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

Concepts of simple and complex substances were of great interest to Wolffians, being one of the primary divisions of substances, and Crusius seems eager to show where Wolffians wen’t wrong with them. He firstly notes that just like the concepts of part and whole, on which the two former concepts are based on, can actually mean very different things. Starting with the parts, these can mean, Crusius says, any group of things we can represent as forming also a one thing, which then is the respective whole. Furthermore, these parts can be actual or such that they can be separated elsewhere than in our thoughts, but they can also be mere thought parts, which can be distinguished in our thinking, but not really separated.

Simple is then for Crusius something that has no parts - in some sense, while complex is something that has parts - again, in some sense. Since the notion of parts was already twofold, this same duality continues with the notions of simple and complex: something may be simple or complex just based on mere thoughts, but also based on something outside our thought.

Even in case of actual simplicity, Crusius notes, there are various levels of simplicity. The epitome of simplicity, he thinks, is God, who is not just a simple substance - that is, something, which cannot be separated into further substances - but also has a simple essence in the sense that no property could be removed from his essence. This is not always the case, Crusius says, because substance can be simple, like a human soul, without having a simple essence. Even a complex substance, like air, Crusius notes, is simpler than, say, a human body, because the former has only integral parts - parts that all have the same essence - but no physical parts - parts that have a different essence from one another.

Crusius also notes that it is a different thing, if something is simple as such or has nothing separable in it, than if something is simple on the condition that the current world exists, Crusius notes that we cannot really distinguish between the two cases and neither can any finite being, but God might be able to do it.

Every force is in some subject, Crusius insists, because no subjectless forces could be thought of. On this basis Crusius argues that in case of complex substances, their force must be determined by forces of their parts. Crusius then concludes that if a complex substance wouldn’t ultimately consist of simple substances, the constituent forces would have no immediate subject where to subsist, which he thinks is absurd. Despite the seeming complexity of the argument, it appears to just assume what it sets out to prove: that the existence of a complex thing must be based on the existence of simple things.

Crusius is especially keen to distance his notion of a simple substance from a mathematical understanding of simplicity. Mathematics, he says, considers only abstract magnitudes, not other determinations of things. In other words, he rephrases, mathematics is only about the concept of space and its possible divisions. Thus, it was natural for mathematicians to assume the existence of points, which should have even no parts that could be thought of as being outside one another. Yet, Crusius states, no true simple substance is simple in the mathematical sense, but is spatial - they just cannot be physically divided further.

Crusius goes thus straight against the Wolffian notion of elements, which are more like non-spatial forces. If we would accept such non-spatial substances, how could we account for spatial matter being generated from them, especially as any concrete matter would require an infinite amount of them? Furthermore, he continues, we couldn’t even say how such pointlike substances could touch one another, as there are always further points between any two points.

Joachim Darjes: Elements of metaphysics 1 - Building bodies

Ever since Descartes suggested that matter is defined by extension, philosophers had been proposing theories as to what Cartesian idea of matter had overlooked, since clearly, extension as such is not yet matter. Darjes enters this discussion in the section on somatology, or theory of bodies or composite entities. He notes that to make a set of multiple entities into a unified entity, it isn't enough just to put them together. Instead, these parts must also cohere with one another.

Now, as we saw in the previous post, Darjes thought that in order that entities can cohere, all of those entities must be non-spontaneous, but also some of them must be active. In other words, there are no completely passive bodies in Darjesian metaphysics, only more or less active. The level of activity in bodies can even be perceived, Darjes suggests, since the difference of fluids and solids reduces to it – fluid bodies have more active entities in them than solid bodies, which have only so much active entities as required for the sake of coherence. Since the difference between fluids and solids is ultimately based on the essential difference between active and passive entities, the difference between fluids and solids must also be essential, Darjes concludes. Somewhat surprisingly, this means that fluids cannot really change into solids or vice versa.

