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

In every world, Crusius notes, things interact by moving, thus movement is a topic that should be studied in cosmology. More precisely, he continues, the topic of movement can be approached with three questions: what is movement, how it can be measured and what laws govern it. Of these three, Crusius explains, the first one is clearly cosmological, while the second one was dealt in ontology. The third one, Crusius concludes, is partially cosmological, because some laws of movement can be deduced from the very essence of movement, although some laws of movement must be proven empirically and thus belong to physics.

Crusius then defines movement as a state of a substance that changes its place. Its opposite is rest or a state where a thing does not change its place. Crusius notes also that some movement is only apparent, when a thing does not change its absolute place, but only its place in relation to some other thing. True change, where a thing changes its absolute place, he further divides into external change, where the whole thing is moving, and internal change, where some actual parts of a thing change their places so that their positions in relation to other parts of the whole are changed. Crusius points out that these two classes are not mutually exclusive, since there can occur situations where a thing moves, while its parts change their place in relation to one another.

What then could move in these different ways? Crusius notes that a simple substance cannot at least move internally, since it doesn’t have any actual parts. Then again, infinite things (or from Crusius’ perspective, God) cannot move externally, because there is nowhere where such an infinite thing could move as a whole. Furthermore, he adds, everything that is finite, can move at least externally, whether it is simple or complex.

Crusius divides external movement into total external movement, where the whole substance moves completely from one location to another, and partial external movement, where actual or ideal parts of the thing change their place: once again, the two classes are not mutually exclusive. While the notion of total external movement seems clear enough, it might be difficult to see how partial external movement differs from internal movement. One example of a partial external movement that is not internal nor total, Crusius says, is such where a simple substance grows and thus its ideal parts change their places, since this involves no change of actual, distinct parts of the substance. Another example would be rotation of a sphere: the sphere as a whole does not go from one location to another and the relative positions of its parts remain the same, but the parts of the sphere do change their absolute positions.

Crusius derives some simple consequences from his definition of movement. Movement, as he sees it, has always a definite direction, and indeed, a start and end point. It also has certain characteristics: velocity and strength by which it withstands resistance. Furthermore, Crusius notes that movement of a complex substance is defined by the movement of its parts.

Movement, Crusius emphasises, is a positive change and thus requires a positive cause. Rest, on the other hand, is for Crusius just a lack of movement and does not therefore require any cause. In other words, a thing rests, Crusius says, if it has no reason to move, and if the cause of the movement vanishes, the movement must also cease. A direct consequence of this is that increase in the velocity of movement requires a similar increase in the cause of the movement. Crusius also thinks that change of the direction of the movement must also have a cause, which would make the Epicurean idea of atoms swerving without a reason ridiculous.

Because motion always requires some cause, Crusius continues, state of movement cannot be indifferent to the matter. By this Crusius means that a moving cause has to at first overcome an inherent resistance in moving a piece of matter. This inherent resistance is, of course, inertia. More precisely, Crusius calls it metaphysical inertia, distinguishing it from physical inertia, where the resistance is not just an inherent property of matter, but also involves a force, although one that is, as it were, dead, that is, suppressed by the moving force. Beyond inertia, motion can be resisted also by a living force, that is, a force that truly can resist the moving cause.

Crusius notes that a finite cause of movement cannot really affect a thing more than the thing resists the movement. Of course, the cause can have more force, but it only uses as much force as is required for overcoming the resistance. Thus, Crusius thinks he has justified the law of action being equal to reaction. Although a non-empirical proof, Crusius clarifies, we still require empirical observations to determine how much a finite cause acts at a given situation.

It is an essential feature of substances that differ from God, Crusius says, that they cannot penetrate one another. Thus, when a finite substance, whether matter or spirit, tries to occupy the same place as another finite substance, it will drive away the other substance, that is, pushes it. Crusius adds that pushing is just an existential effect, in other words, it doesn’t require any force, but the mere presence of one substance trying to occupy the place of the other.

Pushing a substance makes it move: Crusius calls this a communicated movement. Indeed, he says, communicating movement is the only way finite substances can affect one another. Series of communicated movements cannot go on forever, he immediately adds, and such series cannot all derive from God’s miracles, because that would be against the purpose of the world. Thus, Crusius argues, there must be some finite substances that can move their own substance through their inner activity - such movement he calls original. The inner activity causing original movement can be constant or conditional striving, inherent to some elements of material things, or it can be free willing. Because even the activity of elements is ultimately derived from God, Crusius concludes, all movement is generated by some spiritual activity that is not movement.

