Crusius, Christian August: Road to certainty and reliability – Oppositions

Crusius moves from subordination – connection of concepts – to their distinction. Two concepts are distinct, he explains, when at least in one of the concepts is found something that cannot be said of the other. This means, Crusius adds, that some type of subordination cannot be found between them.

Distinction as such is not a very interesting notion, Crusius thinks, because types of distinction correspond simply with types of subordination, and furthermore, we can quite easily recognise distinct concepts through internal sense. A more important type of distinction, he says, is opposition, where the existence of one side of the opposition in a certain concept or subject prevents as such or in some measure the existence of the other side. Of opposition, Crusius adds, the most important kinds are the logical and the causal opposition.

The notion of logical opposition, Crusius begins, is based on the notion of logical subordination, where one concept comprehends all the individuals comprehended by another. On the basis of it, we can first define complete logical distinction or diversity, which means, he explains, that no individual comprehended in one concept is comprehended in the other, in other words, both concepts contain some positive or negative determination not contained in the other. If you are wondering, there is also partial logical distinction, which means that there are some individuals of one concept not comprehended under another, but this is not nearly as interesting a relation.

Complete logical diversity can be merely accidental, Crusius notes, if the diversity is caused only by the concepts being formed with different types of abstraction. Thus, he adds, concepts of human and understanding are completely logically diverse, but only because the concept of human is generated by logical abstraction, but the concept of understanding through metaphysical and qualitative abstraction. Then again, if we add the notion of subject to the latter – that is, if we think of something with understanding – we make the two concepts subordinated, because human is something with understanding. On the other hand, concepts of human and stone are completely logically diverse by themselves.

What is completely logically diverse, Crusius points out, might still not be opposed, which still requires that the concepts exclude one another in the same subject. Thus, understanding and will are completely logically diverse, but not opposed, because they can occur in the same subject.

Crusius divides oppositions into logical and real oppositions. Logical opposites exclude one another only in regard to a common concept or genus, so that an individual of this genus can belong only to one of the opposites, even if these opposites can occur at the same time in the same subject: thus, understanding and will can be called logical opposites, because the force that is understanding cannot be will, although a substance that has understanding can have also will. Real opposites, on the other hand, exclude one another from the same substance, like virtue and vice. An even stronger notion is what Crusius calls disparity, where the opposites cannot exist in the same subject even after one another: thus, eternal and contingent are disparate concepts, because what is at some point eterna can never be contingent.

Crusius states that oppositions can also be divided into those between contradictories and those between contraries. Contradictories come always in pairs, he explains, so that always one of them must hold, while the other is negated, like triangle and not-triangle. All other oppositions are those between contraries, Crusius continues, where the contrary opposite might be a partial or determined negation of a concept, like not-angled compared to triangle, or it might posit some substantial determination that excludes the concept in question, like circle compared to triangle. Contraries can thus be positive or negative and there can be more than two of them.

Crusius goes into more detail with the characteristics of contraries. He notes that they can be recognised as opposite either through senses, like sweet and sour, or from their abstract concepts, like virtue and vice. Furthermore, Crusius says, contraries can be merely comparative, where their distinction is based merely on different levels, such as fast and slow movement, but they can be also absolute contraries, so that their distinction is not just gradual, but a certain quality is cancelled through another, like with virtue and vice.  Finally, Crusius divides contraries also in complete or perfect contraries, where one cancels all the properties of the other, like living and lifeless do, and into partial or imperfect contraries, which are opposed only in relation to certain properties, but have many other properties in common, like waking and dreaming.

Moving on to causal opposition, Crusius begins by noting that it could mean that it is impossible that a certain effect would be caused by a certain cause. Then again, he adds, it could also mean that we are speaking of two kinds of activities of certain causes and we know that one hinders the other and cancels it completely or partially or at least modifies it. In both cases, he continues, one can speak either of causes or grounds of physical existence, like warmth and cold oppose one another, or of grounds of moral existence, such as laws conflicting one another. When we are speaking of causal opposites that hinder or modify one another, this might happen through activity, like in case of a collision between two movements, or then they might just prevent some condition of the other, like when our body hinders the consciousness of our own soul.

Hoffmann: Study of reason – Levels of opposition and connection

From subordination Hoffmann moves on to non-subordination, which holds on between pairs of ideas, one of which can be thought without the other. The most important subgroup of non-subordination is total diversity, in which both ideas have some aspect that is not shared by the other idea, just like body has features that soul doesn't and vice versa. Just like in many cases of subordination, diversity might also be just accidental or dependent on the peculiaties of the person thinking the ideas: for instance, one might not know that humans are animals and hence think that humanity and animality are diverse ideas.

At this point, Hoffmann introduced the notion of ”Punkt”, which we might perhaps properly translate as an aspect. Hoffmann's idea is that all subjects have various of such aspects, which can then be determined in different manners: say, a colour, a figure and speed would be such ”Punkts”. One of these aspects can always be determined only by one complete determination, thus, only subordinated ideas might determine the same aspect (thus, a strawberry can taste both sweet and strawberrish, but not salty). The notion of ”Punkt” is important, because it helps to divide diversity into two different classes. One of these classes is proper diversity, in which the two ideas are not connected, but can still exist in the same subject, because they do not determine the same aspect, like will and understanding. The more important type is opposition, in which the ideas either always exist in different subjects (like the notions of infinity and finity) or then determine the same aspect and therefore cannot exist at the same in same substances.