A significant part of philosophical treatises of corporeal objects from this period often include an account of simple mechanical interactions, in which two bodies collide with one another. Darjes is no exception to this rule. He considers several cases – what if only one is moving or both, what if colliding bodies are solids or fluids etc. We need not get too far into the details, but just to note the general attempt to determine the result of the collision from the constituents and the structure of the colliding bodies. For instance, in a collision between a solid and a fluid, the fluid gives away, because a fluid body has more active constituents, which will move according to their own drive, as soon as bonds of coherence holding them together loosen a little bit, while the solid can remain unified in an easier manner.

As a final part of the first tome of his metaphysics Darjes introduces a discipline called mechanology, a study of machines. Machines, for Darjes, are systems of non-spontaneous entities, in which systems, again, mean collections of entities that can affect one another. Systems and therefore also machines are to be clearly differentiated from cohering bodies – in a system, the constituting bodies do not form a single entity, but remain independent of one another. Darjesian understanding of machines is quite extensive – the constituting parts of machines can be solid or fluid bodies or theoretically even elements. Indeed, the whole mechanology remains on a quite general level, where Darjes finds out such revelatory truths as that the state of a machine depends on its previous state.

The second tome of Darjes metaphysics moves then to the investigation of soul, which shall also be the topic of my next post.

Baumgarten: Metaphysics – Kinds of substances

The primary classification of things in metaphysical treatises has long been that of substances and accidences and Baumgarten's Metaphysics makes no exception. Substances are things that can exist without being attached to something else, while accidences have to exist in something else, namely, in substances. Furthermore, Baumgarten adds, accidences are not just something externally connected to a substance, but a substance must contain some reason why such accidences exist within it. In other words, substance is a force that in a sense causes its accidences – if completely, they are its essentials and attributes, if partially, they are its modes.

Now, substances with modes are variable or they have states, which can change into other states. Like all things in Baumgarten's system, these changes also require grounding in some forces. Changes effected by forces are then activities of substances having these forces. Such activities might be connected with changes in the active substance itself, but they might also link to changes in other things: these other things then have a passion. In latter case, the forces might act alone to produce a certain effect and then we speak of real actions and passions, or then the passive substance also has some activity at the same time as it has passions, and then we speak of ideal actions and passions. The division of real and ideal actions and passions is of importance in relation to Baumgarten's thoughts about causality.

Because all substances have forces, all of them have also activities – if nothing else, then at least activities towards themselves. Furthermore, activity does not define just the essence of substances, but also their mutual presence – substances are present to one another, Baumgarten says, when they happen to interact with one another.

Baumgarten divides substances, in quite a Wolffian manner, into complex and simple substances (Baumgarten does admit that we can also have complexes of accidences, but these are of secondary importance in comparison with complexes of substances). Not so Wolffian is Baumgarten's endorsement of Leibnizian term ”monad” as the name of the ultimate simple substances. Rounding up the division of substances is the division of simple substances into finite and infinite substances, in which infinite substance has all the positive properties in highest grade and thus exists necessarily and immutably – this is something we will return to in Baumgarten's theology – while finite substances change their states and have restrictions.

This concludes Baumgarten's account of the substances or primary entities of the world, and like with Wolff, we can already discern the outlines of the three concrete metaphysical disciples. But before moving away from ontology, we still have to discuss Baumgarten's account of basic relations of entities.

General cosmology (1731)

After Wolff's huge works on logic and ontology, his Cosmologia generalis feels refreshingly short with its under five hundred pages. The shortness of the book might also reflect its lack of importance in the purely philosophical part of Wolffian system. Wolff's cosmology works mostly as an introduction to general natural science or physics and is thus firmly connected with Wolff's more empirical studies. Then again, of other parts of metaphysics only theology is essentially said to be based on cosmology, because Wolff argues for the existence of God from the existence of a certain type of universe.

