already had some reservations on the full Leibnizian theory of monads.

Bilfinger starts from ths established fact that bodies and souls do work in harmony. When an object is brought in front of my eyes, I experience usually a visual sensation corresponding to the object. Similarly, when I have a volition of moving my hand, the hand in fact moves. Thus, the causal series governing bodies and causal series governing souls reflect themselves partially.

Bilfinger considers quickly the possibility that at least one of the series would consist of necessary processes. For instance, Spinoza thought that the series of both bodily and mental events followed necessarily from the eternal essence of God. Bilfinger disregards this option, because the two series do not seem necessary – I could have walked somewhere else etc.

Bilfinger suggests there are only three possible ways to explain the harmony between the two contingent series. Firstly, there could be true causal influx between the two series – this is the common sense explanation. As Bilfinger notes, the influx theory goes against certain assumption of modern science. Observations appear to show that material objects retain the quantity of their motion, unless they interact with other material objects – they either share some of their quantity of motion with others or receive some quantity from others. Because soul doesn't move, it cannot impart motion to material objects, not even to its own body, and cannot thus make the body do anything.

Descartes' stance on the issue was ambiguous. He did accept the physical fact of the stable quantity of motion, but suggested that the soul might still change the direction of movement of the body or some part of it. By the time of Leibniz, it had become evident that this solution would not do – material objects retained also the direction of their motion, unless the direction was changed by the force of other material objects.

The Cartesian school had then slowly turned towards a new explanation. They suggested that whenever body appeared to do something to soul or vice versa, God on this occasion decided to interfere in the causal chain and connect the movement of the body with the respective change in the soul and the change in soul with the respective movement of body. This occasionalism had the setback that it appeared to break the ideas of modern science even more than causal influx. If occasionalism were right, there would be no true causal regularities, but everything would depend on the will of God, who would be constantly making miracles to sustain his creation.

Leibnizian solution is then that God has preordained souls and bodies to work in harmony, like two clocks that a perfect watchmaker has winded up show always the same time. Bilfinger notes that the thesis of pre-established harmony has justification enough in the fact that all other options fail to meet the standards of modern science. Still, he also notes that the harmony becomes an immediate corollary if we just accept other aspects of Leibnizian metaphysics – if souls are monads representing everything and especially the group of monads that constitutes its body, then the representing soul and represented body necessarily work in harmony.

All the previous is pretty straightforward summarising of Leibniz's thoughts. More original are Bilfinger's attempts to answer objections presented against the theory. A good representative of those objections come from Pierre Bayle, the skeptical encyclopedist. Bayle had accused Leibniz that his theory leads to materialism, because he must assume that bodies can run their own course, without any guidance of souls – my body could be writing these apparently reasonable words without me being aware of it. Bilfinger notes that even such complex phenomena like the movement of the planets can happen without any governing soul. Furthermore, he emphasizes that the world still isn't necessary substance of Spinoza, because it has been created by God. Finally, the independence of material world still wouldn't lead to a denial of souls, because mere material things couldn't represent anything – here Bilfinger is following Wolff.

Bayle had also ridiculed the notion of a causal series of the changes of soul. Bayle compared monads with atoms and assumed that monads would also be governed by similar iron laws. Furthermore, he wondered how sudden changes in the experiences of soul could arise, for instance, how could such complex phenomenon like music suddenly appear in our minds. Bilfinger emphasizes the importance of obscure representations in the life of a soul. These obscure sensations make our experiences so varied and thus differentiate monads from simple, featureless atoms. They also help us to understand sudden changes in our mental life. These changes have built up gradually, but only through unaware representations. Only when a certain threshold had been passed will the symphony start to play in our minds.

Even more interesting are Bilfinger's attempt to answer objections he has heard from his own acquaintances. For instance, Bilfinger has to explain why sickness of the body limits also the capacities of soul. Bilfinger notes that this is just natural – because soul is in harmony with the body, the soul sure must follow what the body does and act confused, when the body is ailing. Furthermore, Bilfinger explains that the sequence of ideas in soul must correspond to some movements in brain, which are capable of producing movements of body that appear rational. In effect, theory of pre-established harmony could be reconciled with the idea of human actions being dependent on brain.

So much for pre-established harmony. Next time we'll begin a summary of Wolffian philosophy.

