Crusius, Christian August: Road to certainty and reliability – Divisions of concepts

The first element of thinking, Crusius states, is concepts or ideas. Concepts represent an object that differs from the concept, through which the object is thought, he adds. There are various ways to divide concepts, and the first way Crusius mentions is that according to the cause behind the concept: concept can be a sensation that represents an object, insofar as we sense it, or it can pertain to a memory, by representing something that we do not currently sense. The latter kind of concepts, he insists, are merely retained sensations or they are generated through imagination or through judgement or through both.

As to their content, Crusius continues, concepts can represent either individuals or abstractions. Abstract concepts, he notes, are also called predicables, because they are something that can be predicated of individuals. Individual concept is then simple or complex, depending on whether the individual in question is simple or complex. Individual can be represented through a sensation or it can be called by a name taken from an abstract idea.

Concept may also, Crusius adds, represent an absolute thing or a relative thing. The essence of a relative thing, he explains, consists of a relation, that is, of a concept that is abstracted from two or more things in such a manner that in it is represented something that could not be abstracted from one alone – Crusius exemplifies relative things with the concept of error. Then again, when thinking of an absolute thing, we should be thinking of something more than just concepts that belong together only because one has abstracted from several things at the same time. In other words, Crusius explains, an absolute thing is a unity not just because of our abstraction, but also outside our thought.

Absolute things represented in absolute concept are, Crusius recounts, physical, mathematical or merely existential beings. Physical things, he adds, are substances (like soul) or their active forces (like understanding) and effects (like light). Then again, mathematical beings are such that are determined merely through the type and magnitude of extension. Crusius notes that not all mathematical beings are absolute, but only such that are thought without relation to something else, like ball or triangle. Finally, mere existential beings are not active forces or substances nor magnitudes, but only some properties, regarded as possible or existing, such as immortality, space or property in general.

Crusius divides relative beings into moral, mathematical and relative beings in a strict sense. By moral beings he means such relations of things that they have toward purposes of a willing spirit, that is, relations that are means making certain goals possible or actual. If certain things are considered according to moral relations, Crusius notes, these concern either moral actions or things that are not as such moral, but that are connected to certain moral relations, like gold used as money or bills of exchange. Moral actions, he adds, are regarded either only as actions in general, without any indication of their goodness or badness, or they are represented as virtue or vice, prudence or stupidness.

Relative mathematical beings, Crusius notes, are magnitudes related to other magnitudes, such as square roots or sines. An important type of relative mathematical beings, he says, are mechanical beings that are appropriate for a determined purpose through the figure and placement of their parts, such as weight or barometer.

Finally, Crusius defines relative beings in a strict sense as certain parts or conditions that are taken together in one concept because of considerations of a thinking understanding, but where the relation in question does not occur between magnitudes or goals and means: an example of such a strict relative being is truth. He notes that relative beings in a strict sense include concepts that represent wholes, parts of which belong together only because of a certain consideration of an understanding, such as a poem or a speech.

Crusius notes that relative concepts representing relative things follow certain rules. Firstly, it is very convenient to distinguish them from absolute concepts, because otherwise errors occur especially in morality, for instance, when good of things is held to be absolute. Crusius insists also that relative things should not be understood as always of lesser importance than absolute things, since this depends on the issue in question: for example, it depends on the relation that creatures have toward God, whether they are in happy or unhappy condition. Then again, he notes, all relative entities presuppose certain absolute entities, that is, substances, forces and properties, without which relations would not be possible. Thus, Crusius concludes, we should distinguish in things their absolute and relative essence.

In case of abstractions, Crusius continues, we can think of not just their essence, but also the manner of abstraction, through which we isolate them in thoughts and regard them as particular concepts. Thus, we can distinguish material from reflected concepts. By material concepts Crusius means concepts that represent a certain object that is something else than a manner of abstraction, for instance, light. On the other hand, reflected concepts represent the manner of abstraction, according to which we regard certain concepts, such as genus and species. Some concepts belong to both classes, depending on the viewpoint, for example, substance can be regarded as a material concept, when we think it as a combination of a subject and a force, or as a reflected concept, when we think it as a genus of humans.

Crusius divides concepts also into determined and undetermined. A determined idea contains in itself such determinations, without which it cannot be thought completely and distinctly, while an undetermined concept lacks some determinations that are required for thinking it distinctly and completely. An undetermined concept, Crusius explains, is thought either in an obscure manner or then the thinker attaches to it some possible determinations that they have perceived in an example. Even if we do not know positive determinations of a concept, he adds, it can still be useful to represent what it is not and to determine it thus negatively.

Crusius explains that a concept is undetermined only, if it lacks such determinations that do not concern our arbitrary manner of consideration: thus, a concept of a human being can be perfect, even if we knew nothing about their clothing. Still, he adds, no other concepts are fully determined, except those representing individuals. With other concepts, Crusius thinks, they are to be regarded as determined, if they contain as many determinations as the purpose requires, so that one ignores other determinations, because they are arbitrary to the purpose.