The topic of Wolffian cosmology is then world or universe and general types of objects in it. The very existence of universe is not so much proven by pure reasoning, but assumed – or at least the existence of a universe is justified by certain empirical observations we have. What we actually perceive or observe are certain things – rocks, trees, houses and such. Now, all of these entities are finite, that is, their existence requires a number of other entities, either existing at the same time (like trunk supports branches) or existing before them (like rain requires gathering of clouds).

As they say, no smoke without fire.

The entities we observe are then connected to various other entities in space and time through causal influences. These intricate relations form a kind of web or nexus, in which one thing can be connected to any other thing of the nexus through a string of causal relations. A totality of such interconnected spatio-temporal things is then a world or a universe. There might be different possible universes, because a number of possible strings of events might have occurred, but only one of them truly has occurred, that is, the string of events constituting the history of our world.

I have investigated the nature of this Wolffian universe in quite a detail earlier, but there's no harm in going through it all again. World is a composite of things, and as a composite, its nature is dictated by the nature of its parts. Thus, Wolff concludes, if we replaced just one peck of sand, the world would be completely different, because its identity is determined by the very entities constituting it.

Now, in the actual universe, all things we happen to observe are composite substances, that is, they consist of other things and what they are or their essence is determined by their constituents. If we then want to change these substances, we must essentially change their constitution, that is, remove some parts or add other (for instance, if we want to make blackened metal objects shiny, we must remove all the grime on the surface of the objects), or then we can change the way they happen to move at the moment. All these changes require then direct contact with the object to be changed: you cannot pluck something out, if you are not close enough. In effect, this means that world and all the composite objects that we observe can be changed only through motion that comes in contact with what is to be changed. Wolff can thus add that the world is like a machine or a perfect watch which remains in action, even if its creator fails to wind it.

As we have mentioned number of times, Wolff does not think that his account of world could be called necessary in the strict sense of the word. Indeed, it is easy to see that even if we could explain all the events of a current day, we would be forced to explain them by referring all of them to past events, which would then be completely unexplained and required a new explanation. At the end, these events would be necessary in the strict sense, only if no other series of events would be even conceivable, which is clearly not so.

Then again, Wolff also claims that worldy events are not completely inexplicable facts. Indeed, this non-explicability of some facts should be contradicted even by the principle of sufficient reason, which states that all contingent things and events arise out of some more primary things and events. In case of universe, these primary things and events are movements of material bodies, which with machine-like predictability leads to further things and events. This deterministic view of universe does not completely cancel the non-necessity of the worldly events, because a deterministic series as a whole is not necessitated by anything,

This is enough for the Wolffian scheme of macrocosmos, next time I'll take a look of what he has to say on microcosmos, that is, bodies and their parts.

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.

Christian Wolff: Reasonable thoughts on the effects of nature (1723) and Ludwig Philipp Thümmig: Attempt to most thoroughly clarify the most remarkable incidents in nature, whereby one will be lead to the deepest understanding of them (1723)

Baroque Cycle of Neal Stephenson contains a lovely scene portraying a typical meeting of the Royal Society. A number of curios and weird phenomena are presented to the audience without any regulated order – one members tells a story of fying fishes living in some oceans, another describes a neat trick with a vacuum pump, while third has just developed differential calculus.

Although such a motley of topics seems chaotic, it reveals what has truly captivated the hearts of men for science – it is the extraordinary that interests us. Consideration of curiosities has for long been a part of science – there is even a pseudo-Aristotelian book Problems, which is nothing more than a collection of what the author considered weird and proposed explanations for these dilemmas. Nowadays weird has been used for good measure in popularisation of science – for instance, in the show Mythbusters dealing with such age-old problems as whether cars truly explode when driven off cliffs.

