Hoffmann: Study of reason – Distinct cognition

Hoffmann thinks we should not be interested of ideas just for their own sake, but because these ideas refer to things – either actual or merely possible things. Thus, clarity of ideas is not required just for the sake of distinguishing ideas, but because of distinguishing things through the ideas. Yet, the clarity of ideas is still not sufficient for distinguishing things. For instance, we might have a clear definition of fluids, which would still be unable to distinguish fluids properly from other things – say, the definition might apply to also to sand. It thus makes sense to separate from mere clarity the full distinctness of ideas, that is, their ability of letting properly distinguish things that they refer to.

Hoffmann does not so much consider what distinction means for ideas, but discusses more different ways to confuse distinctions. The mildest form of confusion occurs when we are in some level aware of a distinction, but in another respect fail to use this distinction properly. This happens particularly in two cases. Firstly, we might be well capable of distinguishing individual examples of certain ideas, but we might fail in explaining what this distinction consists of in abstraction from individual examples. Secondly, we might have the opposite problem, that is, we might abstractly differentiate between some ideas (e.g. virtue and vice), but be incapable of distinguishing concrete examples of such ideas (we might be unable to say whether an action was virtuous or vicious).

A more dire confusion occurs, when we are convinced of the existence of a distinction that does not actually exist. In some cases such a confusion might be merely verbal, and Hoffmann is quick to blame Wolff for raising such mere verbal distinctions: for instance, Wolff's definition of possibility cannot be even used to decide whether fictions like golden mountains are possible. A somewhat more substantial confusion happens when the distinction is ideal, that is, something we can think, but which doesn't occur in actual existence – Hoffmann mentions some medieval theories of blood circulation as an example of such distinction. Even a real distinction might be uncharacterised in the sense that one couldn't apply such a distinction in special cases.

Moving on, a false distinction might be inadequate in the sense that one might know only a genus or other abstract feature, which is not enough for making a proper distinction. Hoffmann mentions especially Wolffian definition of necessity as an opposite of impossibility: if the definition is taken to its extremes, one could then say that the sentence ”triangle has five angles” as a sort of opposite of impossible sentence ”triangle has four angles” would be necessary. Another type occurs when one tries to distinguish a genus from one of its species, like when Wolff distinguishes absolute and hypothetical necessity, although, Hoffmann thinks, Wolffian hypothetical necessity as a necessity dependent on some (previously necessary) thing is just a form of absolute necessity. Finally, a false distinction might be based on mere abstract mental opposition – like when we distinguish a person's desire for happy life and a person's desire for good life – or it might be based on some ambiguity of concepts – like when metaphysics is defined both as a study of most general features of all beings and as a study of primary entities behind all beings.

In addition to mild confusion and false distinction Hoffmann also points out the possibility of logical ambiguity, in which one fails to see distinction that truly exists. Such logical ambiguity differs from verbal ambiguity, in which one is quite well aware that one word is used in two different senses. Logical ambiguity can result from confusion of words – like when Wolff uses word ”necessity” both of the opposite of impossibility and of the final ground of all things – but it is always something we are not aware of.

Still, not all logical ambiguities are caused by verbal confusions, but the idea of some genus might truly be equivocal and refer to many different genera. A simple case of such equivocation happens when one is incapable of abstracting from individual instances when thinking of a genus. Thus, one might think virtue sometimes as virtue towards oneself, sometimes as virtue towards other people, without noticing their difference.

A more serious case of logical ambiguity arises when one fails to note that an idea is heterogenous, that is, when different species of same genus have slightly different essential structure – an example of such heterogenity was correspondence, which was different in the relation between picture and original and in the relation between text and author's intention. Hoffmann notes that Wolffian notion of complex things is such a heterogenous idea. Wolff thinks that the essence of all composite entities is based on the particular arrangement of the parts, but this is true only of such machines, like clocks, in which removal of one piece causes the destruction of whole clock, while a lump of clay remains a lump of clay, no matter how much you rearrange the parts. Similarly heterogenous is the notion of infinite division, in which people often confuse potentially infinite with actually infinite division. Further example is also provided by Leibnizian monadology, which doesn't notice that while physical units can be actually separated from one another, this need not hold of metaphysical units.

Finally, logical ambiguity might be caused by the subtlety of conditions, on which the distinction is based. Such conditions might be material abstractions, that is, they might be true part of the idea from which the abstraction is made (e.g. animality is a material abstraction in relation to humanity). Thus, one might deny that the existence of collision of laws, because one fails to recognise the difference between contradictions and collisions. Contradiction occurs when we try to think two opposite at the same time – thus, it would be contradictory that a law would explicitly deny what the other law commands. Then again, collision concerns forces or causes – two different laws might assign different motives for action, which might in particular cases pull to opposite directions.

The subtle conditions might also be reflective abstracts, that is, they might be more the result of the act of abstraction (e.g. genus is a reflective abstraction in relation to humanity). Thus, being in general might refer either to genus of all things whatsoever or to a vague entity that is supposedly identifiable with all individual entities and should thus be called God, and pantheistic thinkers might confuse the existence of the first with the existence of the second.

This concludes Hoffmann's investigation of confused distinctions and also his investigation of ideas in separation from one another. Next on the menu is his study of combinations of ideas.