The man of monads

When I was just beginning the blog, I was suggested to include Leibniz. In the very first post I strictly stated that I would skip him altogether, but I also said I might do some backtracking – and when I learned even Leibniz had written some German texts, I started to reconsider my stance. I still won't do a detailed analysis of all the works of Leibniz – that would set back my progress with another decade. Instead, I shall make one special article on his philosophy. Luckily I received as a PhD gift from Markku Roinila, one of the leading Leibniz-scholars of Finland, a recent Finnish translation of a number of Leibnizian texts, so suitable material was readily available.

I shall probably have to say something about the translation itself. It is a collection of writings of very diverse sort, containing in addition to more philosophical writings also religious texts, physical investigations, papers on logic and even a plan for making money with science. The only connecting element, in addition to the author, is the relative shortness of the texts. Thus, the collection includes mere excerpts of such larger writings as Theodicy and New essays of human understanding. As I don't know the originals, I cannot really say whether the translations are faithful to them, but I am at least convinced that the translating team has consisted of capable persons.

What becomes quite clear after reading this mixed bunch of writings is the multifariousness of Leibniz's talents and the variety of his interests – when Leibniz is not engaged in a philosophical or scientific discussion with other luminaries of the time or busy with yet another system of logic, he is probably spending his free time for the unification of all Christian churches. A good example of the ingenuity of Leibniz is the attempt to wed science with money, where the philosopher suggests a sort of scientific circus in which innovations are used as an entertainment – and which includes also a casino using the theory of probability for making profit (all the money is, of course, meant for further scientific endeavours).

What interests us here is the more metaphysical part of the Leibnizian ouvre and especially its connection to Wolff's metaphysics that we have just finished. I am sure that most of you know at least some rudiments of Leibnizian theory of monads – and those who don't can surely find some text book to study – so I will just skip the details of this theory. What is really fascinating is that Leibnizian philosophy can blend the new scientific innovations of the 18^th century with the traditional religious world view – observations of the microscopic world become evidence for the capacity of God to create an infinite abundance of life.

Many of the details of the Wolffian metaphysics we have investigated derive obviously from Leibniz: the two principles of contradiction and sufficient reason, the division of the substances into simple and complex, the division of concepts according to the different levels of clarity, the relational theory of space and time, the pre-established harmony and the choice of the best possible world by God. That is not to say that Wolff himself wasn't original. Yet, the originality lies more in details than in the big picture, and some innovations of Wolff were far from true improvements: witness, for instance, Wolff's attempt to base the principle of sufficient reason on the principle of contradiction.

The most substantial difference between the two philosophers lies in the difference of Wolffian elements and Leibnizian monads: while former are units of force, latter are units of perception. Yet, here Wolff is actually preferring earlier works of Leibniz to his monadology. That is, Leibniz does suggest in some texts that the ultimate elements of world are essentially forces, but in later works the more famous idea of monads as perspectives to the whole world becomes more apparent.

Still, the true novelty in the Wolffian philosophy was its systematic form, which was the ideal that many philosophers of the time tried to achieve – and which haunted even the later German idealists. Of course, this systematicity was also the reason why Wolff became so scorned by later philosophers- it is easy to see the gaps in the argumentation and unwarranted presuppositions, when the ideas are at least presented in the form of an axiomatic system. Similar faults in Leibniz are more difficult to uncover, due to the fractured nature of his philosophy – although they do surface in his letters to other philosophers, such as Samuel Clarke, who dare to question the ultimate presuppositions of Leibnizian philosophy.

Still, it is probably this fragmentary character that has kept the name of Leibniz alive through the ages – everyone can find something to appreciate in his philosophy. In the days of German enlightenment he was seen as a mediator between atheistic materialism and irrational fideism. Although Kant was against traditional metaphysics, he still appreciated Leibnizian ideas on the capacities and limits of human knowledge. German idealists became fascinated by his insistence on life and consciousness constituting the fundamental essence of the world. Although Russell bewared grandiose philosophical theories, he could still praise Leibniz's logical works. And if philosophy for philosophy's sake loses the remnants of its former glory, I am sure someone will get excited of the idea of scientific circus.

So much for the digression on Leibniz. In next post, the regular schedule will continue with yet another book of Wolff, this time on ethics.

Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - Pre-established harmony

Ever since Descartes suggested that the finite world consisted of two types of substances, material and spiritual, the question of possible interaction between the two had formed a dilemma. Descartes' own suggestion that pineal gland had something to do it was considered a failure. An easy solution would have been to get rid of one side of the equation altogether. But the rejection of spiritual substances or souls, that is, materialism of Hobbesian sort was considered antireligious. On the other hand, the opposite of materialism, which denies the existence of matter and which Wolff called idealism, attracted religious men like Berkeley, but was otherwise seen as rather farfetched.

Spinoza's solution was to deny that there is any true difference between soul and matter: both are merely one and the same thing from two aspects, thus, they do not interact, although changes in one reflect the changes in the other. But Spinoza's answer led to a pantheistic world view, where everything was a mere modification of original unity or God. A more theologically acceptable solution was occasionalism, according to which God had to give a helping hand, whenever an apparent interaction of any substances would occur. Problem was that occasionalism required constant wonders and so undermined scientific discussions.

Wolff follows Leibnizian solution of the problem, that is, he supposes that God had created the material world and the souls in such a manner that they appeared to work in harmony with one another. For Leibniz and Wolff, soul was closed off from any influences and all its states followed from its previous states. Still, soul could represent the world around it, because when the soul had been generated by the God, it represented the world perfectly and thereafer, because of the laws governing both matter and souls, the two will remain in perfect sync (one might object that two clocks that begin by showing the same time might not be synchronised after few days, but I will assume that God has ordained the laws in question so that the harmony remains).

Leibniz's theory is undoubtedly ingenious, but it somehow feels too elaborate. Furthermore, it still appears to verge on materialism. The body is not truly controlled by the soul, thus, whatever words are coming out of the mouth of the person sitting next to me, whatever actions she will perform – all this must be caused by some changes in her body in general and her brain in particular. I know that in myself there is something more – namely, my consciousness that exactly corresponds to the actions of my body – but in case of other persons I might as well assume that they are mere machines.

Leibniz and Wolff had, of course, a reason for adding independent souls to the equation. The material bodies can be destroyed through disassembly of their parts, but partless and simple soul cannot be disassembled. Thus, human consciousness should live on after the death of the body.

What is most unsatisfactory in this account of the immortality of the soul is that it apparently fails in its purpose. True, Wolff and Leibniz do conclude that the soul is immortal. But the connection between the soul and its body has been defined to be very tight: what soul perceives, what it imagines and what it thinks all correspond to some states in the body of the soul. Indeed, Wolff even goes so far as to admit that a fault in person's brain will lead to a fault in the corresponding perception of the soul. It would then seem reasonable that the capacities of the soul would be gravely diminished when its body completely ceased to exist.

Here Wolff relies on some outlandish speculations. He assumes it to be proven by a collague that the soul is generated at the very instance when its body is assembled. The capacities of the soul grow all the while when it is connected with the body (Wolff conveniently forgets cases of senility). Thus, Wolff concludes, as the state of the soul after death is a mystery to us, it is reasonable to suppose that it will continue developing and perfecting itself.

This is a good example about what I think the greatest fault in the whole chapter on rational psychology. Wolff already knows the answer he must get – soul must be immaterial, it must be immortal and its life after death must be happy and perfect. The grounds for these conclusions are then discovered afterwards, and no puzzle about the nature of the soul has ever actually existed.

So much then for soul: there's only God to discuss anymore.

Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - Infinitesimal elements

Because the world is a complex object, it must ultimately consist of simple substances: we have already seen this statement in the chapter on ontology, although the argument supposedly justifying it was faulty. Just like the world was already characterised by its complexity, these ultimate elements of the world are characterised by their simplicity. They cannot, for instance, have any spatial magnitude and thus differ from Democritean atoms. Yet, they must still be placed within some place – or more likely, remembering the Wolffian notion of space, their relations should constitute space.

Wolffian elements should then be infinitesimally small, just like mathematical points. Then again, they cannot be mere points. Wolff uses as a justification anothe principle he learned from Leibniz – the so-called identity of indiscernibles. This principle is based on the higher principle of sufficient reason. All things must have a reason, thus, there must be a reason why one thing is in one place and another in another place. Because the Wolffian space is relational, he thinks that the reason cannot lie in the space itself – space cannot exist without things and their relations. If now the two separate things are supposed to be completely similar, there cannot be any characteristic causing one to occupy a different place from the other – in other words, they must occupy the same place, and indeed, be identical.