Versuch einer gründlichen Erläuterung der merckwürdigsten Begebenheiten in der Natur, wodurch man zur innersten Erkenntnis derselben geführet wird is a similar collection of curios, written by Ludvig Philip Thümmig, whom we have already met as an editor of a book of Wolffian essays. Here we finally see some of Thümmig's own work, as he ponders such scientific problems as why a boy sees everything double, why animals with two bodies combined are sometimes born, why some trees grow from their leaves and why does gravity work in different grades across the globe – Thümmig's solution to this question convinced at least his mentor Wolff, who mentions it in his own book on natural science, Vernünfftige Gedancken von den Würckungen der Natur, which is also the second book I am considering this time.

While Thümmig's book is a haphazard motley, Wolff does not fail to give us a work with systematically arranged topics. Here Wolff is once again just following a far older tradition. The nameless collector of the works of Aristotle arranged his books on nature in the following order: first came books on the general principles of natural world, then followed books on the cosmos in general and the heavens in particular, after which came books on atmospheric phenomena and earthly objects, while the story finished with books on living nature. This formal scheme was so well thought out that even Hegel essentially followed it in his own philosophy of nature. Thus, it is no wonder that Wolff himself applied this often used model of natural science.

In his natural science or physics Wolff is quite reliant on empirical information and rarely wonders from presenting the conclusions of the science of his time. One exception where Wolff's physics comes in contact with his metaphysics is the description of animal sensation, where Wolff reminds us of the Leibnizian idea of pre-established harmony: while human bodies go through certain changes in their sensory organs, their souls have corresponding sensations, although bodies and souls do not interact with one another.

A more detailed crossing of physics and metaphysics occurs in the very beginning of the work, in the description of the physical objects as complex substances. An important conclusion of this definition is according to Wolff that all the properties of the complex should be derived from the properties of its constituents and the spatiotemporal structure according to which these constituents have been combined - I have called this the lego-block view of the world. Although seemingly innocent, endorsing this view leads Wolff to some substantial consequences.

Observations suggest that there are some peculiar properties that are difficult to explain through mere spatiotemporal structure of things – for instance, the characteristic of objects gravitating toward the nearest big collection of matter or the property of warmth. Now, if these characteristics are not explainable through the spatiotemporal form of the bodies, it must be explained through the constituents of them – that is, there must be types of matter that cause gravitation or warmth.

The assumption of special matters was not a peculiarity of Wolff, but a common occurence at the time, and even Hegel commented on this habit of scientists. One just saw a peculiar phenomenon – certain kinds of metal attract or repel one another – which was explained by assuming a new type of matter, in this case magnetic matter. While the notion of caloric or heat matter and similar properties as matters sound rather quaint, we should not assume that such reification of properties is non-existent nowadays. One just has to open a book on particle physics to learn about photons or particles of electro-magnetism, glueons or the particles holding the nucleus of atoms together and perhaps even gravitons causing gravitation.

Physicists may well have good reasons for such reification in these cases, but taken to its extremes it will lead to the philosophical theory of tropes – all general properties are actually individual things, like this redness, this sweetness, this roundness. The individual things are then just mere conglomerate of these tropes – for instance, the three tropes of particular sweetness, redness and roundness combine to form a particular strawberry.

The setback of trope theories is that it is difficult to see how all properties could be reified. For instance, do not the tropes themselves have properties, such as being a trope? Is this then supposed to be yet another trope? Furthermore, a trope theorist has difficulties explaining how to account of our thinking about universals. Redness of this particular strawberry should in trope theory be completely different from redness of this particular flag – how can then we describe both of them as red? If we suppose that the two tropes are connected by being similar in some manner, we face yet another dilemma – isn't the similarity yet another property?

So much for the physics of Wolffians. Next time I shall discuss the first of many atheism controversies to come.

Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - Can soul be material?

