Crusius, Christian August: Road to certainty and reliability – Rules of deduction

Crusius divides deductions or arguments into demonstrative deductions, where the premisses make us unable to think that the conclusion would not hold, and probable deductions, where the premisses make it more difficult to deny than to assume the conclusion. He also states that probable deductions differ from demonstrative only through their matter, while the forms of deductions are always demonstrative and thus always connected with the fundamental principles of deduction.

Crusius thinks it is not necessary to name all possible types of deduction, since this has nothing to do with understanding why the deductions work. Instead, he will concentrate on the most important rules that govern deduction and only later mention some of the more prominent types of deductions that have been considered important enough for being given a name. Now, rules of deduction, Crusius continues, concern only conceptual connection of the very highest level of abstraction. While he admits three fundamental principles of knowledge, all of which could be used for establishing axioms – the principle of contradiction (nothing can both be and not be at the same time and in the same sense), the principle of inseparability (things that cannot be thought without one another cannot exist without one another) and the principle of incompatibility (things that cannot be thought together cannot exist together) – he thinks that only two of them can be used to establish rules of deduction: the principle of contradiction and a specific instance of the principle of inseparability, namely, the principle that everything has to have a sufficient cause.

Crusius begins from rules of deduction that he thinks can be derived merely from the principle of contradiction. I shall not describe in detail all these rules, but merely list them and point out some prominent features Crusius emphasises, if needs be:

The immediate rules of contradiction

1) No proposition can be at the same time true and false.

2) Every proposition is either true or false. Crusius points out that 1) and 2) together imply that of two contradictory propositions, one is true, while the other is then false.

The rules of identity

3) Change in any arbitrary manner of thinking (e.g. change from active to passive voice) changes nothing in the truth or falsity of a proposition.

4) A relation of two concepts based on their essence is not changed when the concepts are thought with different external abstractions.

5) What is true of something, when we think it through certain properties, is still true, even if we think it through other properties (e.g. same things are true of Venus, no matter whether we think it as the morning or the evening star).

Rules of diversity

6) If two objects cannot be distinguished in our thoughts in any manner, it is impossible to affirm the same predicate of the one and deny it of the other.

7) If we have two different things and they can differ only in one aspect, they will differ in this aspect (otherwise they wouldn’t be different).

The rules of diversity, Crusius insists, lead us to what he calls the principle of sufficient foundation of knowledge: 8) it is not reasonable to assume something as true, if we do not have any sufficient reason for it. It is not at first clear why 8) should follow from 6) and 7), but his argument is that truth and falsity – admittedly very different things – must be distinguished through some criterion: either by our understanding immediately seeing what is true or by showing that what is to be taken as truth is connected to something we already know to be true.

Deduction from coordinated propositions: 9) if a proposition describes the only possible manner, in which other true propositions can be true at the same time, the first proposition is itself true.

Rules of deduction based on the relation of whole and parts

10) If a whole is posited, all its parts are also posited.

11) If an essential part of something is lacking, it is not this thing. Crusius notes that this rule does not hold of mere natural parts, which could be replaced by something sufficiently similar without changing the essence of something.

12) If all parts are posited and combined in a manner appropriate to the whole, the whole is also posited, because in this manner the parts are equal to the whole.

13) What is in part is also in the whole. Crusius notes that we still might not be able to predicate the same thing of the part and of the whole (e.g. if there’s brown colour on a spot on a ball, there’s brown colour on the ball, but even if the spot is brown, the ball might not be brown, if it has spots of other colours also).

14) What belongs to all parts belongs in the same way to the whole, as long as we are not dealing with an abstraction of parts as parts. Thus, Crusius exemplifies, if all individual changes of a temporal series are contingent, the whole series is contingent, but although a tile on the floor is rectangular, the floor itself might not be. Furthermore, he emphasises, the rule can be applied only if the same thing belongs to all parts in the same manner and for the same reason: if all molecules of a salt cube can be dissolved in water, then all can be, but if all ingredients of medicine are poisonous, the medicine might not be, since the poisonous effects of different ingredients might be different and cancel one another.