As long as necessary determinations are lacking in a concept, Crusius states, it is partially unknown to us and thus a mystery. If a concept is not even negatively determined, so that it cannot be distinguished from anything else, it is of no use. Crusius thinks that if we add to a concept that we cannot determine some possible determinations just for the sake of distinctness, while remaining aware that these are only possible, but not necessarily true determinations, this does not harm truth, but is useful and often necessary.

Concepts represent an object, Crusius notes, but this object can be something outside our thought – the represented thing that is thought under certain properties for the sake of distinguishing it from other things – or then something inside thought – the representation of properties, by which the thing outside thought is designated. When we thus compare two concepts they can be objectively different, when one has another object outside thought than the other, like human and cow or love and hate, they can be ideally different, when they have the same object outside thought, but represent it through different properties and for different purposes, like rational creature and creature obliged to virtue, or the two concepts can mean exactly same.

Crusius divides concepts also into concrete or unanalysed concepts, analysed abstract concepts and simple concepts. Concrete or unanalysed concepts consist of a manifold of parts and properties, which are not precisely distinguished from one another: they might be represented through an example of this concept, but not thought with distinct separation. Analysed abstract concepts represent a distinct differentiation of their parts and separate such that essentially belongs to it from others, just like in most definitions. Finally, since the analysis cannot go on infinitely, we find simple concepts that cannot be analysed further. A concrete concept, Crusius suggests, is either not yet analysed or then human understanding cannot analyse it at all.

In relation to their usefulness or application, Crusius notes, concepts divide into characteristic and uncharacteristic. A characteristic concept helps to know and evaluate an example, while an uncharacteristic concept does not do this. Thus, Crusius explains, arteries can be defined as blood vessels that lead blood from heart to organs, but this is not a characteristic concept, because one still requires other signs for recognising arteries in the anatomy of the body.

Concentrating on the abstract concepts, Crusius divides them into a priori and a posteriori abstractions. In case of a priori abstractions, it is possible to know merely from the essence of the thing or from a comparison with the essence of God, why it must or can belong to something: for instance, this is the way we know that a human being is obligated to be virtuous. In case of a posteriori abstractions, we know only a posteriori that these abstractions belong or can belong to a thing: for instance, when we consider a colour or length of something.

Crusius divides a priori abstractions further into hypothetical and absolute a priori abstractions. Hypothetical a priori abstraction is abstracted as a part from a presupposed concrete concept, for instance, when we abstract the concept of a middle point from that of a circle. On the other hand, an absolute a priori abstraction is understood as inseparable from what it is abstracted from, for instance, when we regard humans as obligated to virtuous action.

Crusius notes that abstractions can also be divided into perfect and imperfect abstractions. Perfect abstractions can be thought without a connection to other abstractions from the same individual: thus, for instance, intelligence is a perfect abstraction in comparison with virtue, since one can be thought without the other. On the contrary, while an imperfect abstraction can be distinguished from any other abstraction, when they are thought together, there still are some other abstractions that cannot be separated in thought from the original: Crusius gives as examples the concepts of subject and force.

Crusius suggests that perfect abstractions can be thought without one another and they are ideally separable, although there can be other reasons why they are not really separable. On the other hand, imperfect abstractions can be distinguished and they are discernible, but they still must be thought together. With many imperfect abstractions, the relation is reciprocal, like with the concepts of subject and force. With others, the relation is one-sided, for example, will cannot be thought without understanding, but understanding can be thought without will.

Finally, Crusius divides abstractions into pure and impure. Pure abstractions are abstracted not just from the object, but also from essence naming it: for instance, the concept of understanding is a pure abstraction from the concept of a reasoning being, since it belongs to the essence of a reasoning being to have an understanding. On the other hand, impure abstraction is abstracted from individuals with a certain essence, but not from this essence: for example, mortality is an impure abstraction from the concept of a reasoning being, since a reasoning individual can be mortal, although it is not part of the essence of an reasoning individual that it must be mortal. Crusius explains that we need this distinction, because otherwise we might think that we have defined an essence, when we have just pointed out a property distinguishing individuals with that essence from others (thus, I cannot define willing substance by its having sensations). Furthermore, he adds, arguments holding of essence might not hold of impure abstractions, for example, God wills our happiness, because we are reasoning creatures, but this does not imply the happiness of our animal side.

Crusius, Christian August: Road to certainty and reliability – What understanding can do

Crusius defines understanding in the wide sense of the word as any ability of a substance to have ideas. In finite spirits, he explains, understanding consists of many fundamental capacities, thus, understanding is the sum of such capacities, by which a finite spirit represents something. Crusius notes that we also have a more restricted notion of understanding, which refers only to higher capacities of understanding that has achieved the level of reason.

Reason Crusius explains to mean such a grade of perfection of understanding that is it is capable of consciously knowing truth as truth. In finite spirits this means such a sum of cognitive capacities that enable conscious knowledge of truth. Crusius notes that we can speak of reason in another sense, as a sum of truths that can be known through the power of reason in the first sense, just from the consideration of natural things.