Whatever one thinks of Wolff's attempt to justify the principle, it is clearly against taking mathematical points as true existents: point cannot be distinguished from another point through nothing else, but its position. Wolffian elements resemble then more Leibnizian monads, with the exception that Wolff does not take seriously Leibniz's idea of perception as the essential characteristic of all monads. True, he does pay lip service to the idea, but only in the restricted sense that all the elements reflect the whole world by being in harmony with it, in other words, by being in harmony with one another: the state of one simple thing matches the state of other simple things, e.g.. when one thing is in a state of activity, another is correspondingly in a state of passivity.

We have already seen in a previous text (http://thegermanidealism.blogspot.com/2011/11/units-of-force.html ) what actually individuates Wolffian elements: they are all units of force or activity, each developing independently of all others. What Wolff adds in this chapter is the explanation how bodies are generated out of the elements. Just like states of all the elements are harmonious in general and this general harmony constitutes the world, the states of particular elements might have a stronger harmony and thus form a complex unity or body.

Wolff goes to great lengths in explaining what characteristics all these bodies have: for instance, bodies consist of an essence (the structure of having been assembled in a certain manner from elements), matter (their activity of resisting externally induced movement) and moving force (their activity of moving themselves and mediately also other bodies). This analysis is not very original, but in essentials lidted from Leibniz's physical writings, and not philosophically fruitful, so I shall ignore it.

What interests me more is the relationship of the elements and the bodies. The existence of bodies is dependent on the existence of simple elements: a faulty assumption, perhaps, but one which Wolff endorsed. The divisibility of bodies has then a limit, because the elements cannot be divided anymore. This limit Wolff places outside possible experience, when he once again confirms that elements as simple things cannot be seen. This time he even has a proper argument: elements cannot be affected by movement, hence, light will not interact with them and they are therefore invisible to us.

On the other hand, bodies as spatial must be divisible into further spatial things, that is, further bodies. Wolff appears then to accept both infinite divisibility of bodies and the existence of a limit for that divisibility: indeed, his arguments for both are almost exactly those Kant will use in his second antinomy. Kant's antinomies are based on the assumption that the two arguments are both convincing and that both of their results cannot hold at the same time: Kant can then note that this apparent paradox is avoided by adpoting his own transcendental idealism. We have already seen at least one argument in the second antinomy is far from convincing. If we can also find out a convincing reason how Wolff could accept the two arguments without falling into contradiction, Kant's ”negative argument” for transcendental idealism would fall apart.

The simple solution for the seeming contradiction is that the indivisible elements are not extended, but point-like entities: thus, they are dimensionless and cannot be divided anymore. Analogically, mathematical figures can be divided into further and further figures, but no division leads into anything smaller than indivisible points. In other words, elements are the result of a practically impossible infinite division of bodies: thus, after every finite division we are in a point where the antithesis of Kantian antinomy works, although there is a final limit which no finite division can reach and in which the thesis holds.

This is enough of Wolffian cosmology. Next time we are back with studying human soul in rational psychology.

Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - Truth vs. dreams

At least since the days of Descartes the problem of the reality has perplexed philosophers. Is the world that we perceive truly real, and not a mere dream, hallusination, figment created by a powerful daemon or mere fiction fed into our brain by a mad scientist? Wolff himself notes the problem, but apparently fails to take it very seriously. Wolff simply decrees that in dreams all processes are less ordered than the truth. By order Wolff means the occurence of some similarity, that is, of a pattern or a rule, which the things follow. Ultimately the basic criterion is the principle of sufficient reason or causality: processes in dreams do not follow any causal laws.

Wolff's criterion is perhaps enough for distinguishing our usual dreams from what we happen to call reality. He is not interested of a possibility that a new, even more real world might be discovered beyond the world of experience. This might be a consequence of Wolff's pragmatic nature – after all, there has to be some limit for the demand of indubitability. Furthermore, Wolff could continue, if we some day discover that we have been dreaming all along, at least this discovery will be made through the very same criterion of the regularity of processses. Here Wolff is once again paving the way for German idealists, who also had some doubts about the need to find any ultimate reality beyond the world of experience.