15) What can be denied of all parts and is not an abstraction of whole as whole can be also denied of the whole.

Rules for logically subordinated concepts

16) What can be universally affirmed or denied of a subject can be similarly said of concepts logically subordinated by the subject (that is, individuals and species belonging to the subject).

17) If an idea B is in logical subordination to another idea A and a third idea C is logically subordinated or opposed to the idea B, the idea C is logically subordinated or opposed to the idea A, at least particularly, but it is subordinated only if A and C are not two different species of B (otherwise, they would not share any individuals), and a sign for this is that the proposition where C is predicated of B is universal or if one can universally affirm of idea B the idea A.

18) If an idea is posited, so is also its proprium, same holds also of naturalia, but only in a limited manner.

19) If a relation toward an idea is posited, the same relation toward its proprium or genus must also be admitted, insofar as one regards the proprium or genus according to same manner of abstraction as in the original idea.

20) If all species are denied, then genus is denied, and if all individuals are denied, then species is denied.

21) What holds of all logical parts must hold of the whole, that is, what holds of all individuals must hold of species, and what holds of all species must hold of genus.

22) What belongs to species as actual belongs to genus as possible (e.g. if a human being can be learned, then an animal can be learned).

23) What belongs as possible to genus does not belong as possible to each species (e.g. an animal can be a monkey, but, for instance, a lion cannot be a monkey), but if we want to expressly take something that is possible for genus to be impossible for a determined species, we must prove it to be impossible for this species.

Rules concerning relations

24) If a relatum is posited, its correlate must be assumed also. Crusius notes that such deductions have only a hypothetical power, as long as one has not at first proven that something is a relatum, for instance, if the world is an effect, it must have a cause, but we then still have to show that it is an effect.

25) If an idea has a relation towards another, the other has the opposite relation to the first.

26) If an idea C presupposes another idea B and this a third idea A, C also presupposes A.

27) If in continuing relation the first member relates to second as the second to third, the first member relates in the same way to the third, as long as the distance between the related terms is not important (e.g. descendant of your descendant is also your descendant, but child of your child is not your child, because the concept of a child inherently involves the notion that it is an immediate descendant).

Rules concerning magnitudes

28) The more to something belongs such features, which describe a certain essence, the more one must ascribe to it that essence

29) In the same measure as the number of similar parts or units in an integral whole increases or decreases, the whole also increases or diminishes

30) If two magnitudes increase or decrease in same proportion, they retain the earlier geometric relation, and if they are equal, the relation of equality remains also, if to both sides is added or from the is taken away the same

All the previous rules, Crusius insists, depend merely on the principle of contradiction. Principle 39), he thinks, does not, that is, the principle of sufficient cause: all that is generated has its sufficient efficient cause. Crusius thinks this implies that it is generated through an active force of some substance, which has been active and in which nothing is lacking that is required for generating the generated thing. Although the principle of sufficient cause cannot be deduced from the principle of contradiction, according to Crusius, it can be proven from the principle of inseparability, because our internal sensation shows that it is not possible for us to think a generated thing without asking for a cause, from which it is derived.

The principle of contradiction, due to its generality, Crusius thinks, applies to everything, thus, it can also be applied to the relation of causes and effects. Hence, he concludes, there must be rules of deduction derived from both the proposition of contradiction and the proposition of sufficient cause. I will continue listing them:

Rules for the inevitability of effects

32) If it is assumed that a sufficient cause is active and unhindered, the effect is generated inevitably. Crusius adds that when an active cause acts, in addition to active force and what is directly dependent on it there are also other things that have an influence in the effect only through their existence and that thus can be called existential grounds. These existential grounds use no special rules, since, on the one hand, they are mere circumstances of the efficient cause, making it sufficient, and if they are taken as independent existential grounds, they are covered by rule 8.