Reason in both senses, Crusius explains, can be regarded concretely, as it is found in a certain individual, or abstractly, when its essence is regarded in itself and the subjective conditions of particular persons are ignored. Thus, we get four different meanings for the word reason. Firstly, we have a concrete capacity of reason found in a particular subject. Secondly, we have the abstract human reason, which means the sum of essential capacities of human understanding in general, together with the effects that these capacities enable in themselves. Thirdly, we have the concrete sum of reasonable truths, known and considered as reasonable truths by a particular subject. Finally, we have the abstract sum of truths that can be known from the consideration of natural things through experience and correct deductions. Crusius notes that part of the truths included in the final sense of the reason might still be unknown to all humans, due to insufficient sensations and deductions.

The opinion of Crusius is that the first fundamental capacities of human understanding cannot be discovered, thus, that we can only distinguish capacities dependent on and derived from these fundamental capacities, as distinctly and in as orderly fashion as possible, and show how these derived capacities follow one another or receive new determinations through their use. Hence, he suggests as his next task to find the least complex cognitive capacities that we can know. These capacities Crusius will then call the main cognitive capacities and he will derive from them more complex capacities.

Crusius takes as the first main cognitive capacity sensing (Empfindung), which he defines as a state where understanding is immediately necessitated to think of a certain object as existing and present, so that the presentation of this thing is not first generated from other concepts through a deduction. Due to this immediacy, he explains, ideas of sensing or sensations are much livelier than others. Distinct sensations, Crusius states, engage understanding fully, and when we are dreaming, our representations are not distinct enough so that liveliest of them are confused with sensations, until we wake up.

Crusius divides sensing into external and internal sensing. In external sensing, he explains, we sense something that we represent as being outside the soul, while in internal sensing, we sense something that we represent as in our soul. Crusius identifies internal sensing also with the capacity of being conscious. Through internal sensing, he points out, we sense that we think, parts, properties and relations of our concepts, and certain activities and conditions of our will. Internal sensing does not then involve anything that happens in our body, which Crusius takes to be a type of external sensation. He also differentiates sensation from perception, which means either any representation at all or then a condition of understanding where representation becomes lively or we start to become conscious of it.

Both external and internal sensing, Crusius tells us, direct themselves in accordance with certain conditions of our body and are connected with certain changes in it, which is one reason why we know our body before others. External sensations correspond to certain organs in our body, and as long as the organs are in good condition, the sensations appear when the present objects cause changes in these organs. Thus, Crusius argues, not just the possibility and actuality, but also the characteristics of external sensations correspond positively to certain conditions in our body.

On the other hand, Crusius insists, characteristics of internal sensations do not follow the body, but their possibility and actuality and the reason for their ease and liveliness are negatively connected to conditions of the body. In other words, when our body is in bad condition, our internal sensations might be hindered. Crusius explains that for this reason babies and old people cannot think well and violent movement of bodily humours can hinder our thinking. Still, he says, because conditions of bodies can be only movements and representations are not movements, conditions of our bodies are not causes of representations.

Since causal relations cannot be sensed, Crusius explains, experience cannot tell generally what is the reason for the constant conjunction of changes in the body and changes in the understanding. He is still adamant that we need not assume an occasionalist explanation for this conjunction. Indeed, Crusius is very much against the idea, since occasionalism would make God the originator of sin and because it is connected with what he takes as a ridiculous hypothesis that animals are mere machines.

Crusius is equally critical of the Leibnizian idea of pre-established harmony. Indeed, he suggests that metaphysics has shown that matter and finite spirits must necessarily truly affect one another, because otherwise the existence of the world would have no purpose. Furthermore, Crusius thinks that mere mechanical structure of the body can only enable, but not cause certain movements in our bodies. He also finds it problematic that pre-established harmony would mean that the soul will fall into eternal sleep, after its body has been destroyed, unless it somehow gains a new body.

After all these considerations, Crusius is certain that there occurs some real interaction between soul and body and that this interaction at least enables sensation. Still, he notes that it is not the case of movements affecting our sense organs changing directly into ideas of soul, since ideas are spiritual activities, not physical movements. Furthermore, Crusius is convinced that sensations – or ideas in general – are not outside our soul nor things between substances and accidents that we just observe.

Crusius begins his own explanation of the interaction by noting that we can observe sensations directing themselves according to certain states of body. He has also argued in his metaphysical writings that souls can move, which explains the possibility of matter and soul interacting. Bodily movements cannot directly generate sensations, Crusius thinks, because then the effect would be more perfect than the cause. Similarly, he suggests, an idea cannot be the closest nor sufficient cause of motion, because an idea contains only activity for representing something in understanding and does not by itself enable activity outside the soul. Crusius concludes that when an idea seems to follow bodily motion, this motion is a condition, the presence of which enables an idea to be generated through a mental activity. When a bodily motion appears to follow an idea, this motion must be generated as an additional state from the effect of a mental activity caused by the idea.