Communicated movement, Crusius notes, need not always be just an effect of the impenetrability of finite substances, but can also involve an inner activity of a substance. He is thus against the Cartesian idea that interactions of material things would have to be explained solely through geometric properties: God can give material things some inner activities. Crusius faces the possible objection that such activities are what were disparagingly called occult qualities by noting that we can know such activities as well as finite creatures can, when we can distinguish them from one another and deduce their existence from their effects.

Crusius progresses then to describe several rules involved in the communication of movement, such as parallelogram rule and behaviour of elastic substances. I will not follow him to these details, but I shall take a look at a few conundrums concerning movement that Crusius considers. First of these involves the question of the quantity of movement in the world: is it always constant? Crusius’ answer clearly has to be negative, because this would preclude the possibility of spirits to interact with the world. He even denies the weaker assumption that the world would have a constant amount of moving force, because spirits should be able to choose how strongly they move other things.

Another conundrum concerns the question whether all the matter in the world is moving constantly. A reason for upholding such an opinion would be that a constant movement is required for explaining why shapes of things remain stable: without the constant movement of the surrounding matter, a thing could just change willy-nilly its shape. Crusius does not find this argument convincing. The shape of a complex thing is determined by the shape and position of its parts, while the shape of a simple thing is either chosen by God, with or without any reason, or caused by themselves or by external forces - where is the need for movement here?

The answer to the question, Crusius concludes, belongs to physical, not metaphysical cosmology. He does state that the ultimate limits of the world cannot move and similarly all things that God has determined to rest. Other things, then, probably at least strive to move, whether through their own inherent activity or through being spurred to movement by things outside them.

Finally, Crusius ponders the question whether movement of one material thing necessarily sets all other material things in motion. He notes that if the world contains spaces void of any finite things, movement of one thing could go through this void without communicating movement to other things. Furthermore, he continues, even if there is no void, certain material things could also just switch places without affecting other material things.

Crusius also thinks that these arguments disprove the idea endorsed often by Wolffians that from state of any substance in the world could be determined the state of all other substances. This proposition of Wolffians was explicitly based on the supposed continuous causal nexus of all the parts of the world, where movement of one piece would eventually affect all the other pieces. If this nexus fails, as Crusius deems very possible, the states of the substances in the world would not be as closely interlinked, although they would be really connected.

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

A common topic in ontologies of Crusius’ time, not that usual in modern ontologies, is quantities - back then, general philosophers were keen to explain what mathematics is all about, while nowadays this question is more and more left for special branch called philosophy of mathematics. Crusius follows the tradition and starts by defining quantity as such a property of a thing, by which something is posited more than once.

Crusius notes that at least complex concrete things naturally have a quantity - they consist of many things. Furthermore, even simple concrete things have quantifiable features - they have forces, and even though they are indivisible, they still are spatial and thus have some magnitude. Then again, some abstractions are not quantifiable, Crusius says: there are no levels of existence, but all existing things exist as much as others. Crusius also notes in passing the possibility of infinite quantities, but at once declares that we finite beings cannot really know anything about them.

Quantities come in different types, Crusius continues, for instance, quantity of a force differs from a quantity of an extension. The difference between these types becomes important, when we start to measure the quantities. Measuring, Crusius says, involves determining a relation of a quantity to some known quantity. As such, this kind of comparison is possible only between quantities of the same type (there’s no sense in measuring weight with a ruler). Still, Crusius admits, quantities of different type can be compared indirectly. Firstly, we can compare them through relations of quantities - for instance, we can say that punishments should be proportional to the crimes punished. Secondly, the comparison can be done through causal links, for example, the resistance of a body can be compared with the striving of a soul, because one has the effect of hindering the other.

To determine a quantity perfectly, Crusius says, we must represent its parts distinctly. This requires expressing the quantity as a number of distinctly thought units. These units might be naturally distinct - for instance, when we count things distinguished by natural limits, like cows - or arbitrarily chosen, for example, when we compare length of a thing to a measuring stick. Since a given quantity might not be expressible as a number of arbitrarily chosen units, Crusius also introduces fractions (no mention of irrational numbers, though).

An extreme case of natural units, for Crusius, is naturally provided by simple substances. Crusius admits that measuring complex substances by their simple parts is impossible, since we do not perceive these ultimate constituents. Still, he continues, understanding the nature of these simple parts can help us in picking suitable units for measurement: for instance, when we note that movement should be ideally measured by checking how many simple substances move through smallest measures of space, we can surmise that movement could be measured by checking how many things move through a certain space.