33) What is not a free fundamental activity of freedom is generated from its efficient causes inevitably in such a manner that the efficient causes could have generated it with the assumed circumstances only in this manner and not otherwise. Crusius emphasises that if we are dealing with free fundamental activities, we can only deduce that the activity has a sufficient cause, but not that this cause determines the effect inevitably.

Rules for modalities involving causation

34) What can be causally and distinctly conceived as possible, when some causes are assumed to exist, is actually possible.

35) What can be understood as inevitable, when some causes are assumed to exist, holds inevitably, insofar as new causes do not hinder it.

Rules for similarities and dissimilarities of effects

36) Similar sufficient causes generate similar effects.

37) Dissimilar and still sufficient causes must be dissimilar in their effects, insofar as they do not act according to different laws, according to which they would differ more than according to mere direction and magnitude. Crusius explains that acting according to different laws means that the causes differ in the constitution of their internal activity, so that different causes could be directed to similar effects due to different internal essences. He adds that such essentially different laws are even necessary, because otherwise the infinite cause or God could not achieve with their omnipotence what creatures can do with their finite powers.

38) Adequate effects of opposed causes are equally opposed.

Rules for proportionality of causes and effects

39) Each effect is proportional to its sufficient cause, and as the sufficient cause increases or decreases in its causality, so does the effect.

40) If a cause vanishes completely, what is connected to it as an effect vanishes also. Crusius emphasises we are speaking of a case where the cause is not replaced by an identical cause.

41) There cannot be more in the effect than in the cause

Rule 42) states that nothing false can follow from a true proposition. Crusius justifies the inclusion of this rule as one following from both the principle of contradiction and the principle of sufficient cause by saying that a falsity can be derived from a true proposition neither through the proposition of contradiction, as its ancillary effect, nor as an adequate effect of the true proposition. The former is immediately absurd, he says, while the latter would mean that truth or a correspondence of thoughts with the objects should make falsity or their non-correspondence possible, which means that an effect would contain more than its cause. Crusius adds that something true can follow from a false proposition, because a proposition is false when any circumstance in it is false, but other circumstances in it can be true and from these true propositions can be derived.

Rules about causing wholes and parts

43) A sufficient cause that generates a whole generates also a part

44) What acts toward a part acts also toward the whole

Rules about effects of effects

45) If the cause generates something, it is also the cause of what is inevitably connected with the first effect. Crusius adds that the mediate effects still do not always belong to the intentions of the distant causes, because intentions depend on insight and wisdom of the acting cause.

46) If the cause generates something, it is at least a cause of possibility of effects depending on the effect. Crusius notes again that the original causality is still always expressly directed toward causing this possibility, because this possibility might just be an inseparable ancillary circumstance of its causality.

Crusius, Christian August: Road to certainty and reliability – The ultimate foundations of knowledge

After propositions Crusius proceeds in a rather conventional manner to deductions or arguments, where the truth of a conclusion is based on the assumed truth of premisses. He underlines that the conclusion of a deduction is not held to be true because of its content, but because of the specific relation it has to these premisses. Thus, Crusius suggests distinguishing this relation as the form of the deduction from its individual propositions (that is, premisses and the conclusion), which then work as the matter of this deduction, while the form provides the rule that the deduction follows. He also emphasises that although we can express deductions in words and usually communicate them to others through this medium, this use of words changes nothing essential in the proceedings and can therefore safely be ignored.

Before going on to classify the rules followed by different deductions, Crusius suggests investigating the first principles on which all these deductions are based on. He begins from the capacity of human understanding to think, combine and separate concepts, but notes that it has its natural limits: there are certain seeming concepts or their combinations or separations that we cannot think of. Since human souls strive naturally toward perfection, Crusius argues, and in case of understanding this implies a natural drive to truth, we should follow this natural disposition and accept as true (and respectively as false) what we cannot think as anything but true (and respectively as anything but false).