With the particular case of external sensing, Crusius determines further, movement in the organs of external sense causes a movement in the substance of soul through stirring of nerve fluid, because movement can only cause movements. This movement in the soul is then a condition for activation of some mental capacities that are true effective causes of representation. Crusius explains that we cannot further determine this process, since we are unable to sense what is simple and even the smallest organic parts of sense organs are still greater than the fluid matter in nerves and the smallest movements of its parts. In addition, he states, deductions can at most convince us of the existence of this process, but not reveal its further characteristics. In any case, Crusius thinks, laws of external sensation are contingent, and God could have provided us with very different sense organs: more perfect spirits follow more perfect laws of sensation.

In case of internal sensing, Crusius adds, the process is somewhat different. When the soul consciously thinks, it posits its own substance in movement. In other words, Crusius explains, the mental activity generating our consciousness is combined with another that causes a certain movement of the substance of the soul. This movement should be able to push away the matter surrounding our soul, and if this isn’t so, our consciousness can be completely or partially hindered. Determined characteristics of this movement cannot be known, Crusius notes, but its effects can be felt on our foreheads.

Crusius answers the objection that so many motions of the soul could not all co-exist with the assumption that these movements are quick like lightning. He also counters the objection that the soul should have unnaturally precise knowledge of the direction of these movements, in order to not be mistaken of them, by suggesting that it is not absurd to ascribe to soul ideas of all the motions it produces in the body. The soul is not just conscious of them: every soul must have an idea about its body, in order to be alive, but consciousness requires further conditions and need not be connected with all ideas.

Sensing, Crusius thinks, is our first and original cognitive capacity, providing a basis for all our thoughts: we are combined with a world and form a part of it and this combination happens through our own body, so that the activity of our thoughts must be combined with the movement of matter in and through our body. On the contrary, he adds, God requires no such conditions and hence perceives things in a completely different manner. Indeed, Crusius insists, God could create beings that did not need sensations for thinking and the Bible suggests we will have such cognition in the next life.

The second main capacity of understanding Crusius mentions is memory or the capacity to continue having ideas that have already existed. In other words, memory either retains for a while the original vividness of ideas, or after this vividness has diminished, reproduces it wholly or partially under certain conditions. We need memory, Crusius explains, because otherwise we couldn’t use our ideas further: we know only as much as we have in our memory.

From memory and internal sensing, Crusius notes, is generated our capacity to recollect or to recognise that an idea is the same as the one we had earlier. This recollection requires memory, so that we can have earlier ideas, and internal sensing, so that we are conscious that an idea is the same as earlier. Crusius is careful to distinguish this human power of recollection from the general capacity of memory that makes an idea lively also in the absence of its object and thus makes an animal having this idea act like the object would be present. Because internal sensing requires bodily efforts, he adds, recollection also requires bodily efforts.

Crusius explains that we need not assume any special fundamental force behind our capacity of memory: every idea is an activity with a certain grade of strength and duration, and just like in physics movement tends to continue, if nothing hinders it, same holds of ideas as mental activities. Still, Crusius emphasises, since we do not know the ultimate constituents of mental activities, we cannot say whether memory is based on just one or many fundamental forces.

Third main capacity of understanding, Crusius says, is judgement or the capacity to use one’s thoughts for the purpose of evaluating what is true and false. Judging presupposes sensation and memory, he notes, but also a capacity to distinguish one idea from another. Judgement could then be taken also as a capacity for making division of ideas. Through such a division, Crusius explains, a part or condition of an idea is regarded by itself in its isolation and differing from others. In other words, it involves abstracting, that is, isolating a concept in thoughts from another, in which it is contained or to which it is connected, and regarding it by itself. Abstraction does not destroy the whole, Crusius points out, but merely highlights some aspect of it.

Abstraction does not work in isolation, when judging, but only in connection with internal sensing or consciousness. Thus, Crusius explains, if the effects of judgement lack a sufficient grade of consciousness, understanding cannot make use of it: it doubts and does not make decisions. Furthermore, he adds, because irrational animals do not have consciousness, they cannot make judgements, even if they would have as fine ideas as humans. Finally, Crusius notes, because internal sensing can make our body exhausted, it is understandable that a really concentrated judicious meditation meddles with the force of our body.

Crusius divides abstraction into causal abstraction, which differentiates thing generating or enabling from thing generated or enabled, and existential abstraction, which differentiates things, which are together or follow one another without one generating or enabling the other. Furthermore, he divides existential abstraction into logical abstraction, which starts from individuals, but ignores individuality in thoughts, generating a universal concept (e.g. abstracting a concept of human in general from individual humans), external abstraction, which separates something from its external conditions or relations (e.g. abstracting a place and time from a human being), metaphysical abstraction, which distinguishes characteristic from its subject, (e.g. abstracting humanity from a human being), mathematical abstraction, which differentiates manifold into integral parts (e.g. dividing body into two parts) and physical abstraction, which differentiates manifold into non-integral parts (e.g. dividing soul into understanding and will).