Crusius spends the majority of the rest of the chapter discussing a hotly debated topic of the time, namely, the so-called question of living forces. The point of the debate, at least as conceived by Crusius, is how to measure the quantity of an action, such as movement. Crusius’ take is that while abstractly taken this quantity can be expressed as a multiple of the strength of the action (in case of movement, mass of the moving object) and its velocity, we must also account for the resistance encountered by the action and thus use the square of velocity to determine the action.

Martin Knutzen: Reasoned thoughts on comets, in which their nature and properties, together with the type and causes of their movement are studied and presented, including a short description of a remarkable comet in the present year (1744)

If there’s one thing Martin Knuzen was famous for, then it was introducing Immanuel Kant to Newtonian physics. Yet, Knutzen’s own understanding of Newton’s ideas was at least in some regards rather shallow, especially when it came to the mathematical machinery behind Newton’s physics. For instance, Knutzen predicted that a comet would appear during 1744, because the same comet appeared regularly every few years. A comet did appear then, but as more capable astronomes noted, it wasn’t the comet Knutzen identified it with.

Knutzen himself was apparently rather unconcerned about such criticism. Even his book on the topic, Vernünftige Gedanken von den Cometen, darinnen deren Natur und Beschaffenheit nebst der Art und Ursachen ihrer Bewegung untersuchet und vorgestellet, auch zugleich eine kurze Beschreibung von dem merkwürdigen Cometen deß jetztlauffenden Jahres mitgetheilet wird, has no indication of Knutzen even considering such a possibility. Knutzen’s motivation for his book, beyond introducing the comet of 1744 to a wider audience, is to criticise superstitious ideas where comets are regarded as harbingers of doom.

This motive lies even behind Knutzen’s more questionable thoughts, like the false identification of the 1744 comet. Knutzen emphasises the regularity of the comet’s movement, as a guarantee that they are natural phenomena. He uses a simple induction to justify the assertion that comets continue to move with the same regularity as they have appeared to do - it is equally justifiable, Knutzen says, as when Adam noted after a few days that the sun will always rise in the morning. Such regularity statements seem the more justified, the shorter the time between two appearances. Thus, Knutzen is very eager to show that 1744 comet was the same as had been seen a couple of years ago. This leads him to insist more generally that there are less comets in our solar system than other astronomers and even Newton had assumed - seemingly different comets have often been just appearances of one comet, seen in different parts of the sky due to slight changes in the comet’s orbit, crossing Earth’s ecliptic at different points at different times.

Knutzen’s main point against taking comets as omens is based on showing a failure of another inductive move. Knutzen notes that if comets were such omens or signs of bad events, they would either be causally connected to such events or then the connection would have to be an effect of God’s arbitrary choice, similar to when he in the Bible sets up rainbow as a sign of his promise to not flood the world again. Knutzen then points out that neither possibility really works. If God had set comets as an arbitrary sign, he would have had to teach this sign to us, either through revelation or through experience. There’s no mention of such a sign in the Bible - in fact, the book even speaks against looking at such astrological signs. Even experience speaks against this - if God had meant comets as arbitrary signs of bad things, then he surely would have meant them especially as a sign for astronomers, who are most certain to see these omens, but astronomers who have found most comets have not been particularly unlucky.

Similarly, Knutzen shows that there seems to be no natural connection between comets and bad events. Undoubtedly sometimes comets have appeared during a time when a war has been going on or some king has died or some other calamity has fallen upon some country. Indeed, since Earth is big, it is almost inevitable that some type of disaster is almost always going on at some point of the globe. If a comet would have some noticeable effect on the earthly goings-on, it would have to be a global effect, but there’s no correlation between global crises and appearance of comets. In fact, Knutzen continues, there’s no clear causal mechanism by which a comet could influence such events. For instance, suppose someone would say that comets could cause wars by having a force to aggravate people. Problem is, such a force would not just cause wars, but Hobbesian chaos, where everyone attacked everyone else. If comets would cause only wars, then such a force would have to affect only royalty, but it is unclear how and why such a lifeless and unconscious object as comet could pick out kings and queens as its target.