In modern analytic philosophy one is accustomed to mean by truth a characteristic of propositions, beliefs etc., while here Wolff essentially refers by truth to the reality. Furthermore, he almost instantly extends the notion of truth to apply to all sorts of processes. Truth thus becomes a quantifiable characteristic: the more regular and law-governed a thing is, the truer it is.

Wolff also introduces the notion of perfection (Vollkommenheit), which he then immediately characterises as a coherence of a manifold, which is yet another form of regularity in addition to truth as a regularity of processes. The regularity in its various guises appears then to be the primary value characterising simple things: the goal the finite simple things try to acheive is the regularity both in their internal processes and in the system of things they causally engage with.

Like with truth, Wolff also suggests that perfection is a quantifiable characteristic. Indeed, he appears to suggest that there could be a calculus of perfections for counting from individual perfections the quantity of their combination. Yet, the value of this combination is not a simple sum of the perfections, because one must also take into account how well the perfections fit together. For instance, the perfection of a house is not to be determined by its beauty and its utility, but one must also consider how well the beauty and the utility serve one another.

A complex thing with several constituent perfections might not then be perfect as a whole, if the perfections clash with one another. Similarly, harmony of apparent imperfections can produce a greater total perfection. It takes no Leibniz-scholar too see where this line of reasoning is heading to – we might indeed live in the best possible world, although its individual elements might seem quite unpleasant.

Before moving to the next issue, I will shortly recapitulate what Wolff has to say about the division of things. We have essentially three possible types of entities. Firstly, there are the complex finite things, and we know from experience that they exist all around us. Indeed, the whole world is a complex of all finite things. Then there are the finite simple things, and we know that at least some of them must exist – otherwise we wouldn't have even complex things to discuss about. Furthermore, although we do not yet know it, our own soul will also probably be finite, but simple. Finally, there might be an infinite thing, although we do not yet know whether there is any actual infinite thing – if there is, it will play the traditional role of God. Thus, even in his ontology Wolff has preliminarily outlined the three other parts of metaphysics: cosmology, psychology and theology. Next time, we shall move to the more concrete parts of Wolffian metaphysics.

Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - Units of force

I have always found the concept of infinity, as used by many historical philosophers, to be rather confusing. This is probably due to my own background as a student in mathematics, where by infinity one means a number so great that all the regular numbers are way little in comparison. Because the infinities of which these philosophers speak – particularly God – are supposedly something beyond numbers, I have tried to avoid the ambiguous term. Indeed, one of my articles was once rejected, because the reviewer had something against me speaking of perfections, instead of infinities. Yet, I still feel that the two concepts are rather close. Infinite substance, for instance, is something ”way awesome”, superior in all relevant senses compared to a mere finite substance – shouldn't we then say that it is perfect in comparison with the finite substances?

Wolff describes infinity of a thing as a lack of all bounds (Schranke), and while he never explicitly defines what he means by these bounds, he in several occasions appears to relate them with how a thing is determined and classified. The identification of boundaries and determination resembles Hegel's statement that ”all determination is negation”; Hegel says that he borrowed the statement from Spinoza, and it would be interesting to know how widely it had circulated.

The identification of boundaries/negations and determinations may be difficult to understand. With Wolff, we should remember the notion of essence: a possible structure, which can be actualised in concrete things. Essence determines then at least some characteristics of an actual thing, but other characteristics might be determined by its relations to other things. These relations, then, are what bound the essence and divide it into different species: if the essence in question would be a hole in the wall, the windows and the doors would be differentiated by their differing relations to persons using them. The word ”boundary” is here used somewhat metaphorically: boundaries of a figure are also its relations to the things surrounding it. Essence and all the relations determine then an individual thing completely, because by knowing the essence of a thing and its relations to other things we know everything there is to know about the thing.

Infinite thing is then something that is not bounded, that is, it is determined only by its own essence and not by any relations to other things. In other words, an infinite thing cannot be distinguished from other infinite things. Instead, it is completely inclassifiable – it cannot be put into a same class with finite things, because their nature or essence is too dissimilar. Thus, all we can do to describe an infinite thing is to use meaningless superlatives – it is beyond anything we can imagine, or indeed, just ”way awesome”.