The final main capacity of understanding Crusius mentions is ingenuity or the capacity to make discoveries by moving from one idea to a new, but connected idea, but not through abstracting division.This ingenuity, he explains, is not the capacity to perceive or affirm possible connections, which requires mere judgement. Indeed, Crusius adds, it is the hardest capacity of understanding to explain, and there’s less to learn about its fundamental essence. It might well be, he surmises, that in the hidden essence of ideas lies something that awakens a similarity with other ideas and thus unites them. Since such a process does not require consciousness, Crusius explains, animals might have ingenuity.

After the least complex capacities of understanding Crusius moves to the most important derived capacities, one of which – recollection – he has already mentioned. After it, the first derived capacity he mentions is the imagination, which is a capacity of using a lively idea in making other ideas lively. Crusius notes that rational beings imagine consciously, but in irrational animals the imagination has a true effect on determining their actions. He also divides imagination into imagination of memory, which reawakens ideas that have been thought earlier, and imagination of ingenuity, which awakens new ideas.

Next derived capacity Crusius investigates is the capacity to develop imperfect ideas by making them more determined, somewhat like colouring a pencilled sketch. He notes that it involves more than just making ideas more distinct, which requires nothing else but judgement. Crusius divides this capacity into two types: first of them involves positing from a concept of cause its nearest effects, for instance, in discovering causal deductions, while the second involves positing from an undetermined concept its possible determinations, for instance, in discovering disjunctive existential deductions.

The final derived capacity mentioned by Crusius is the capacity of making deductions. He lists this capacity only for the sake of completionism, but says it will be investigated in more detail later. He does remark that this capacity requires especially sharpness of internal sensing and attention. Since these are so difficult, Crusius remarks, people often make only easy deductions or even no deductions at all.

Having gone through this list of cognitive capacities, Crusius notes that external sensing, memory and ingenuity and imagination are called lower capacities of understanding, while higher capacities include internal sensing, judgement, capacity of developing ideas and capacity of making deductions. The reason for the division is, he says, that we share the lower capacities with irrational animals, while higher capacities belong only to rational entities. Whether lower or higher, all these various capacities, Crusius thinks, can have only three effects: concepts, propositions and deductions. Furthermore, all capacities of understanding can be cultivated, Crusius explains. This cultivation can be material, where we find more truths to know and use them more time, or it can be formal cultivation, where we ponder truths with more thoroughness and sharpness.

The capacities of understanding, Crusius continues, are by their nature earlier than capacities of will. Still, he admits, experience shows us that drives of will affect these capacities: we can direct our sense organs to objects we desire, we can choose to retain a current representation in our judgement etc. This means, firstly, that the state of understanding can be evaluated morally. Secondly, it means, Crusius notes, that effects of understanding can be divided into pure or unmixed, which are not affected by the activity of will, and mixed, which are so affected. Pure effects include, he thinks, sensing, retaining ideas in memory, distinguishing, at least insofar as it consists only in being aware of certain distinctions present in concepts, propositions or deductions, and free play of imagination, where we imagine now this, then that concept. Mixed effects, on other hand, include propositions and deductions, since they both require keeping attention willfully on relations of ideas, and also purposeful observing and reflecting.

Crusius notes that when we become accustomed to judging – that is, doing abstraction – our memory and ingenuity appear to weaken. This occurs, because we are habituated to start analysing new ideas, which makes it more difficult to retain this idea in our minds for a while, for the sake of memorising it or finding ingenious connections involving it. This is why adults seem not to have as good a memory as youngsters, Crusius explains, although the truth is that adults just use memory differently, memorising more easily ideas known through judgement. When reaching old age, he continues, the body starts to hinder our internal sensing, through the stiffening of nerve fluids, which makes it harder to recollect what lies in our memory to gain what truly lies in our memory. Just like memory, Crusius thinks, a free play of ingenuity appears to weaken with years, if one is accustomed to stifle its wilder suggestions, but practical and political ingenuity can still increase.

Crusius, Christian August: Road to certainty and reliability – Truth and logic

Crusius finally begins the proper study of logic, after the introductory chapters, from the theoretical part, studying powers and activities of understanding (Verstand) that make the knowledge of truth possible. By truth he refers to the correspondence of thoughts with their objects, or to put it more precisely, such a relation between an understanding that thinks and the object it thinks, so that if the former thinks that the something about the object is, is not, is possible or impossible, this something respectively is, is not, is possible or is impossible also independent of this thought. Crusius emphasises that in this definition one should not speak of the object being something independently of the understanding, since the definition should apply also in cases where the object handled is understanding itself.

Crusius notes that truth must be distinguished from both error and ignorance, where error means a lack of correspondence between thought and its object, while ignorance means a lack of any thought about a topic. In other words, we cannot speak of truth if there is no thought that has ideally exactly that which object has really. Crusius underlines that we are speaking here only of truth in its logical meaning, and in addition, there is also a notion of truth in moral or ethical sense, that is, truthfulness, which means correspondence of a state of mind with the intended meaning of external signs that are used for communicating this state of mind. Finally, Crusius also points out that sometimes we speak simply of truth, when we actually mean some true proposition.