In his wish to show that comets have not harmed Earth in any manner, Knutzen goes a bit too far and insists that comets could never have an adverse effect on Earth, discounting even the notion that a comet could hit the Earth or at least fly so close that its gravity might cause some disturbances. Thus, Knutzen discounts the worries of his contemporary, William Whiston, who had suggested that such catastrophic meetings had indeed occurred before - Jewish tradition told that Noah had seen a comet before the flood, which Whiston saw as a sign of the mythical flood being an effect of a watery comet hitting Earth. Knutzen was convinced that this tale was just yet another coincidence, and since comets had never hit Earth, they would not hit it in the future. Then again, he suggested that the Jewish tradition might explain historically why comets were universally feared: Noah associated for the rest of his life comets with disasters and taught his descendants to also do so.

Although Knutzen did not then believe in comets as divine signs, he did speculate on their having some purpose in the divine plans. Comets, Knutzen deduced, are just like planets in being mostly solid objects, surrounded by an atmosphere formed from gases and dust. The main difference with the regular planets is that the orbit of comets is very oblong and so a comet is sometimes very close to the Sun, sometimes very far away from it. When the comet approaches the Sun, the increasing gravity and the heat make the comet’s atmosphere appear as a tail. When the comet again changes its course to the outer reaches of the Solar System, it still retains some of its heat - and perhaps, Knutzen suggests, the whole purpose of a comet doing such a trip is to transfer some of this heat to where it wouldn’t otherwise get.

Next time, we shall once again return to Wolff's account of natural law.

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.

Gottsched: First grounds of whole worldly wisdom (1733)

I've already described Gottsched's original take on poetry and I am now about to embark on the first part of his work on the whole of philosophy, Erste Gründe der gesammten Weltweisheit, and especially its first part that deals with theoretical philosophy. Since, the number of such philosophical compendiums is about to grow and I assume they mostly follow the same formula, I am not about to make a thorough series of posts about each individual book on metaphysics. Instead, I shall merely make some general remarks and comment on the novel features of each work.

Before starting the work itself, Gottsched begins with a short presentation of the history of philosophy, and just like the pietist Joachim Lange, begins with the account of Genesis. Whereas Lange's vision of philosophy was one of depressing downhill, in which humans had lost the original wisdom that consisted of a connection to God, Gottsched has a more positive view, no doubt tied to a very different idea of what philosophy is all about: for Gottsched, just like for Wolff, philosophy is worldly wisdom, which then is a science for discovering happiness in this world, which can clearly become more perfect as we discover more things about the world around us. Curiously, Gottsched's take on history is rather unhistorical: he goes through nations and asks what philosophical or scientific discoveries they had made. This feeling of ahistoricity is heightened by Gottsched's decision to end the history of philosophy quickly after Socrates.

After this pseudohistorical introduction begins the work itself. Gottsched's take on what belongs to theoretical philosophy is pretty traditional: the book considers much the same topics as Wolff had done in his logical, metaphysical and physical writings. Still, Gottsched's arrangement of these topics is rather peculiar. After logic comes metaphysics, but this contains only ontology and cosmology. Metaphysics is followed by physics, which is then followed by a section on pneumatology, study of spirits. I shall briefly go through all novel and surprising features in Gottsched's treatment of these topics.

Gottsched's logic does not at first sight hold much surprises and seems rather Woffian in tone. True, Gottsched does mention other philosophers as inspirations of the study of logic, but it is clearly Wolffian logic, which Gottsched thinks is nearest to the truth: he explicitly mentions Wolff's German logic, while the organisation of the logic reveals clear influences of Latin logic. Still, Gottschedian logic has tendencies not existing in Wolff's logic. While Wolff accepted experience as one source of cognition among many others, Gottsched instead tries to reduce empirical judgements to reasoning. His justification is rather original: empirical judgements depend on the reliability of our sensory apparatus, but this is something that might be proved (for instance, Descartes tried to justify it by relying of the goodness of God). One could protest that such a reliability guarantees still only a probability of empirical judgements, but not necessarily their truth. Yet, this still would not be fatal to Gottsched's position, because in the Wolffian tradition probabilities were also something that could be reasoned with.

Although Gottsched mentions no names, it is clear even from the chapter divisions that he is closely following Wolff's Latin Ontology. The only clear deviation is the lack of a direct proof of the principle of sufficient reason. Instead, Gottsched favours the transcendental argument that this principle is required to distinguish dreams from reality. As this had been done by previous Wolffians, it still means no great leap forward. The other part of Gottschedian metaphysics, cosmology, seems at first sight also rather Wolffian. But while the details truly are lifted almost verbatim from Wolff's works, there is something novel in Gottsched's separation of cosmology as a part of metaphysics from the pneumatology that does not belong to metaphysics. Gottsched explains this division by noting that world must be a topic of metaphysics, because souls also are part of the world. Now, this is something that was at least unclear in Wolffian account of philosophy, and in fact, it is much easier to see Wolffian souls as not belonging to the world, which is causally closed whole, which souls most likely cannot directly interact with.

