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.

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

A key pair of ontological concepts in traditional metaphysics has been that of infinity and finity, thus, it is no wonder Crusius investigates them also. Simply put, finite is that which has limits, while infinite is that which has no limits. These definitions leave it still unclear what having limits actually means. Crusius explains that limit means an end to that where thing is thought, that is, something where the essence of the thing cannot continue to a higher grade, cannot spread into larger space or cannot have a longer duration. This definition implies, Crusius says, that a limited or finite thing can be multiplied in grade, space or duration, in other words, something greater than it can be thought.

Infinite in some aspects, on the other hand, is such that greater of it cannot be thought. Crusius continues that there are then three types of infinity, as there are three aspects involved with every existing substance. Firstly, every substance has an essence, which is ultimately based on its fundamental forces: here, infinity means that a substance is capable of all possible actions. Secondly, in addition to essence, substances exist in space and time, both of which have their own types of infinity: immeasurability, where a substance occupies all possible spaces, and eternity, where the duration of a substance has no beginning or end.

Crusius also notes that none of the three types of infinity should be confused with what could be called infinity of progression, which is no true infinity, but a mere series of ever greater things, which still always remains finite. For instance, a thing generated at some point of time could continue existing without any end and still its duration would always have been just finite. Crusius suggests that such an infinity of progression is the only way we humans can think also the infinity of the past: we set out a past moment, then a still further past moment etc.

Interestingly, while Hoffmann rejected the so-called ontological - or as he called it, Cartesian - proof of God’s existence, Crusius appears to accept it. He starts with the notion of a substance with an infinite essence, that is, with capacity to do anything - such a substance has then an infinite grade of perfection. Now, Crusius continues, if a substance should be capable of everything, it should be capable of ensuring its own existence, or existence belongs to the perfection of the infinite essence. This means, he concludes, that a substance with infinite essence must necessarily exist everywhere and at every time.

Crusius argued earlier that necessary things can only be simple - otherwise they could be broken - and this must then apply also to an infinite substance. Its simplicity then implies that an infinite substance cannot be reduced. In fact, he points out, there can be no quantitative relation between the infinite substance and finite substances. In fact, nothing could be added to a finite substance to make it infinite, and finite and infinite substances differ by their essence.

Crusius makes the remark that one might think as an infinite force a determined capacity for doing a certain type of action in as great a magnitude as possible. Force of an infinite substance is not of this sort, he clarifies, but a general capacity to do anything whatsoever, even what any of these determined infinite forces could do. Indeed, an infinite substance should have only one force, which it can then apply in different manners. Of course, Crusius admits, the infinite substance cannot do anything impossible, but this is more of a clarification than any real limitation. The infinite substance does not then need any instruments for its actions, but if it so chooses, it can use them. In fact, since no effect of the actions of the infinite substance could be the highest possible, it can freely choose the magnitude of its effects.

Infinite substance should be able to do anything that just is possible. Crusius argues that creation of all finite simple substances is one of the things the infinite substance has done. True, he admits, it is inconceivable to us mere humans how an infinite substance has done this, but as contingent they must have been created by something, and since a finite mind cannot apprehend an infinite substance, it is understandable that we cannot fathom everything it could do. Crusius notes that there is also nothing contradictory in finite substances creating finite simple substances, although it is again inconceivable how they could have done it. Still, he assures the reader, we should not assume any finite substance to have such a power, because this assumption would undermine our ability to investigate natural causality, which is based on the premiss that finite substances can only bring about something by combining existing substances or by dividing existing combinations.

Crusius also considers the question, whether there could exist at the same time an infinite amount of things. His first point is that we certainly can always think of a number greater than any given number, thus, we shouldn’t be able to think any infinite number (of course, nowadays mathematicians do think of infinite numbers or cardinalities, but since they also form a never ending series of infinities, these would not actually be infinite in the sense Crusius means; still, this is a distinction that we can ignore when speaking of what Crusius had in mind).

Now, although we cannot think of an infinite number, this might not imply anything for the possibility of an infinite amount of real things. Here the crucial question is, Crusius suggests, whether this infinite amount is meant to be added up from actually different, perfect things. If it is, Crusius insists, we should be able to divide this amount into two groups. Since neither subgroup is the greatest, they are both of a finite amount, but then an infinity would be made up of two finities, which contradicts the idea that an infinity cannot be quantitatively compared with something finite.

Then again, Crusius notes, the previous argument works only if it is really distinct things that are added up and divided into groups. Thus, God might be able to think at once an infinite amount of possible things, since these possible things are not really distinct. We finite beings cannot comprehend how God can do it, but this does not restrict God’s capacities.