Crusius notes that when an object is compared to an understanding, this understanding can be either a possible understanding or an actual understanding that has some knowledge of the object. In the former case, he clarifies, we are speaking of objective or metaphysical truth, which means thus truth or possibility of an object itself, insofar as it is regarded as something that could be known by any understanding, while the latter is then subjective or logical truth, which means truth in an actually existing understanding or such a relation between a representation and its object, where the representation and the object correspond and thus some truth is known. Furthermore, Crusius notes, all objective truth is subjective in relation to divine understanding.

In human understanding, Crusius continues, all subjective truth is generated by the impossibility to think opposite of what one is conscious of, where the impossibility can happen in all cases or only in the current conditions. He notes that our first thoughts are always sensations, while other thoughts are then abstracted from sensations, so that we become thus conscious of relations between our thoughts or propositions and can attend to them. Furthermore, Crusius says, when we attend to what we can and cannot think, we generate a very special kind of propositions or rules indicating awareness of deductive relations: if certain propositions are connected in certain manner through the ideas they contain, we are bound to take one as true, if we take the other as true. With such rules, we receive a capacity to make deductions with such rules. Now, Crusius argues, since we know the truth of every proposition from the falsity of its opposite, all knowledge of truth in human understanding happens through deduction, although we are usually not aware of these deductions, because they happen so easily.

On the basis of the previous considerations, Crusius states that subjective knowledge of truth in human understanding is dependent on the capacities of sensation, abstraction and deduction. According to him, these capacities are physical, hence, we can abstract physical laws from their use. In a similar vein, since these capacities are under the control of our free will, the laws of free will can also be abstracted from their use. Thus, Crusius concludes, the human understanding can find truths concerning the whole created world (both the physical bodies and the free will), if it just follows its own nature.

Conclusion that Crusius thinks he has proven is that human understanding works just fine by its own nature, even without any further education. Then again, he at once admits, errors are in this case possible, because our representations of the rules of deduction are obscure. Logic is thus required to make understanding more capable of knowing truth. In its abstract sense, Crusius explains, logic is a science that represents distinctly and exactly the effects and laws of understanding and thus shows its correct use. Logic has also, he adds, a concrete sense, according to which it is a capacity of a subject to know fundamentally the effects and the laws of understanding and its correct use.

Crusius considers the capacity of our understanding to work and thus to know truth without logical education and calls it natural logic, which means thus an inherent feeling of true and false that generates a capacity to evaluate grounds for and against something. A person with good understanding can thus recognise through this natural feeling, if some suggested laws and rules of understanding are untrue, which Crusius takes as a justification that incorrectness of suggested logical laws can be shown also a posteriori from experience, just like in arithmetics. Yet, he adds, there are more differences of opinion in logic than in arithmetics, since reflection on kinds of abstraction and on grounds of truth is more difficult than thinking about more concrete topics. This difficulty makes humans ignore the investigation of their understanding and thus rely too much on their natural logical capacity, which has a tendency to error. The wilful ignorance is furthered, according to Crusius, because treatises of logic seem to be so far removed from the use of understanding in practical life.

Logic teaches the kinds of abstraction and methods of knowledge, thus, Crusius thinks, it is the only means to make cognition sharp. He even calls logic the soul of philosophy and scholarship, because it makes them correct and distinct. Because of logic, he underlines, knowledge is fruitful, and logic gives understanding the ability to know truth and evaluate judgements, hence, it strengthens our capacity to study. In effect, Crusius concludes, logic is the subjective foundational science, just like metaphysics is the objective foundational science.

Crusius identifies two weaknesses in natural logic, which the proper logic can fix. Firstly, he says, when we are dealing with complex topics, natural logic is not enough for distinguishing true from false and for arranging our studies in a suitable order. In other words, he explains further, when we use natural logic for dealing with a complex topic, we might find material for justifications or grounds, but we still cannot give them the proper form, that is, place them in such relations that would make them justifications of something. The result would then be, Crusius insists, that we may end up suggesting many grounds or justifications that in their current state do not justify anything. He thinks that this is especially true with probable proofs, where recognising true and false is more difficult. The conclusion of Crusius about the first weakness is that the natural logic is applicable only, on the one hand, in common tasks of human life, where object is characterised with sensuous properties, and on the other hand, in distinguishing moral good and bad, because our understanding of good and bad is supported by conscience and a feeling of guilt. The second weakness Crusius finds in natural logic is that the lack of proper logic often leads to errors and even outright scepticism.

Crusius goes on to divide the parts of logic. First of these parts is, according to him, the theoretical part that handles grounds that make the knowledge possible in the human understanding, and in addition, must also consider the powers of human understanding and its effects or concepts, propositions and deductions. The study of the powers of human understanding Crusius calls noology, necessary truths of which belong also to metaphysics. Crusius also emphasises that noology needs to investigate only what lies in the soul, together with the general features of the dependence of certain effects of understanding from the body. Then again, external conditions of sensations in bodies belong to the study of nature.