Gottsched's account of physics is, as is to be expected, full of references to sources beyond Wolff – Gottsched is drawing on developments that were still unknown in time of Wolff's physical writings. Most of what Gottsched recounts feels nowadays very trite – like the account of Ptolemaic and Copernican systems and Kepler's discoveries – or then quite dated – like a theory that first chapter of Genesis describes a time when Earth was still not rotating and each day took one year, while the dust covering Earth's surface slowly flew away, first to reveal light and only couple of ”days” or years later the Sun and the Moon.

What is truly revolutionary in Wolffian setting is Gottsched's pneumatology, which contains, in addition to empirical and rational psychology, also natural theology (God is also, after all, a spirit). We might firstly note that by the time Gottsched was writing this work, Wolff had not yet published Latin versions of these themes. What is truly novel is not Gottsched's new arrangement of topics, but Gottsched's rejection of the pre-established harmony as the explanation of soul/body – interaction.

This development seems remarkable at first, but in some sense is quite natural. We've seen that Wolff moved to a position, in which the pre-established harmony had only a status of a likely hypothesis. Gottsched now suggests that if it at this stage all theories are mere hypothesis and none of them is truly certain, we should choose the option that is most familiar – that is, the theory of a true interaction between soul and body. The problem how souls as substances beyond world can have any effect on world as a closed series of causes and effects Gottsched solves easily through his earlier admission that souls are part of the world and thus the soul/body -interaction belongs to the natural course of events.

Gottsched's pneumatology thus shows a new tendency in Wolffian school. Furthermore, Gottsched wasn't even the only figure to do this. He explicitly refers to a study of one Martin Knutsen - best known as the teacher of Kant - in which the interaction was defended. But what did Wolff himself had to say about the topic? We shall see soon, as I am now about to embark on Wolff's rational psychology.

Reduction of physics

At least since Aristotle's Posterior analytics, mathematics has been the model of science, in which everything should be deduced from self-evident axioms and definitions. Indeed, mathematics was quite long considerably more advanced and certain than any other field of research. It is then no wonder that Descartes tried to fit physics and especially mechanics into this model. Even more, he suggested that basic laws of mechanics could be derived from mere geometrical considerations: after all, matter was defined by extension, so the characteristics of the motion of matter should be reducible to the extensional characteristics of matter, such as size and velocity.

What Descartes had failed to take into consideration was that the nature of matter is not exhausted by its extension and that it cannot be identified with mere space. Thus, one had to take into account also the mass of bodies, when considering e.g. how two bodies behaved in a collision. Recognizing this made it a necessity to empirically observe the actual movement of bodies and to look for regularities that could be generalized from these observations. Inconsistently, such studies were still often called mathematical and even a semblance of mathematical deduction was upheld.

Followers of Leibniz in Germany were more aware of the inability to reduce physics to mathematics. Hence, we see Christian Wolff admitting that his cosmological considerations had an empirical basis and that reliable experiences in general must supplement the inabilities of human understanding. In light of the empiricist tendencies of Wolff, it is interesting to see that Bilfinger supposed that it might be possible to derive basic laws of physics apriorically. I do not think Bilfinger is necessarily going against Wolff, but merely explicating the Wolffian position from a different angle: true, in practice we must use empirical method, but in principle we should be able to use deduction.

Bilfinger still doesn't advocate a return to supposedly geometrical demonstrations of Descartes. Instead, he supposes laws of physics should be derived from metaphysics. In other words, Bilfinger doesn't want to state that physical laws would be necessary like laws of logic and mathematics. Instead, they are based ultimately on the decision of God. According to the Wolffian position, God has created the best out of all the possible worlds. Hence, all the laws that the world follows must also be as perfect as they could be – and if we knew what is objectively best, we could know the laws chosen by God.

What Bilfinger's position makes clear is the contingency of physical laws. Specifically, the creator of the laws still holds the power to suspend these laws for a limited period and place. In common parlance such local suspensions of laws are called miracles. In effect, Bilfinger is saying that miracles are possible and that God has power to make them – another defense of Wolff against suggestions of atheism.