A far simpler question, Crusius thinks, is that of an infinite series of causes and effects, because Crusius smells a contradiction in that notion. In a series of causes and effects, he argues, all terms are either generated or not. If not, the series has a first cause and is therefore finite. Then again, if they all are generated, then the individual members have all not existed at some point and therefore the whole series has not existed at some point and has thus a beginning. Key part of this argument is clearly the move from all parts of a whole to the whole itself. Crusius notes that this move does not work in all cases - if parts of a whole weigh 1 kg, then the whole will definitely not weigh 1 kg. He unconvincingly tries to argue that usually and in this particular case this move is guaranteed by a principle of non-contradiction, because whole just is parts taken together.

Whatever the validity of the argument, Crusius believes he has shown that a series of causes and effects cannot be really infinite. He does admit it can have an infinity of progression, that is, it could have more members. These members could also be added to the beginning of the series, that is, we could think that the series began from an earlier point than it does, but this just means that it is completely arbitrary where such a series begins.

Because all series of causes and effects are thus finite, Crusius says, the essence of an infinite substance cannot consist of such a series of changes. Even more, he insists, the infinite substance cannot go through any series of changes, because it would undermine its eternal perfection. Crusius might be arguing here against the idea that God could be persuaded by a series of reasons to do something. In any case, he notes that an infinite substance should be immediately everything it can be.

The lack of changes in the infinite substance means according to Crusius, firstly, that all the actions of the infinite substance must be fundamental, free actions. Secondly, the infinite substance cannot be affected by a finite substance, at least not directly. Crusius does admit that finite substance could hinder actions of the infinite substance by not fulfilling certain conditions the infinite substance has placed for its own action. Furthermore, finite substance could resist finite effects generated by the infinite substance.

Although Crusius speaks against the idea of an infinite series of causes and effects, his attitude toward an infinite duration is quite the opposite. Indeed, he is committed to the idea that the first, uncaused cause has existed an infinite amount of time or eternally. One might argue that Crusius’ commitment should fall to the very same argument he himself used against the infinite series of causes and effects, creating then a dilemma reminiscent of Kant’s third antinomy, where we cannot accept either that there is an uncaused cause nor that there isn’t. Crusius’ solution is once again to differentiate between actual and merely possible. A series of causes and effects involves an actual succession of things, while an infinite duration consists only of possible succession of things, whereas nothing really changes during the existence of an eternal substance.

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

It has taken Crusius this long to finally get to the definitions of two concepts mentioned in the very title of his book: necessity and contingency. Like definitions of modalities tend to do, Crusius’ are ultimately circular: necessary is what cannot be otherwise, while contingent is what could be otherwise. Yet, he at once gives a more substantial explanation of the terms, linked to causal terms: necessary is such that no cause could make it otherwise, while contingent is such that requires a cause making it so, without which it would be otherwise or not at all.

Crusius also suggests a criterion for recognising what is necessary and contingent: if we cannot think contradictory of something, it must be necessary, while if we can, it must be contingent. Crusius underlines that this criterion is not foolproof and definitely does not reveal the essence of necessity and contingency. Indeed, he points out, even a fatalist could think that a world might be otherwise, even if his worldview would mean that the world is necessarily what it is.

Crusius notes that necessity and contingency can concern both the essence and the existence of a thing. In case of essence, he clarifies, the question is whether a thing cannot have different properties, because changing them would make the existence of the thing impossible - this means that the essence is necessary.

Necessity and contingency of the existence of a thing, then, refer to the respective impossibility and possibility of the non-being of the thing. Crusius notes that necessary existence of a thing can be either independent necessity, where the thing exists continuously and is necessary in all circumstances, or consecutive necessity, where the thing exists necessarily in certain circumstances, when it is generated. Respectively, contingent existence of a thing can be either dependent contingency, where thing doesn’t always exist, but must have an origin, and consecutive contingency, where thing is generated in such a manner that it might have been otherwise or even not at all.

Crusius’s concepts of independent and consecutive necessity resemble the concepts of absolute and hypothetical necessity in Wolffian tradition. Yet, Crusius sees a difference. He defines absolute necessity as something, which as such cannot be otherwise. The most obvious type of absolute necessity, Crusius notes, is such where contradictory opposite of something contradicts the very principle of non-contradiction - something which many Wolffians also recognised - but it is not the only type, since similar forms of necessity should arise also from the other two basic principles.