Hoffmann: Study of reason – Clear as mud

Hoffmann begins a new topic by noting a familiar experience. Picture yourself a shadowy evening, when light is already beginning to fade away, walking in an unfamiliar environment. Ahead of you is a building, but you cannot really say what colour it is. You must have seen buildings of similar colour before, but you just cannot say in these conditions whether it is, say, brown or red. The idea of the colour of the building lacks clarity or it is obscure.

We might first notice a bit of terminological difficulty. What I have here called clarity, is called deutlichkeit by Hoffmann. In case of Wolffian tradition, I have usually translated deutlich as distinct, while clear I have reserved for the word klar. Turns out, Hoffmann uses another word, distinct, which it is just convenient to translate as distinct, and as Hoffmann doesn't use the word klar, I chose to use clear for deutlich in this case. In any case, although Hoffmann's and Wolff's two pairs of concepts share similarities, they ultimately refer to different distinctions.

Hoffmann means by clarity the capacity to distinguish an idea from other ideas and thus to identify it, if we happen to think about it in different times; the opposite of clarity is then obscurity (dunckelheit). It should come as no surprise that Hoffmann points out different levels and modes of clarity. The most external of these types is the verbal clarity of words, in which we recognise words used by speaker or writer. Verbal clarity, of course, doesn't mean that the thoughts expressed by the words are clear, and Hoffmann is eager to suggest that Wolffians often manage to get only to the level of verbal clarity.

Somewhat more substantial is what Hoffmann calls objective or external clarity, which essentially means the clarity an idea has in relation to a particular person thinking about it. This is undoubtedly dependent on the person involved, and e.g. a book containing thoughts that are as such quite clear might be truly obscure to a person who has insufficient cognitive skills to follow the argument of the book.

Distinct from the objective clarity is then the internal clarity of the ideas, or as Hoffmann also calls it, ideal clarity, and it is this type of clarity that is a topic proper for logic. Why is it then important to obtain ideal clarity? Hoffmann points out that only through clear ideas can we hope to distinguish objects, because obscure ideas might ambiguously refer to various objects. Now, because objects are differentiated by their qualities, clearer ideas must somehow helps us to discern more of the inherent qualities of things. This is an important criterion for clarity of ideas. In many cases we just cannot see directly the inherent qualities of things, but must satisfy ourselves with some analogies or symbolic presentations. Indeed, Hoffmann goes so far as to suggest that we can have truly clear ideas only of material things, and perhaps only of their mathematically expressible characteristics, while e.g. all ideas of spiritual things are inherently obscure, because we can characterise them only negatively, i.e. by telling that they are not material, or through qualities common with material substances.

The connection of clarity with inherent qualities provides Hoffmann also with a criterion for intelligible philosophy. If we cannot know any qualities of a thing, we cannot even think or have any idea of it. Thus, Hoffmann criticises Leibniz, because latter's monads have only relational characteristics: they are subjects or have a relation to a force and they are constituting level in relation to matter etc. In comparison, Hoffmann notes that idea of God is defined by many qualities, such as omnipotence and omnipresence.

Ideal or internal clarity comes in three different varieties, two of which are fundamental and all of which are required for a complete clarity. First variety is what Hoffmann calls vulgar existential clarity, which means simply put just a capacity to exemplify certain idea through sensations – e.g, when we can show what redness is like. Like the name implies, vulgar existential clarity is not enough for scientific purposes, but it is important, because only through such clarity should we be convinced of the existence of some thing corresponding to an idea. One can e.g. use analogies to make up for the loss of liveliness in non-sensational matters, but such analogies cannot guarantee any existence. It is no surprise that Leibnizian monadology is expressed as a warning example – analogy of two clocks does explain perfectly the relation of soul and body, but it still remains mysterious, whether anything existent corresponds with this idea.

The second type Hoffmann calls essential clarity, in which the idea is to see how well analysed some idea is, that is, to distinguish various parts and aspects in the idea and then combine them into a totality (note how this essential clarity means essentially what Wolffians had called distinction). Hoffmann notes that some sensuous ideas, such as those of colours, we cannot analyse in this manner, due to inherent limitations of our understanding, but otherwise one should try to analyse everything one perceives to make one's cognitive state as perfect as possible.

Essential clarity, Hoffmann tells, is dependent on what he calls logical existential clarity, which means having a clear idea of abstract ideas in separation from all other ideas. Indeed, having a clear idea of a defined structure, one must have clear idea of the parts of the definition, and once again due to inherent limits of human cognition, we must ultimately in the course of analysis face ideas that we cannot define, except by using the very ideas as a part of the definition. These basic ideas would thus be what Kant later calls categories, and the list which Hoffmann provides seems quite familiar, although it has only seven ideas: unity, diversity/multiplicity, negation, external connection, causality and subsistence. All the Kantian categories of relation might be said to be present in some form, categories of quantity lack only totality and categories of quality is represented by mere negation. The most glaring omission are the categories of modality, which Hoffmann has already stated to be too ambiguous.

Notion of clarity is then important as defining the limits of intelligibility. Yet, mere clarity itself does not make for a good cognition, as we shall see in the next post.

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.

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.