While in the chapter on empirical psychology Wolff merely observed the mental capacities of human beings, in the chapter on rational psychology he tries to determine the nature of the soul or the thing that has such capacities. Nowadays it is easy to think such an attempt as completely ridiculous: after all, Kant should have shown that rational psychology was based on mere sophistic reasoning. We shall have to speak of the Kantian criticism in the future. At this point we may just note the surprising fact that Wolffian theory of the soul begins with a reasoning of transcendental nature. That is, Wolff begins from the fact that human beings are conscious of themselves and investigates the presuppositions of this fact.

The beginning of Wolff's reasoning is innocent enough. We are conscious of something, Wolff says, when we can distinguish it from other things. For instance, I am conscious of a hand mirror, only if I am able to differentiate the mirror from e.g. hands holding it. Particularly, consciousness of oneself implies the capacity to distinguish between oneself and other things. In other words, consciousness is connected with a clarity of thoughts, which for Wolff meant a capacity to distinguish the object of thought from other objects.

Furthermore, in order to distinguish different objects from one another and to recognise them as different, one must be able to contrast them with one another and to consider them one after another, Wolff continues. In order to do this, the conscious being must have imagination and memory, that is, he must be able to think of things that are not present and to recognise them as having been present. Indeed, consciousness is generated, because we can think of a thought for a period of time, note that the time has changed, but the thought itself has remained.

The arguments thus far have been essentially about characterising what it means to be a conscious personality: e.g. a person needs to have a memory, in order that she would have a sense of continuity of self. I cannot see why Kant or his followers would have any reason to argue with these considerations. In fact, much of the Kantian and post-Kantian German philosophy consists of such theorising on the nature of human consciousness, although in a somewhat deeper level.

What Kant and his followers would probably find unacceptable is the next move where Wolff tries to prove the immateriality of soul or the thing that is conscious. Wolff starts by noting that all material processes must be explicable through mere mechanical movement of material objects. Thus, if soul would be material, thinking would also be such a mechanical process. Now, human beings can be conscious of their own thinking, that is, they can note that the starting and the end point of thinking are different and still parts of a continuous process of one thing. Here Wolff simply states that such representation of continuity is impossible with mere matter: material objects as complexes can at best represent only other complexes, but they cannot represent a unified process of thought.

Wolff's blunt statement that matter as a mechanism cannot represent thought processes is quite unsatisfactory, especially as we nowadays don't think that matter consists merely of lego-like blocks that interact only through mechanical contact. Wolff does try to amend his reasoning by noting that material object can represent things – for instance, we can make a clay model of a building – but it cannot represent the original as separate from the representation. I have a feeling that Wolff has here confused first- and third-person perspectives. Surely an external observer cannot see e.g. brain as a representation of the process of thought,but this does not mean that the brain could not represent this to itself, if it just were conscious.

The situation appears even worse, when we consider that by denying the complexity of the soul Wolff has to accept the possibility of a simple thing representing complexities, which appears at least as difficult as a complex representing a unity. Indeed, how could a single partless entity represent a complex of many entities correctly? The only possibility appears to be that the complex is characterised through passage of time: at one point soul represents one part of the complex, at another point other parts and at final point the combination of the two previous phases. Indeed, we might well believe that human consciousness does work in this manner: e.g. when looking at a boat moving at the sea, we concentrate first on its rear end and then on the other end and only after that note that both parts go together.

The problem with this solution is that it once again threatens the supposed unity of consciousness. Suppose that I am thinking of myself. This act of thinking then represents some state of my mind, say, a memory of yesterday. But this act as simple can only represent one thing, thus, it cannot represent itself. We could then begin a new act of thinking that had the original act as its object. This procedure could be iterated indefinitely and so a problem is revealed: no matter how far we'd go, there would always be left at least one act of thought that had not been combined with other acts, that is, the very act of thinking all the other thoughts. This problematic was something that intrigued some of the later German philosophers, although Wolff appears to not have noticed it.

Wolff's argument for the immateriality of the soul was then unconvincing. Next time we shall see whether he can at least characterise this supposed immaterial entity.

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.