The hypothetical necessity Crusius defines as such where something cannot be otherwise in certain circumstances that are based on a series of conditions, ultimately caused by something that at the moment of its occurrence could have happened otherwise. This concept of hypothetical necessity is obviously a form of consecutive necessity, but with a distinct characteristic that it is based on some free action. On the other hand, if no such free action is to be found behind consecutive necessity, then it will be, Crusius insists, just absolute necessity. This distinction is especially geared against the notion that God would have had to create the best possible world, without any free choice in the matter, which would make the existence of this world absolutely necessary.

Crusius thinks that only such things exist with absolute necessity, where their non-existence would contradict their essence - it is not yet made explicit, but he is clearly implying that only God fits this requirement. All other things are contingent or they could be thought to not exist, so they must have been generated by something else, that is, God. With something of a sleight of a hand, Crusius notes that since these other things cannot then be necessary in the absolute sense of the world - they could fail to exist - but they still have consecutive necessity, being necessitated by the creative act of God, this act of creation must have been free.

Crusius still has some loose ends to tie. Firstly, he notes that complex substances are always generated from their constituents, so that all absolutely necessary substances must be perfectly simple. Secondly, he defines moral versions of all the modal notions he has introduced: this is clearly something that influenced Kant in defining ethical categories of modality. Thus, Crusius begins from the notion of moral existence - what is a goal of a free person, or in effect, what should be - goes on to define moral impossibility - that something shouldn’t be - moral possibility - of which cannot be said that it should or that it shouldn’t be - and finally moral necessity - that something should be done, because of a presupposed goal. These notions and their somewhat strange definitions, where moral impossibility is not contrasted with moral necessity, but with moral existence, parallels closely Kant’s later division of the ethical categories of modality.

Crusius finally discusses the notion of coercion (Zwang), where the necessity of some action is caused by something outside the thing acting. He is especially interested to show that lack of coercion by an external thing still does not mean something would not be necessary - even an uncoerced necessity would be real necessity.

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.

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

From the very start of metaphysics, in the book with that name by Aristotle, the concept of one was regarded as an important topic. Thus, it is no wonder that Crusius would consider it. Indeed, he thinks that we have many different notions of one, distinguished by what concepts they are opposed to. First of these is the concept of one thing in contrast to several things. This concept, he insists, cannot really be defined, but can only be exemplified. In essence, a thing, no matter what it is, is always one or a unit, because we can think what it would be like, if it were multiplied into several similar things.

Another concept of one, Crusius continues is that of something unified in contrast to what is disunified. By unification Crusius means a relation where things are so intrinsically related under certain conditions that when one is assumed to exist, the other must be assumed to exist also. Unification can come in many forms, the primary ones of which are unification merely in our thoughts and unification in real existence. Crusius notes that we cannot really know all the subdivisions of unification and mentions only a few examples, such as metaphysical unification of one thing subsisting in another (e.g. property in a substance), existential unification of two perfect things connected so as to become inseparable, such as a hand and a torso, and moral unification where two persons are united by having common goals. In any case, Crusius emphasises, all cases of real existential unification are ultimately based on causal interactions. Thus, he insists that Leibnizian pre-established harmony would be no real unification of body and soul.

A third notion of one is connected with the notion of identity. Crusius defines the concept of identity as the opposite of difference, where two things are different if in one is something that is not in the other - Crusius notes in passing that this notion of “not” or denial is again something simple, which we cannot really define. Identity as the denial of difference can then be just similarity, where things share something, but also identity in a strict sense, where one thing - here is the connection to one - is represented through two concepts, of which one is found to contain nothing that wouldn’t be contained in the other.

Crusius considers the question, when we can know that the objects of two concepts are identical. The criterion he suggests is that one should be able to replace what is thought in one concept with what is thought in the other without any consequence. He also emphasises that mere same essence is no true criterion of identity, since we could have substances that are just numerically different, that is, that would agree in their absolute properties, but would be e.g. in different spaces at the same time.

Although Crusius' definition of identity might seem rather rigid, he does admit that identity can fluctuate according to the viewpoint chosen. For instance, when we are considering whether things at different points of time are the same thing, we might get different results depending on what we focus on: corpse is in a sense different from a living body – they have different essence - but in another sense they can be identical, because they share the same matter. Then again, if an essence of a thing consists of a certain relations of parts, the thing can remain identical, despite its parts being replaced by different, but similar parts.

Crusius chooses at this point to give a list of simplest concepts. This list is a development of a similar one from Hoffmann, and we could consider it to be a precursor of Kant’s list of categories. Crusius' list contains the following concepts:

• Subsistence, that is, the relation between a property and its subject
• Relation of one thing being spatially within or outside of another thing
• Succession
• Causality
• Relation of one thing being figuratively outside of another thing, in the sense of not being its part, property or determination
• Oneness in opposition to plurality
• Relation of things being unified
• Thing’s being somewhere in space.