How does the division of infinite and finite things then relate to the earlied division of simple and complex things? Wolff notes that infinite things cannot really change, and by change he means specifically a change of the bounding relations: an essence of a thing cannot be changed, but at most one can replace a thing having one essence with another thing having a different essence. Infinite thing is then all that it is ”at once” and not by going through successive stages. Then again, a complex thing might change e.g. its spatial characteristics, which for Wolff are essentially relations to other things. Thus, an infinite thing, as atemporal, must be simple.

Complex and infinite things are then two classes with no common members, but are there any finite simple things? Well, all the complex things, says Wolff, must be founded on some simple things, the combination of which has generated the complex thing. Now, a combination of simple things is undoubtedly a relation of them, and furthermore, a relation which might change. Thus, the simple things that are the final constituents of complex things must be capable of change and therefore finite.

Boundaries of complex things can be spatial or relate to the number of things it consists of, but what about boundaries of a simple thing, which is not spatial and does not consist of other objects? Remember that by boundary Wolff refers to a non-essential classification caused by the relations of a thing to other things. He apparently seems to think that such a classification must at least be analogical with the relations of magnitudes. A good example of this sort of scale would be one consisting of temperatures: temperatures do not consist of smaller temperatures, although they can be related like one number relates to another. Wolff calls quantities of such scale grades: this concept was used later by Kant and Hegel.

Wolff shares with Kant and Hegel also the idea of relating grades to forces (Kraft). Indeed, beyond numeric and spatial magnitudes, it is rather difficult to imagine any quantities, but those which measure the effects of a thing. For instance, temperature can be quantified, because a certain grade of temperature has a clear effect on the size of certain substances. Thus, Hegel later suggested that all grade-scales are not just similarly structured as scales of numeric and spatial magnitudes, but also essentially connected to such.

Wolff's simple, but finite things are thus indivisible units of forces. In this Wolff appears to move beyond Leibnizian monadology, where the ontological units were characterised by perception, and towards the identification of activity as the most essential characteristic of true existence, which is a common theme in German idealists.

By a force, furthermore, Wolff does not mean a mere capacity, the activation of which is completely contingent. Instead, force is active and causes some effects, unless it is countered by a contrary force. Furthermore, the force of a finite thing is bounded or has a definite grade. In other words, the activity of a simple, finite thing is somehow limited. This limitation is not essential, and the simple, finite thing could well change it, which proves the possibility of applying temporal terms to these things.

Wolff does not stop here, but suggests that simple things are constantly striving towards changing their boundaries. Wolff's only justification for this statement appears to be the principle of contradiction: a thing cannot counteract its own actions. The justification appears once again

somewhat loose: although the thing itself cannot nullify its own force, other things might well affect the thing, that is, if the opposing force is strong enough, the simple thing becomes to a standstill or even starts to become weaker. Wolff also apparently thinks that static states of standstill are merely transitory phenomena, which cannot hinder the almost constant change of the strength of the forces.

We could thus picture a finite simple substance through a graph where every moment of time is connected with some grade in the scale measuring the quantity of the force. The graph goes up, when the force achieves its goals, and when it goes down, it is hindered by other forces. In the shadowy distance above, there is the infinity, unreachable by mere finite things.

Wolff does not say as much, but it appears reasonable to suppose that it is this infinity towards which the finite substances probably strive. The notion of infinity thus produces an objective criteria for making value judgements in the realm of finite substances: the more the finite things resemble the infinite thing, the better they are. We shall see next time what sort of value scale of things Wolff suggests.

Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - Relational view of space and time

In the years 1715 and 1716 a philosophically significant correspondence occurred between Leibniz and Samuel Clarke, a proponent of Isaac Newton. Particularly Leibniz attacked the Newtonian idea of an absolute space and an absolute time that exist independently of any things within them. Leibniz based his criticism on the principle of sufficient reason: if there would be an absolute space, God might have created world few meters away from its actual place in the absolute space, but since all the places in an absolute space are completely similar, He would have had no reason to create it in any particular place and would thus have been unable to create the world anywhere.

Instead of an absolute space and time, Leibniz suggested a relational view of them: space and time are nothing but orders of things – space an order of coexistent things and time an order of successive things. An important consequence of this view is that it becomes meaningless to speak of space and time without any things. (Note that this view is not relativistic: spatial and temporal magnitudes are still stable, despite the differences in the velocity or the effects of gravity.)