All our thoughts originally derive from external sensation, Crusius begins his study of these natural dispositions. External sensation provides us with concepts of objects, and as long as a distinct sensation continues, he underlines, we are forced to think of these objects as existing and present. Such an external sensation also makes our internal sensation active, and through this internal sensation, Crusius explains, we become conscious of characteristics, parts and circumstances of external sensations. Then again, he adds, such external sensations induce in us also other concepts that are not externally sensuous and that lead us to universal propositions that we should think as true.

It is no surprise that the first of these universal propositions Crusius mentions is the so-called principle of (non-)contradiction. He at once adds that this proposition as such is just identical, saying nothing more than that what is, is, and what is not, is not. Thus, Crusius argues, the principle of contradiction requires the establishment of further concepts, to which it can be applied, in order to make any use of it. The established concepts might not refer to anything real, he states, and then the applied principle of contradiction has a merely hypothetical reality. Hence, Crusius insists, we must know from elsewhere that the concept in question refers to something real.

Crusius suggests as a further rule for the establishment of concepts following the essence of our understanding: combining concepts that the sensations represent as combined or that we are necessitated to think as combined, because disappearance of one makes the other one vanish also, and similarly separating concepts that sensations represent as separated. Concepts established in this manner generate propositions that are not identical and form the positive core in our knowledge, Crusius thinks: every force is in some subject, all that is generated is generated by a sufficient cause, every substance exists somewhere and at some point in time etc.

Crusius insists that these propositions are not merely derived from the principle of contradiction, but adds that this does not mean that these propositions are not certainties: it is merely a question of how they are generated in our understanding and how we thus come to know them. Furthermore, it does not mean that we could not deny the opposites of these propositions through the principle of contradiction, but only that this principle is not sufficient for establishing the concepts involved. Finally, it does not mean that the principle of contradiction itself would be uncertain, but only that it is empty and thus not the only principle of human certainty. For example, Crusius explains, the principle of contradiction easily explains that every effect presupposes a cause, but only because by an effect is meant something generated by a cause and thus the concept of effect involves the concept of cause. Furthermore, he adds, the concept of effect still refers only to a hypothetical reality, since we do not know what things are effects: even seeing something being generated doesn’t tell us that it is an effect, since causeless generation is just absurd, but not contradictory.

The argument of the emptiness of the principle of contradiction is probably targeted against the Wolffian school, who were famous of basing intricate ontological truths on it (of course, it might well be, and I’d argue that it is so, that especially Wolff himself referred by the principle of contradiction to a stronger principle that is not identical, but this is beside the point here). Crusius still finds some reasons why anyone would hold the principle of contradiction to be the only principle of our knowledge. Firstly, he says, demonstration from the principle of contradiction seems comparatively easy, since otherwise we would have to use internal sensation and attention to account for the physical possibility or impossibility of our thoughts. Furthermore, Crusius thinks, the principle is the only fundamental proposition required for pure mathematics, and someone might want to extend the indubitable certainty of that discipline to the whole of knowledge. Finally, he concludes, we are more used to deducing from already presupposed concepts than searching for the ground of reality in the establishment of concepts.

The true fundamentals of all our deductions, for Crusius, are then three propositions: the principle of contradiction (nothing can both be and not be at the same time and in the same sense), the principle of inseparability (things that cannot be thought without one another cannot exist without one another) and the principle of incompatibility (things that cannot be thought together cannot exist together). He adds at once the cautionary remark that while the first principle is indubitable – no understanding could think of any contradictions – the two others might mislead us, since due to our finite nature, we are sometimes incapable of thinking things that an infinite understanding can think. Especially if the two principles are used to contradict the very principle of contradiction, Crusius underlines, we should reject this use as unfounded. Furthermore, he adds, revelation by a higher form of understanding can show us truths we cannot comprehend: thus, we should accept such a revelation, especially if we can have at least a symbolic concept of what is described by the revelation. Crusius gives as an example the case of limits: we can never think anything existent without the notion of limit, but this does not mean that something unlimited couldn’t exist, just that we are too limited to think about it. Similarly, although we cannot think of two pieces of matter existing in the same place, this does not mean that God could not be omnipresent in every part of the universe.