Crusius also clarifies further the relation of these simple concepts to the seemingly simple concepts of sensation, like colours. Crusius’ idea is that while the above mentioned simple concepts are the ultimate result of analysing more complex concepts for any understanding, it is we humans who are incapable of analysing sensations just because they are caused by unknown activities affecting us in a confused manner, so that we cannot distinguish these causes from one another. Crusius also distinguishes the simple concepts from indeterminate, symbolic concepts, which we cannot really think, but which we can only represent by saying what it is not and what its relations to other things are.

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

All things make other things possible and are therefore causes, Crusius says. This possibility of another thing could be called a force. Problem with this definition, Crusius says, is that such forces seem to explain nothing: it does not really tell us anything to say that the stomach has a force to consume food. Indeed, such a force might be a combination of many causes or then it might be just an abstraction of some more substantial process.

For this reason, Crusius advocates looking for forces in a more substantial sense or fundamental forces (Grundkraft). These fundamental forces should be something special and distinct even outside our consideration and also something constant in the thing. When then can we say that something is a fundamental force? Well, Crusius notes, as long as we cannot causally explain the supposed effects through the force, this cannot be fundamental - or at least we do not understand the fundamental force distinctly. This means that at least the first or nearest effects of the fundamental force should be affected only by conditions within the subject. In fact, these nearest effects should be something in the subject itself, while further effects appearing in other things or objects are influenced also by fundamental forces in those objects.

Crusius continues determining fundamental forces. If a fundamental force is finite, it should have only one kind of nearest effect, while all further effects should be understood through these nearest effects - otherwise, causal chains would offer no explanation. Of course, the same finite subject can have several distinct fundamental forces and could thus be part of many kinds of causal chains with many types of nearest effects. Furthermore, the limitation affects even less an infinite force, Crusius says, because it should be capable of literally all kinds of effects. This implies that we can never really know what having an infinite force would feel like.

Fundamental force should be truly fundamental, Crusius emphasises. In other words, it should not be causally dependent on some other forces in the same subject nor be just a modification of some force. Then again, if one knows that some occurrence in a subject cannot be explained through one force, then this occurrence cannot be just a modification of this one force, but requires the influence of some other force. For instance, Crusius suggests against Wolff, human volition cannot be explained through mere force of representation.

Forces can cause something through their mere existence, Crusius says and gives as examples all mechanical causes that affect things through their mere position and shape. Then again, force can also be active in the sense that it affects things through an inner property directed to bring about certain effects. Such activities can form causal chains within a subject, Crusius notes, but these chains must end in some fundamental activities, which are immediate applications of some fundamental forces. These fundamental activities cannot be mechanical, thus, cannot depend on mere movement of the subjects. Furthermore, they cannot depend on anything external to the subject nor be generated merely by a previous activity of the subject, although previous activities can be conditions of a fundamental activity.

Crusius notes that some fundamental activities continue constantly, because of the essence of the underlying substance. In the case of divine activities, Crusius insists, the very underlying substance is necessary and thus the activities are also necessary. If the underlying substance is not necessary, like in case of elements, the fundamental activity is dependent on its existence.

Some fundamental activities do not occur constantly, Crusius says. Of these contingent fundamental activities, some happen always in a certain manner under certain conditions, like human sensations. Then again, other fundamental activities are just enabled by certain conditions, but not necessarily actualised: the primary example here is human will. Crusius insists that such free activities are not contradictory, and indeed, that their existence must be assumed, in order to justify the notion of moral accountability.

Free activities can be sufficient grounds, Crusius says, in the sense that they can make things actual. Then again, he continues, they are not determining grounds, that is, what they make actual could also be otherwise. In cases not involving free activities, Crusius endorses what he calls the principle of determining ground: what is not generated through free action must have a ground that not just makes it actual, but also determines it to be such and not otherwise.

The principle of determining ground concerns only real grounds, in other words, relations between real substances. Thus, Crusius explains, it should not be confused with an epistemic principle that nothing should be assumed without a good ground or reason or with a moral principle that nothing should be done without a good reason. Still, determining grounds do provide us also with ideal or epistemic grounds, he admits: if we know that something is a determining ground for some phenomenon, we know that this phenomenon cannot be otherwise.

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

Crusius begins a new chapter by pointing out that our thinking begins from sensations. This implies that we already implicitly begin with a notion of existence, sensation being its criterion. Crusius admits this, but adds that we must still abstract the notion of existence from our sensations.

