Hoffmann: Study of reason – Subordination of ideas

Next task in Hoffmann's logic is to investigate the various relations ideas might have to one another. Here the notion of grounding plays an important role: in a pair of two ideas, either one is a ground of existence for the other or then neither is, that is, either one cannot exist without the other or both can exist independently. The former possibility Hoffmann calls subordination, and it contains a subset consisting of pairs in which both ideas could be the ground and were thus necessary to one another's existence – in that case, the ideas are said to be equal, somewhat like 12 – 3 and 9. Note that in the case of subordination, one can always abstract from the grounding idea the other idea. This does not mean that the possibility of abstraction would be a sufficient criterion for recognising subordination, since in case of external abstraction (for instance, when we abstract time and place from a concrete event), what is abstracted is not subordinated to the starting point of abstraction, because e.g. certain time can exist without an event occurring in it.

As we saw in the previous post, in many cases Hoffmann distinguishes between cases where things truly have some structure and cases where the things have this structure only in relation to understanding. In case of subordination, we might speak of absolute and relative subordination, where relative subordination means cases in which subordination exists only in thought, because we have abstracted both sides of the subordination at the same time. An example would be the notional pair of high and low. We couldn't call anything high without at the same time assuming the existence of some relatively low places and vice versa, but places that we happen to call high might well exist without the places we happen to call low – we just wouldn't call them high in that case.

The notions of relative and absolute subordination are not clearly divided, since from cases of absolute or proper subordination we can produce examples of relations, if we move to a new order of abstraction. That is, birds and animals form one example of a proper subordination, since birds cannot exist without animals existing. Yet, we can abstract from the relation of birds and animals the more abstract relation of genus and species. The notions of genus and species are then relations, since both notions are dependent of the other – while animals could exist without bird existing, no genus can exist without some species.

Although relations are then, according to Hoffmann, somewhat dependent on understanding, we can still distinguish between proper and accidental relations. In latter it is not so much a case of relations that are not really relations, but of relations that are not as natural as could be. Thus, the idea of species is naturally related to the idea of the closest genus, but only accidentally related to the idea of a more proximate genus.

In an absolute subordination, one type consists of cases where the subordinated actually exists in its ground. This could either mean metaphysical subordination, in which the ground is subject and subordinate is something subsisting in that subject, like figures subsist in matter, or existential subordination, in which the subordinated is a part of the ground, which is then its respective whole. Hoffmann only mentions the metaphysical subordination and concentrates mostly on the existential subordination.

Existential subordination is then just another name for the relation of whole and part. Hoffmann notes that there are in fact many wholes. Whole could be an essential whole and the subordination then essentially qualitative, in which parts are independent of one another and also of the whole: this is the relation between humans and their souls. Then again, whole could be an integral whole and the subordination then quantitative, in which parts cannot really be detached from one another nor from the whole: this is a relationship holding between numbers, like 6 and 12. Slightly different is the case in essential mathematical subordination, in which a whole is essentially mathematical and parts can at least in thought be separated from the whole, since they are of completely different type, like sides of a triangle as lines differ from the two-dimensional triangle. But most interested Hoffmann is of the logical subordination, in which whole is a logical whole, like animality, and its parts (different types of animals) share the essence with the whole, but can be separated from one another.

Logical subordination is then either total – both ideas are subordinates of the other, just like rational animal and animal capable of deliberation – or then partial, in which only one of the ideas is subordinated to the other. The partial logical subordination seems on a closer look just another name for the relation of some genus to a species – the genus is considered extensionally as a class of individuals and species is then a part of this class. One could then think that there isn't that much of interest that Hoffmann could really say about this tired old topic. Yet, it is of interest how Hoffmann notes that this relation has varieties differing from the usual norm embodied in the classification of living creatures.

Thus, just like in many other cases, logical abstraction might be accidentally logical, or it might hide a further, non-logical abstraction within it – thus, when I seemingly subordinate the species of electric eel to a genus of animals capable of producing electricity, I am actually describing its causal capacities. Even in properly logical abstraction, the connection between supposed genus and idea might be just accidental. For instance, when I divide learned persons into those who are pious and those who are not, the piety is not intrinsically connected with being learned. Indeed, one might as well begin with a class of pious persons and divide them into learned and unlearned

Then again, the supposed genus might also be impure in the sense that it contains attributes not necessarily existing in the species. Thus, Hoffmann says, we might speak of the idea of a theologian and consider it as a species in the genus of academics, yet the genus would be impure, because a theologian need not be academically learned person. In addition, genus might also be incomplete in the sense that what belonging to a genus means might be dependent on what the more determined species if. As an example Hoffmann notes the idea of correspondence: the notion is incomplete, since correspondence between, on the one hand, a picture and the original, and on the other hand, purpose and means are quite different in nature.

Hoffmann's divisions of different modes of logical subordination serve then once again to reveal paralogisms in reasoning. Even more so is the case of distinguishing cases where the subordination between ideas is based more on possible connection, that is, where the ground, as it were, potentially contains the subordinated idea. This is what happens in various causal relations, in which then, Hoffmann thinks, cause and effect must be necessarily connected.