Crusius proceeds to explain how the other true propositions can be generated from the three principles. Firstly, he begins, we can apply these highest principles to propositions discussing certain characteristics of objects that we cannot think without these characteristics: the connection between the object and the characteristic forms then an axiom. Then again, Crusius continues, we can also apply the three principles to such relations between propositions, where one proposition must be true if the other propositions are assumed to be true: this relation is inscribed in some rule of deduction or argumentation. Just like axioms are immediately connected to the three principles, the rules of deduction connect all the other true propositions to them, he concludes.

The justification of axioms and rules of deduction, Crusius insists, is an example of what he calls a subsumptive deduction, where the conclusion concerns a concept or an individual or a set of individuals contained in a concept that is the topic of the premisses. Yet, he clarifies, this does not mean that all deductions should be subsumptive, unlike the Aristotelian tradition had assumed. Indeed, he separates primary or formal deductions, which justify axioms and rules of deduction and are always subsumptive, from secondary or material deductions, which concern more specific topics and which might not be subsumptive. Thus, Crusius exemplifies, while we can subsumptively deduce from the principles the rule that if a cause brings about a whole, it brings about its essential parts, when the rule itself is used, the resulting deduction is not subsumptive. True, he admits, all deductions can be transformed into a subsumptive form, but this is just jugglery that hides the essential manifoldness of types of deduction.

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

Looking at the various classifications of propositions or judgements in the Classic German philosophers, it has become quite clear that while Wolffians were still rather distant from the classic Kantian division of judgements, Hoffmann’s classification resembled it more, while still having important differences. The classification of Crusius shares distinct similarities with Hoffman’s, but is still a bit different and perhaps a step closer to Kant’s.

Before introducing his classification, Crusius naturally explains what he means by a proposition: a representation of a relation between at least two concepts. This means, he argues, that all propositions have three essential parts: the concept to which the other concept is related (the subject), the concept related to the subject (the predicate) and the concept of their relation (the copula). Crusius makes the further remark that in the simplest form of a proposition “A is B”, the “is” is usually just partially an indication of copula (the relation between subject and predicate), while the implicit reference to the existence of B is actually part of the predicate. Still, he adds, we should not completely assimilate the notion of copula to that of predicate, since the idea of relation of concepts is so essential to that of proposition. Furthermore, he notes, in some propositions the copula might contain more than just this word “is”. Of the two other components of the proposition Crusius notes that the subject is by nature the concrete concept, from which the predicate is abstracted, but in actual propositions their roles might be reversed or at least reversible.

Crusius suggests eight divisions of propositions – quite a lot more than Kant will do. The first point of division, Crusius begins, is suggested by the fact that a proposition relates at least two concepts, which provide then the matter of the proposition. He implies that propositions could thus be divided according to disciplines they relate to, but adds that this does not concern logic. Still, he says, some divisions are necessary, firstly, between propositions expressing judgements of our understanding (e.g. rock is hard) and those expressing certain volition (e.g. I want you to come here). Crusius divided the first class or that of enunciative propositions in a manner reminiscent of Hoffmann to nominal propositions connecting concept to a name (e.g. first emperor was Augustus), ideal propositions representing conceptual connections (e.g. physical extension presupposes actual parts) and real propositions connecting concepts to existence or existent things to concepts (the example of the first case would be “there are immaterial substances” and of the second “my soul can reason”). Some of the ideal and real propositions concern concrete individuals – hence, they are called individual propositions, which are either simple individual propositions (e.g. Earth is round) or combined individual propositions, in which the subject represents a collection of several individuals (e.g. Athenians fought at Thermopylae). Propositions that are not individual concern then abstractions from individuals.