So much for physical laws, next time I shall deal with the difference between intuitive and symbolic cognition.

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.

Andreas Rüdiger: Divine physics, the correct road between superstition and atheism, which guides towards the natural and moral well-being of humans (1716)

Some readers might remember that I was rather charmed by Lange's habit of beginning the philosophy of history from biblical times. Well, the same trick does not work as well the second time, hence, I was somewhat dissapointed by the author's insistence that true physics could be found in Genesis and that the further development of philosophy mostly ruined this fabulous start.

The similarity is not accidental, because the obscure author of Physica divina, Andreas Rüdiger, belonged to the same loose circle of philosophers as Lange. Both Rüdiger and Lange were Thomasians, named by their affiliation to Christian Thomasius, first-ever philosopher to write in German. And like Lange, Rüdiger also spent a great deal of his time for criticising Wolff's philosophy, as we shall see in the future.

As the title indicates so well, Rüdiger's book is aimed against both superstition and atheism: superstition divinises the natural world and atheism gets rid of the divine altogether, and the task is to stick with God, but not confuse him with the natural world. True, the book also contains nowadays rather quaint sounding physical theories, which concern all the questions of contemporary natural science – the nature of space, time and motion, movements of planets and stars, basic elements and their combinations, meteorological phenomena, magnetism, plants and animals. But Rüdiger is not satisfied with expounding his own theories, but he also criticises theories of earlier philosophers and shows how his own ideas can help to refute both two extremes.

Most of Rüdiger's enemies are easy to guess: Aristotle and atomists. But the inclusion of Descartes as one of the enemies is somewhat surprising, considering Lange's appreciation of the French philosopher. Yet, Rüdiger's view on Descartes reveals that he understood the implications of Cartesian and generally the modern natural science. In a Cartesian world view, the material things move each other mechanically, through push and pull. The nearest explanation of an event involving material things is another event with other material things. No God is therefore needed, because the eternal movement of matter is enough for explaining the continuance of the movement of matter, and Cartesian physics opens in this way a door to atheism.

Rüdiger's views on Descartes bear a striking resemblance to Jacobi's idea of all modern, mechanistic philosophy leading to atheism, but even more interesting is Rüdiger's idea why Descartes had to fail. The main mistake Descartes made, Rüdiger suggests, is the overt mathematization of physics. Mathematics is a science of possibilities, Rüdiger states. This might be a quip against Wolff, who had stated that philosophy is the science of possibilities. For Rüdiger philosophy is instead the science of what there actually is.

Whereas possibilities meant for Wolff mainly the actual capacities for generating things – real definitions – the possibilities of Rüdiger refer mainly to mere nominal definitions, that is, to mere words which might have no actual reference. In mathematics we can just put together descriptions without any consideration as to whether they describe anything that could be actual. Indeed, mathematics, says Rüdiger, is at least partially false: nowadays we might say that mathematics idealises and hence abstracts from certain characteristics of the actual world. Just because mathematics is an idealised picture of the world, it cannot grasp the true physics.

Rüdiger's idea that mathematics and philosophy are two completely separate disciplines is something that the later German philosophers agreed with: for instance, Hegel made fun of philosophers who tried to use mathematical method, although it was completely unsuitable for philosophical purposes. Interestingly, Kant admits the difference of the two disciplines, but for almost completely opposite reasons than Rüdiger. For Kant, philosophy is the discipline that can only analyse the meanings of concepts, but it cannot construct them – that is, philosophy does not have the means to actualise its concepts, while mathematician can draw his figures at least in pure intuition.

Rüdiger also argues that mathematization of philosophy eventually makes Cartesian proofs for the existence of God futile: Descartes starts by assuming the nominal definition of God, which is completely ineffective in stating anything about what there actually is. Rüdiger's criticism is reminiscent of Kant's later comment that concept of God as such does not involve existence, although ontological proof attempts to deduce one from the other. Rüdiger's further comments that Cartesian mistake is repeated by Spinoza who just assumes the definition of substance as something completely independent of anything else – without noting that such definition might not make sense, because we cannot generate anything corresponding to it: a similar criticism against Spinozan definitions is later voiced by Hegel.

I think that this will suffice for Rüdiger's Physica. Even if I found it philosophically valuable to investigate his theories of air and aether as the basic elements, I would still be in a hurry to move beyond mere physics. That's right, next time I shall begin to do some serious philosophy and tackle the first ever German book on metaphysics.