We have seen Wolff defining existence as something added to possibility - in effect, this was no real definition of existence, but existence was a combination of various concepts, namely the existences of complex things, simple things and God, some of which we can define and understand, while others we can’t. Crusius does admit Wolff’s point in some sense. What Wolff was trying to do was to define existence in terms of how it is generated (for instance, complex things are generated by combining simpler things), and Crusius accepts that we cannot ultimately know where existence comes from. Yet, he insists that this is a false way to approach the problem and says that we can define existence rather simply as being in space and time.

What then are these space and time for Crucius? Starting from space, he says that space is just where we think all existing substances are and what is left, when we remove all substances in our thought. Space is then independent of all substances in it or absolute.

Crusius defends his notion of space with an argument that clearly inspired Kant’s discussion of space, although the conclusions of both are very different. Indeed, Crusius begins by pointing out that space is not considered to be a substance, since otherwise we would fall into an infinite loop, because all substances are thought to be in space. Then, just like Kant, Crusius considers the possibility that space might be taken as a property of some substance, but decides against it, because space is not thought to be in some subjects, but subjects are thought to be in space.

Finally, Crusius looks upon the idea that space might be a relation. He notes that if space would be a relation, it would have to be a relation of substances being next to one another (here the inclusion of the notion of a substance in the definition is necessary, because e.g. music also has things next to one another, namely, sounds, but space is the only thing, where these beings next to one another are substances). Still, Crusius concludes, even this possibility is unsatisfactory, because even a single substance would have to be thought of as being in space.

Crusius’ argument is meant to show that his notion of space agrees with what everyone thinks space is. There’s still the possibility that space is a kind of collective delusion or mere imagination. Crusius rejects this possibility by referring back to his criteria of truth: since we cannot separate in our thoughts existence from space, they should be accepted as truly connected, unless this incapacity of separation is somehow connected to limitations of our understanding. Kant would later argue that we really can’t say, if it is down to some limitation of our cognition, but Crusius does not consider this possible: otherwise, we would have to reject also the principle of sufficient reason as susceptible.

Crusius admits that some people have rejected the notion of absolute space as something independent of substances and taken it as a mere relation of substances. One reason for this is simply that they assume space must be substance, property or relation, and because the two first options seem impossible, they have assumed that it can only be a relation. Crusius notes that his very point has been that these are not all the options: while notions of substance and property are concepts linked to essences, spatiality is a component of or abstraction from concrete existence.

More concerning for Crusius seems the objection that the absolute space would rival God in dignity, because both would be eternal and necessary. Crusius’ answer is that space is not a complete thing or substance, but a mere abstraction from existence of all substances. Thus, even God is in a sense spatial, because he could be said to exist everywhere. Of course, Crusius thinks that God’s existence is not bodily and so cannot be sensed. Therefore space could be empty in the sense of being without any bodies, even with God present in it. Extrapolating from this, Crusius suggests that all simple substances might be in space in a similar non-sensuous fashion, or as he puts it in terms that Kant was to borrow later, they fill space, but do not extend it.

After defining some concepts related to space, such as location, Crusius turns to discuss time. His main point is similar as with space: time is not a substance nor a property or a relation, but an abstraction out of existence of actual things, and more precisely, their succession following one another. Importantly, Crusius thinks that time is absolute or independent of things and that it is not mere imagination. A point Crusius did not make with space is that although we cannot think of an infinity of time or eternity, this only tells of the limitations of our understanding.

Crusius then returns to the notion of possibility. He suggests that the criteria of possibility earlier considered - that of non-contradiction - delineates only the realm of ideal possibilities or possibilities in thought. A more substantial form of real possibility, he continues, refers to things that do not yet exist. In other words, such a real possibility will at some point come into existence, and its possibility outside thought is guaranteed by causes that will eventually make the possibility actual. Crusius notes that such real possibility is dependent on the existence of something, namely, its cause. Thus, if nothing exists, nothing will be possible.

When the realm of possible is restricted, the realm of impossible grows. Thus, not just contradictions make something impossible, Crusius explains, but anything that prevents something to have causes that would make them existent. Crusius refers especially to the principles he has inherited from Hoffmann that combination or separation of concepts we cannot make are impossible, barring the possibility that our incapacity is due just to our limited understanding.

We already saw earlier a few reasons why the principle should not hold, such as a revelation by some more perfect spirit. Here Crusius outlines a few further reasons, which he has again inherited from Hoffmann. Firstly, although we could not separate something from a negative concept, this might not be true of a more perfect being, for instance, although we cannot abstract things from limits, another being might be able to think infinities. Secondly, although we could not combine things, this might not be impossible, if we are dealing with immaterial entities.