The other or practical part of logic, Crusius says, explains how the powers and effects of understanding should be used for the purpose of truth. It also deals with the illnesses of these powers, the experience as a modification of the power of sensation, use of concepts in divisions and definitions, use of propositions in judgements, and use of deductions in proving, recognition of seeming proofs and decision over colliding proofs. All the effects in unison, Crusius adds, are handled by the study of method and also in some special topics, such as interpretations, special kinds of probability and disputation.

Crusius, Christian August: Road to certainty and reliability – Logical jargon

Before entering the logic proper, Crusius introduces the reader to the most important terms used, with a full acknowledgement that they will be properly explained only within the logic itself. In effect, Crusius is presenting a preliminary division of the kinds of thoughts present in logic, and indeed, in any science, where by thoughts he means activities of understanding for representing something, no matter whether only in understanding or also e.g. in words. This division, he says, can be done either according to the internal distinction of their essence or according to the purpose for which they are introduced.

Starting with the internal distinction of the thoughts, Crusius notes that they either define a certain condition and activity of will or represent certain effects of understanding. He is quick with the first type, mentioning only that it includes at least explanations of our intentions. Thoughts representing effects of understanding, on the other hand, he divides into concepts, propositions and proofs. Of these, Crusius says, concepts include definitions that are abstract concepts that can distinguish something from everything else. He divides definitions into nominal definitions, which define a word for the sake of determining its meaning, and real definitions, which define a thing that is first thought in an unanalysed concept, which we want to change in such a manner that we can distinguish its parts with conscious abstraction and thud distinguish the thing from all others. Such real definitions, Crusius notes, are either first concepts, proof of which presupposes no other definition of thing and can thus be primary in regard to our knowledge, or deduced definitions.

Moving on to propositions, Crusius divides them according to their ground into arbitrary and real propositions. Arbitrary propositions, he explains, are not meant to indicate a truth independent of our will, but to show what one assumes to be or wants to be observed as true, like when one states that a circle is to have 360 degrees. A real proposition, on the hand, ascribes to things something that truly belongs to them and should not depend on our arbitrary choice, such as when we state that every circle has a middle point.

As one kind of real proposition Crusius indicates postulates, which must be supposed to be true, although they cannot be proven with regard to all conditions. He divides postulates into postulates according to truth and postulates according to humans. The first type of postulate, Crusius explains, contains in itself something false or uncertain that is still so insignificant that it can be disregarded or that plays no role in the consequences of the postulate, such as when we e.g. determine the meridian of a city only approximately. Postulate according to humans, on the other hand, does not contain in itself anything false, but is of such kind that it cannot really be proven otherwise, but by everyone perceiving and judging it by themselves, for instance, when certain experiential propositions are assumed to be universal. Crusius states that unlike divine knowledge, all human knowledge is ultimately based on postulates, which implies that there are certain questions the humans cannot be certain about. He emphasises that we shouldn’t postulate willy-nilly just anything, thus, that the right to postulate something must be proven carefully. He also notes that something can be postulated, although it might as well be provable.

Compared to postulates, Crusius divides propositions provable according to all conditions to propositions requiring their own particular proofs and to propositions, the truth of which is once and for all shown in logic. He includes in the latter type, for instance, experiences and immediate propositions or axioms. By experience Crusius means a proposition, in which the combination of subject and predicate or antecedent and consequence is perceived immediately through the sensation. He provides many different ways to divide experiences. Firstly, an experience can be an internal experience, which is perceived through internal sensation, or an external experience, which is perceived through external sensation. Then again, an experience can be a regular experience, where not just the combination of subject and predicate is sensed, but also the subject and the predicate themselves are something sensuous, or a reflective experience, where the combination of subject and predicate is sensed, but the subject and the predicate are abstract. Finally, an experience is either a pure experience or a mixed experience, where a proposition is connected with an experience through a deduction that is easy and requires nothing else, but assuming experience.

By an axiom or an immediate proposition Crusius means a proposition, in which is immediately perceived such a relation of subject and predicate that if we want to deny the latter, the subject cannot be thought anymore. He explains that an axiom differs from an internal experience, because in axiom we perceive through sensation only the connection of subject and predicate, since denying the connection would go against truth, but we still can think the concept of subject in itself without thinking the predicate. Thus, something might be an axiom, even if it is deduced through mere axioms, and furthermore, individual persons might require proofs of axioms, although by nature this axiom might not necessarily require any further proof.

Crusius divides axioms into three classes. Firstly, an axiom might be an axiom of identity, where denial of predicate would cause a contradiction. Secondly, it might be an axiom of causality, where a sufficient cause is connected to its nearest effect, without which the cause cannot be thought of. Finally, it might be an axiom of inseparable related concepts, where one simply perceives an impossibility to think the subject with the denial of predicate, although predicate is not the effect of the subject and denial of predicate does not cancel the content of subject and thus produces no contradiction.