The next three points of divisions concern in some manner the copula of the proposition as the relation of two concepts. Firstly, Crusius begins, we must see what type of relations the concepts could have to one another and these correspond to types of subordinations. Thus, he first divides propositions into relative propositions, such as “the higher presupposes the lower”, and non-relative propositions that then divide into existential and causal propositions. Existential propositions divide into five subclasses: propositions of existential abstraction, which combine only externally connected concepts, such as sign and what they signify (“when my teeth hurt, it will rain”), propositions of metaphysical abstraction, where subject is a subject in a metaphysical sense and predicate is something subsisting in it (“a body has a shape”), propositions of mathematical abstraction, where one concept is an integral part of the other (“triangle has three sides”), propositions of qualitative part, where one is not a mathematical part, but a qualitative part of the other (“a reasoning soul has a capacity to speak”) and propositions of logical abstraction, indicated by the word “is” (“human is an animal”). Causal propositions, on the other hand, divide into propositions of ideal and real causality. Crusius notes that a proposition of ideal causality, such as “if two persons equal in their height a third person, they equal in their height also themselves”, differs from a proposition of external abstraction, because in the former the subject of the proposition (the first proposition) is the ground of the predicate (the second proposition), while in the latter the subject is only the sign of the predicate. He also divides propositions of real causality into physical propositions stating efficient causes (“Sun warms the Earth”), moral propositions stating means (“willingness to learn from others is a means to wisdom”) and mathematical causal propositions stating relations of determination between magnitudes (“two sides of a triangle and an angle inscribed by them determine the rest of the sides and the angles”).

The second point of division related to copula concerns the question whether the relation between subject and predicate exists or not, which Crusius calls, as Kant later, the quality of the proposition. It is not surprising that Crusius divides propositions in this sense to affirmative and negative, but a more peculiar is his point that both affirmative and negative propositions can be such contingently or in themselves: for instance, “God is not mortal” is in itself a negative proposition, because it expresses the non-relation of God to a concept of mortality, while proposition saying exactly same, namely, “God is immortal”, is contingently positive proposition, because it expresses the relation of God to a negated concept of mortality. Crusius explains that such contingently affirmative or negative propositions are possible only with logical propositions, with mere “is” as a copula. With other types of propositions, he says, a similar transformation would change the truth of the proposition: for example, it is a completely different thing to say that a good conscience makes one joyful and that a good conscience makes one nothing more but joyful. Furthermore, Crusius notes that in common speech a contingently negative proposition implies that the predicate belongs to the subject only in a mediocre grade, for instance, saying that someone is not unskilled implies that they are only mediately skilled.

Contingently affirmative and negative propositions are infinite propositions – another term Crusius shares with Kant – that is, propositions with negative concepts as predicates. Then again, Crusius appears to imply that there can be infinite propositions beyond contingently affirmative and negative ones (and unlike Kant, he does not treat infinite propositions as forming an independent class besides affirmative and negative propositions). Indeed, he adds, it is sometimes unclear and even dependent on context whether a proposition is infinite or not: “cows cannot learn to speak” seems like a regular negative proposition, but if it is used in a deduction with a premiss “that which cannot learn to speak, although having means for it, has no reason”, it works like an affirmative infinite proposition.

Crusius divides negative propositions further into incomplete and complete negations, depending on whether the negation is still taken as doubtful or assumed to be certain. The distinction is useful, he explains, because only complete negations demand proving. Furthermore, he adds, sometimes further obligations might force us to act according to incomplete negations, as if they were complete negations: for instance, if we could not with utmost certainty prove that there is only one God, but we did have some grounds to suspect it, we would still be obligated to believe that this is so and worship only one God. Just like negations, Crusius suggests, affirmations can also be incomplete or complete, which he deems to an especially important distinction in case of propositions concerning possibilities: for example, when we say that it is possible that some stars move and do not seem to move because of their distance, this is an incomplete affirmation, but when we say that it is possible that affections make people furious, this is a complete affirmation.