Hoffmann then goes on to classify different varieties of opposition: we have e.g. logical opposition, in which ideas are opposite, because they are different species of same genus, such as external and internal sensation, contradictories, one of which is always merely negative idea (visible and invisible), and contraries, both of which are determined ideas, like love and hate (note that with Hoffmann contraries can be contradictories, on the condition that the negative idea is something we can have a determinate idea of). Philosophically most interesting is perhaps the notion of causal or physical opposites, which are such that in addition to not existing in the same subject also have the tendency to cancel the other, if it happens to be just in its vicinity, like cold and warmth – this notion clearly resembles Kantian notion of real opposites.

Just as important as determining what types of opposites there are, it is also as important for Hoffmann to determine what is not opposed, although might seem to be. We might have difficulties to understand how some ideas can be combined in the same subject, like non-sensuality and cognition, but there still might be entities having both of these characteristics, just like God is supposed to know things without sensation. Similarly, one might have difficulties to understand how some entity could cause something, like how spirit could move material objects, but this doesn't necessarily mean that being a spirit would be opposed to being a cause of movement.

Hoffmann also notes that there are various levels of opposition between ideas, that is, they might cancel each other only partially, just like perpendicular and horizontal movement, which put together do not completely cancel one another and lead to a state of rest, but change into a diagonal movement. Some contrary ideas might have various intermediary stages, just like temperature can have many degrees between the extremes of cold and hot. Some contraries might be even said to exist in the same subject, if they merely cancel high degrees of the other contrary, just like vices merely cancel perfect, but not imperfect levels of virtue.

Just like there are various levels and types of subordination and non-subordination, Hoffmann thinks there are various levels between subordination and non-subordination. At the most extreme ends are essential connections and absolutely impossible connections, which are based on the very structure of the ideas. For instance, in case of essential connection, two ideas might necessarily exist together, like force and subject, or one idea might necessarily cause the other, like virtue causes good actions. Similarly, in case of absolutely impossible connections, two ideas might be unable to exist in the same subject, like roundness and squareness, or one of them might fail to cause another, like brute animals and speech.

Moving away from absolute impossibility we come at first to unnatural connections, which usually do not happen, but which might be effected by some third thing (obviously, at least God is meant here). At the other extreme are natural connections, which are something that occur, either because of the very structure of the ideas or because of some constant cause connecting them, unless some other thing hinders this connection, just like newborn humans usually have five fingers, unless some external causes hinders their development. At the very middle of this hierarchy, are then contingent connections, which occur sometimes, and merely possible connections, which are not impossible nor unnatural, but still just never happen to occur.

It is obvious that these levels of connection are modal notions, and Hoffmann is quick to note that he finds the use of such notions as necessity and possibility largely ambiguous and thus asks the reader to avoid those terms. It is not clear e.g. whether someone speaking of necessities means just essential existential connections or also essential causal connections or even merely natural connections. Furthermore, what is necessary and possible is more related to how we conceive things and what ideas we have. Thus, before trying to make any modal statements, one should carefully analyse what ideas one has. It is impossible to say what is e.g. necessary for human blood, unless one knows what one means by blood.

So much for relations of ideas, next time I shall take a look at what Hoffmann has to say about the clarity of ideas.

Immutable necessities

Principle of contradiction denies the existence of contradictions, that is, the existence of combinations of contradictories. What then are these contradictories one might ask? Contradictories themselves are a kind of opposites, Wolff answers. Opposites, on the other hand, are such things that cannot exist at the same time, in the same situation (for instance, complete blackness and complete whiteness cannot exist in the same surface). Contradictories are then opposites, one of which must exist in a situation.

It is a well-known fact that when one modal notion (e.g. possibility) is defined, the rest of the modalities can be defined from that beginning. Thus, impossibility is contradictory of possibility: what is not possible, is impossible, and vice versa, and things must be either possible or impossible.

More importantly, when the opposite of something is impossible, this something itself must be necessary. That is, when some situation or thing has no capacity of ever becoming actual, it's opposite must undoubtedly have the power to actualise itself in every situation. For instance, a figure with three sides, but not three angles would be something impossible and could not ever be actualised, thus, if we do have an actual figure with three sides, it must be actualised with three angles. Generally, all such combinations or propositions describing them are necessary, if the predicate could be deduced from the definition of the subject.

Now, there is a special case of necessary propositions, that is, propositions describing the existence of something necessary. Here it is not any feature of the thing that is necessary, but the very entity is supposed to be such that its non-existence would be impossible. In other words, the actualisation of the haecceitas of such an entity would be necessary. Because this haecceitas or individual essence would contain at least implicitly all the predicates of the thing, it could not really have any other predicates. In other words, it could not change into anything else, but would eternally be what it is.

Wolff leaves it open for now, whether there are any concrete necessary individuals – this is a task left for other branches of metaphysics. Then again, Wolff does find examples of more abstract necessary entities. In Wolffian ontological scheme, what is absolutely possible is defined by its non-contradictoriness, and thus, one cannot change what is possible. If something is then possible, it is necessary possible. Then again, essences or coherent combinations of essential predicates correspond to certain possibilities. These abstract combinations or lists of predicates are then necessary, which means merely that it must be possible that some things satisfy these combinations of predicates.

Wolff also points out that there are actually two different concepts of necessity. Firstly, one can speak of necessity plain and simple or absolute necessity – this is essentially what we have considered now. Then again, there is also hypothetical necessity, that is, necessity under some assumption. Wolff's example of hypothetical necessity is the relationship between a feature of a thing determining what other features the thing has: for instance, if a certain figure has three straight lines as its sides, then it is necessary on this condition of its trianglehood that it also has three angles.

This mathematical example is a good point to move to consider how mathematics is presented in Wolff's ontology, which will be the topic of my next post.