When we are speaking of causes, Hoffmann elucidates, we might be either discussing proper or efficient causes or then mere ground of possibility, which merely determines a simultaneously existing thing, which is then dependent on the ground, but still not created by it, just like two sides and an angle determine the rest of the constituents of a triangle. Hoffmann complains that Leibnizians have often confused the two topics, speaking of proper causes, when all they had was a ground of possibility and sometimes even just an ideal ground for cognising something. Cause is a ground, but its a very peculiar type of ground.

It is then of interest for Hoffmann to distinctly separate proper causes from various grounds. Thus, Hoffmann notes, cause must have existed previous to the effect it causes – hence, if world is eternal we cannot say that God has caused its existence. Furthermore, cause must have proper force, by which it makes something happen – thus, unlike Descartes thought, mere geometrical shapes cannot be causes of anything. Finally, force must be directed to produce this very effect – hence, in Leibnizian pre-established harmony soul cannot be said to be cause of bodily movements, since the force of soul is directed only to changes in soul itself.

An important notions pertaining to causes and grounds are perfection and sufficiency. Cause is perfect, Hoffmann defines, when the cause is the cause of the whole effect, down to every last detail and circumstance. Ground is sufficient, on the other hand, when it lack nothing that is required to make what it is ground of to exist. Imperfect cause is might still be sufficient – it just cannot account for all the details of it has made to exist. Then again, a cause that is an insufficient ground, is always sufficient ground for some detail in what has been caused.

A perfect cause must then account for why something exists, why it has the properties it has and why it continues existing. All of these three aspects must be based on some acting force in the cause. All of these causes might then be analysed into various partial causes and grounds. For instance, within a cause of existence one might distinguish between sufficient cause of existence, which truly makes that something to appear, and efficient cause of possibility, which merely adds some ground to make the final result possible. For example, in case of sensation, the human body acts like a cause of possibility – without bodies we couldn't sense – but the actual sufficient cause is the thing affecting sense organs.

Causes in general can be analysed into various constituents, Hoffmann notes. Firstly, there is the cause as a concrete subject with a certain active force directed to something – this is what Hoffmann calls principal cause. Then again, we might abstract from the fact that this force belongs to some concrete subject – then we are investigating merely the causality or act of causation. We might also be interested just of the impulsive cause or the events that the cause makes happen and activates. Finally, we might be interested of the various modes or intermediaries between the act of principal cause and the final impulsive cause.

The principal cause might be mechanical or act merely through figure and magnitude of matter, like force and pressure of lever. Then again, it might also be physical or based on inner activities of matter, like movements of elements. It might also be ideal or based on understanding and ideas, like memory can be caused by sensations. Finally, it might be voluntary or based on force of will acting toward some end, like reproductive urges of animals.

Of the various types of principal causes, Hoffmann is especially interested of voluntary causes. Voluntary causes, he says, can be physical or unintentional, like a feeling of desperation, or they might be intentional or moral, like love. Focusing on moral causes, Hoffmann notes that these can be analysed into the act of will in pursuing something or the subjective final cause, the object that the subjective final cause strives to make happen or objective final cause and the intermediary effects of subjective final cause meant to produce the objective final cause or means. All the three notions can then be further analysed and classified: for instance, we can regard the means merely as the formal activity directed toward some end or as a material object, like gold, good for making some things happen.

Moving then from principal to impulsive causes or from the subject of causation to the events caused, Hoffmann notes that these either mechanically make some other forces act, like compressing air makes it expand later, or then ideally affects some spiritual entity, like some sensations make a person anxious. Hoffmann is again more interested of the affairs of persons and notes that ideal impulsive causes are either natural, that is, not caused by a free agent, like certain bodily reactions may make us feel uncomfortable, or moral, that is, caused by a free agent, like a piece of oratory may arouse in us some emotions. Hoffmann also notes that some ideal impulsive causes may be internal to the person affected, somewhat like anger might make us act aggressively. These internal impulsive causes must then be carefully distinguished from final causes, since the former are not intentional.

Finally, Hoffmann speaks of the intermediary modes. Of course, an act of causation might not use any intermediaries, but if it does, these either somehow modify the events caused or then merely remove some obstacles preventing them. They may mere passive instruments of the principal cause or they may have their own active force meddling with the proceedings, and they might be either necessary requirements or not. An important subgroup is formed by what Hoffmann calls objective causes, that is, the nature of the object of causation itself modifying the act of causation.

Hoffmann also notes that causation might activate only relativistic effects, that is, effects occurring only within an understanding. Thus, when summer changes into winter, nothing happens with a temperature of well insulated cellar, but to human touch the cellar now feels warmer. Completely different matter are then accidental causes, for instance, when a known gambler happens to lose all his fortune playing cards and because of that changes his complete lifestyle. In such an accidental causation, the cause itself is not directed toward the effect that follows it or it is not controlling cause, unlike in a case, where a gambler changes his lifestyle because of a convincing speech made by his psychiatrist. This does not mean that such a controlling cause could be certain – psychiatrists cannot help all their patients – but might be assisted or prevented by various external factors. Indeed, Hoffmann goes on to classify various grades of certainty in causal acts: causation might be e.g. such that it cannot be stopped, once it has started to affect, or then it might be prevented, although its effects are otherwise quite certain, like death caused by cutting of the artery might still be prevented by quick surgery.

Hoffmann's account of subordination is thus full of detailed analysis and classification of various relations, and especially his study of causality is quite extensive for a book that is supposed to concern only logic. Next time I'll take a look of what more Hoffmann has still to say about relations between ideas and deal especially with varieties of opposition.