Crusius also mentions hypothetical or merely seeming axioms. Such hypothetical axioms are generated by just arbitrarily concocting a definition or by joining such concepts, no necessity to combine which is immediately sensed. Such hypothetical axioms clearly cannot be assumed to be real axioms or even true propositions without proof. Thus, Crusius notes, if axioms are extended to include all propositions understandable from a definition, we must divide them into absolute or natural axioms and hypothetical axioms, because if this distinction is not made, anyone could prove anything by choosing suitable axioms.

Crusius notes that propositions requiring their own particular proofs could be divided into theorems, which are proven from many propositions and concepts together, and consequences or corollaries, which are proven from a single proposition assumed to be true. Then again, he continues, often to the definition of theorems is added the requirement that they must be very notable or not easily understandable and thus in need of a detailed proof, and then the propositions that would otherwise be theorems, but that are not significant enough are classed together with corollaries. Crusius suggests calling theorems in the first sense theorems by essence, while theorems in the second sense would be theorems by use. Furthermore, he mentions problems that are propositions explaining how a certain goal thought earlier in an undetermined idea should be determined. Such a problem, Crusius explains, is in its essence a theorem, but usually problems are distinguished from theorems.

Crusius explains that theorems and corollaries are not characterised by demonstrative method, because some sciences also use probable proofs, although mathematics by its nature uses always demonstrative methods. Thus, theorems of philosophy must be divided into demonstrative and probable theorems. One type of a probable theorem, according to Crusius is hypothesis, by which he means a proposition that is at first posited only as possible and then justified as probable by showing that it corresponds to actual conditions.

Crusius points out still further kinds of propositions. These include rules, which show a certain way to act, questions, which state something without affirming or denying it and posit a goal to decide whether it should be affirmed or denied, divisions, which aim to represent all possible determinations that an undetermined concept can have according to some aspect, and lemmas, which are borrowed from another science or from another part of same science to the current topic as grounds for proving certain things.

After concepts and propositions, Crusius turns to proofs, which he defines as distinct representations of a connection of a proposition with one or several other propositions that are assumed to be true, so that from this connection one knows that with the position of the truth of the other proposition also the first must be admitted as true. He notes that a proof concerns either the truth of a judgement of understanding or the reasonableness of one’s method, and this latter type he calls justification.

Furthermore, Crusius divides proofs into a priori proofs, where truth of a conclusion is derived from a ground that makes it true in such a manner that from this ground one understands not just that, but also why the conclusion is true, a posteriori proof, where one derives the truth of conclusion from a ground that only shows that the conclusion is true, but not why it is so, and mixed proofs, which share properties of both a priori and a posteriori proofs. He also divides a priori proofs into hypothetical proofs, where conclusion is contained in its justifying ground as a part, so that when the ground is thought distinctly, the conclusion is found and also assumed with the ground, and absolute proofs, where conclusion is not contained in its justifying ground, but only understood as a consequence inseparably connected with the ground. On the other hand, Crusius notes that a posteriori proofs prove either also the necessity or only the truth of the conclusion.

Crusius suggests further ways to divide proofs. Firstly, he says, proofs are either proofs according to truth, where the grounds of the proof are taken as true, or proofs according to a human, which show only that someone must admit something as true, because they assume certain propositions as true. Furthermore, Crusius notes that the method of proof is either demonstration or probability. Of the two methods, demonstration shows that the opposite of the conclusion cannot be thought at all, showing either that the opposite contradicts itself or that it cannot be thought due to the essence of our understanding. On the other hand, the method of probability shows that although the opposite can be thought, it cannot be assumed here as true. Crusius notes that probability is either common or infinite, so that the propositions shown by method of probability are either fully certain or reliable. Finally, he points out that usually proofs follow the propositions to be proved, and if they precede these propositions, they are called deductions.

At the very end of the chapter Crusius finally mentions the other way to divide thoughts, that is, according to their purpose. In this regard, he notes, thoughts are presented either because of objective or subjective causes. Presenting thoughts because of objective causes, Crusius explains, means that the nature of the topic in itself demands this, since the topic couldn’t otherwise be known distinctly and determinately enough, even by a trained understanding, or it could not be sufficiently proven or significant aspects of it would be ignored. According to him, all definitions of thoughts fall under this class.

Presenting thoughts because of subjective causes, Crusius continues, means that they are presented only because of subjective conditions, although the study of the topic in an abstract sense does not demand them, assuming that the reader of the study has been acquainted with science and its practical application. Thoughts presented in such a manner, he says, are called remarks or scholia. Scholia can then be divided into explanatory remarks, which improve the knowledge of the topic, for instance, by making it easier to understand, giving it a more secure foundation or giving insight how to use it, and into remarks that serve merely the enjoyment of the reader. If a scholium is of significant size, Crusius notes, it is called a digression.