Leibniz's view was accepted by Wolff, and indeed, it appears to have been in favour throughout the German idealism. Kant, for instance, appears to take Leibniz's view more seriously than Newtonian absolute space: Kant attacks in Critique of pure reason the relational view more vigorously and also appears to apply a modified relational theory of space in his metaphysical foundations of natural science. Indeed, presupposing an absolute space and time adds to an ontological system two rather strange entities, which are not things as such, but also not based on things.

Now, if one would take Leibniz's description of relational view literally, one could instantly derive all sorts of absurdities. For instance, if space was nothing more than an order of things, space would change at once, when the order of things changes: space would become larger, if a thing went farther from all other things than any thing before. As Leibniz himself appears to have been aware, these problems could be avoided by defining space and time through possible, rather than actual order of things. Thus, space could continue beyond the actual positions of things, because the things have the capacity to or at least could be conceived to move further than they are.

Wolff, on the other hand, seems not to be aware of the possible problems and suggests that space and time could be defined as the actual order of things. Thus, he is able to say that even a single thing by itself would be non-spatial or that spatiality required at least two things and their actual relation.

Because Wolff's simple things should have no things as their constituents, their internal constitution could not be spatial, because it would involve no actual relation of several objects. As we noticed in the previous text, Wolffian notion of a simple thing is ambiguous, because it leaves out the possibility of Aristotle's potentially divisible and still actually unified substances. Similar problems arise with Wolff's notion of space. According to Wolff's definition, the Aristotelian divisible substance without any actual parts would be non-spatial, which is clearly absurd, when we think of e.g. a portion of water. Here we should obviously add some modalities to Wolffian account of space: Aristotelian substance is spatial, because it can be divided into parts that have spatial relations.

Even this correction might not be sufficient. Democritean atoms were supposedly indivisible substances, but still spatial. Wolff notes – consistently with his own definition of space – that this atomist notion is contradictory. Yet, it seems quite possible to imagine that a thing would be physically indivisible and still have some spatial magnitude: spatiality is here not connected to a capacity to divide a thing, but to a possibility of conceiving the division of a thing.

For Wolff, spatiality is something connected with the inner consitution of complex things. What sort of characteristics are then left for simple things? I shall return to this question in the next blog text.

Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - Lego block view of the world

System builders do love to divide things into two classes (unless they are German idealists and probably more into threefold divisions). Wolff follows this tradition and distinguishes between simple and complex things. (By the way, one just has to appreciate German language for its capacity to make such important concepts easy to grasp. Simple things are ”einfache”, which could be translated as ”one-folded” - simple thing has but one part. Complex things, on the other hand, are ”zusammengesetzt” or ”put together” out of smaller things. English equivalents are less transparent.)

How does Wolff then justify his division? The existence of the complex or assembled objects he accepts as given in our experience: the things outside us can be seen to consist of smaller things. In addition to being assembled of other things, complex things have various other characteristic properties:

• complex things have a magnitude (after all, they consist of many things)
• complex things fill space and are shaped in some manner
• complex things can be enlarged or diminished and the order of their parts can be varied without changing anything essential
• complex things can be generated by putting things together, and they can be destroyed by separating the constituents
• the existence of the complex things is always contingent
• the generation of complex things takes time and is humanly intelligible

Simple things, on the other hand, cannot be found in the experience, Wolff says, so their existence must be deduced. Here Wolff invokes the principle of the sufficient reason: the existence of a complex thing cannot be explained completely, unless there is some final level of things from which the complex thing has been assembled. These simple things have then characteristics completely different from the complex things:

• simple things do not have any magnitude
• simple things do not fill space nor do they have any figure
• simple things cannot change their internal constitution (because they do not have one)
• simple things cannot be assembled from other things nor can they be disassembled; they can only be generated ”at a single blow” (einmahl)
• simple things are either necessary or generated through something necessary
• the generation of simple things is atemporal and non-intelligible to humans

Wolff's scheme reminds one probably of atomism, yet, atoms have usually not been described as non-spatial: in this Wolff's simple things resemble Leibnizian monads. Yet, if we ignore for now the nature of space, which I shall be discussing next time, we can discern a common pattern shared by atomism, Leibnizian monadology and Wolffian ontology of simple and complex things.

This pattern is based on the idea that world is like a game with legos. There are magnificient buildings and vehicles, but they are all made out of small objects – lego blocks – which in themselves cannot be broken down to smaller pieces. No complex of legos is necessary and you can even see the revealing lines that tell how to disassemble a ten-story castle into individual blocks. Indeed, in all the various combinations, lego blocks remain distinct individuals that just happen to be attached together.

The lego block view of the world is so common these days that it is difficult to remember other possibilities. It was different with Aristotle, who in his physical studies casually notes that substances might also be mixed, that is, combined in such a manner that the combined substance vanish and a new substance appears in their place. We may easily picture such a mix through an example of adding sugar to water: the powdery sugar vanishes, but also mere water, and in place of the two a sugary liquid appears.

One might oppose my example with the observation that the sugar and the water do not really vanish when mixed, but sugar molecules merely disperse among the water molecules. Yet, this observation itself is based on empirical studies and one could not decide a priori whether this particular case was a true mix or a mere assembling of lego blocks. In other words, the example shows that Aristotelian mixes are a conceivable possibility. Furthermore, it is also a possibility which we could well comprehend and imagine: we could model any Aristotelian mix through the picture of sugar combining with water.

Indeed, we need even not think of mixing two substances of different sorts. It suffices to picture a portion of water combining with another portion of water. The result is not two portions of water, but one bigger portion, or in other words, the original things have vanished in combination and been replaced by a new thing. This conceptual possibility is ingrained in the mass terms of some languages: things like water do not appear to behave like the lego block model, thus, we cannot e.g. speak meaningfully of several waters (we have to speak of many portions of water etc.)

If the possibility of an Aristotelian mix is admitted, Wolff's whole division of simple and complex things becomes somewhat suspect. The simple things should, on the one hand, be the ultimate constituents, which are required for explaining the existence of the complex objects: they should be the independent substances, while the complex substances are contingently assembled from them.

Then again, simple things should, on the other hand, be indivisible and they could not have been generated through a combination of other things. Yet, if a thing has been or at least could have been generated through an Aristotelian mix, it would not be simple in the second sense, while it well might be simple in the first sense, that is, an independent substance. In other words, a substance might be generated from other substances, but still not have any parts or constituents.

Wolff himself actually considers the possibility that a simple thing could just change into other simple things, somewhat like Aristotelian elements – fire, air, water and earth – can change into one another. Yet, he quickly disregards this possibility, because either it would be a miracle where one substance is instantly destroyed and another takes it place or then the apparently independent things are mere states of one thing. Only with the latter option, Wolff adds, does the previous state explain the latter state.

Wolff's denial of Aristotelian change of elements is itself unfounded. Even less convincing it is as a criticism of an Aristotelian mix. Although an apparent change of one thing to another thing should be interpreted as a mere change of state, an Aristotelian mix involves a combination of several things into one unified thing, and it feels rather awkward to call two separate things a mere state of their combination or vice versa.

The flaw in Wolff's division of things is important, because it suggests a similar flaw in Kant's second antinomy. The antinomy should consist of two equally convincing statements that could not hold at the same time: ”everything in the world consists of simple things” and ”there is nothing simple in the world”. The two statements could well be both true, if the simple things in the first statement meant final constituents of assembled things, but the simple things in the second statement meant indivisible substances. That is, the final constituents might have no parts, but they could be so manipulated that in place of a particular thing, many things would appear (this division is essentially a reverse of the Aristotelian mix, and indeed, Aristotle himself apparently thought divisions worked this way). We shall have to return to the issue when we get to Kant's Critiques (it will probably take twelve years).

Wolff's theory of simple and complex things has other problems as well. For instance, Wolff merely assumes that simple things cannot be observed. He does not mean that we could not imagine what simple substances would be like, and indeed, he admits that we perceive very small things as having no discernible parts. Yet, Wolff notes that magnifying glasses have proven that these apparently simple things are actually complex – but this empirical evidence does still not prove the general inobservability of simple things.

A more substantial reason for the unobservability of simple things is Wolff's conviction that simple things cannot be spatial, while all observable things are. But why simple things couldn't be spatial? This is a question I will consider next time, when I investigate Wolff's theories of space and time.