The final point of division regarding copula, Crusius states, concerns the grade of the relation between subject and predicate. Crusius calls this division one of modality – this is another term shared by Kant. We have already seen earlier that Crusius recognises six forms of modality: essential relation, natural relation, contingent relation, merely possible relation, unnatural relation and impossible relation. Interestingly, Crusius regards the division of properties into universal and particular – what he calls a division according to the extension of propositions – as a mere imperfect expression of the division according to modality: a universal affirmative proposition is either an essential or natural proposition, while a universal negative proposition is unnatural or impossible.

The next real point of division – fifth, if you haven’t been counting – concerns the possibility that a proposition might consist of more than two concepts, which occurs, Crusius suggests, if a proposition is a combination of several propositions. This combination might be just rhetorical, for instance, made just because of shortening the expression (“gold is heavy and yellow”). Then again, the combination might be necessary in the sense that the constituent propositions alone would not say the same thing and might even contradict their combination: these combinations Crusius calls logical. The logical combinations require then two concrete concepts, from which something is abstracted.

Following Hoffmann, Crusius suggests that this double abstraction can happen in such a manner that both of the concrete concepts are contained in the subject, from which the predicate is abstracted: both Hoffmann and Crusius call these composite propositions according to subject. This class includes, Crusius explains, hypothetical propositions, where the subject is of a form “A, if a proposition x holds” and thus connected only conditionally to the predicate (“the price of grain, if the harvest is good, will fall”). Then again, he adds, it also contains cases where the subject is a combination of coordinated concepts, of opposed concepts, of seemingly, but not truly opposed concepts and of subordinated concepts. In the case of coordinated concepts, we might be dealing with copulative propositions where the predicate is an absolute concept (“heat and oxygen cause eruption of fire”) or with composite relative propositions where the predicate is some kind of relation (“two plus two equals four”). If the concepts are opposed, Crusius calls the proposition exceptive (“no one but God is omniscient”), and if they are just seemingly opposed, extensive (“all bodies, even the thickest, have pores”). Finally, if the concepts are subordinated, this subordination concerns the whole essence in reduplicative proposition (“law as a law differs from a mere rule”), an essential part in explicative proposition (“human beings, regarding their souls, are immortal”), a contingent circumstance distinguishing a particular species of the more universal concept in specificative proposition (“reasoning souls, even without bodies, retain distinct concepts”) or a contingent circumstance forming a mere external abstraction in determinative propositions (“humans, when getting older, become weaker”).

Needless to say, the double abstraction can also happen according to predicate, Crusius explains, when we first abstract or at least try to abstract something from a subject and then again abstract something from the relation of the first abstraction to the original concrete concept. This double abstraction, he continues, might result in a disjunctive proposition saying that only one of two predicates will belong to a concept. Then again, it might also merely serve to determine original predicate further, in the already familiar reduplicative propositions (“electors choose the emperor as the emperor”), explicative propositions (“sciences improve soul, when it comes to understanding”) and determinative propositions (“Christians were persecuted, during the first three centuries”) – specificative propositions do not occur with predicates, Crusius insists, because the seeming examples of such are mere rhetorical combinations.

The final three points of division can be dealt with quickly. First of them concerns the certainty of the propositions: a proposition can be certain (its opposite cannot be true), merely probable (there are more reasons for it than for its opposite), reliable (it is safe to act according to the proposition) or merely possible (there are no grounds for or against the proposition). The second point of division concerns the expression of the proposition: the expression agrees with the sense in a regular proposition or not in a cryptic proposition. The final point of division concerns a relation between different propositions: they can be equivalent (perfectly or imperfectly, that is, in some context, but not in others), subordinated (one can be deduced from the other), opposed (either contrary or contradictory) or completely unrelated.

Crusius, Christian August: Road to certainty and reliability – Using concepts and words

Crusius ends his discussion of concepts with a consideration of where we use them. He begins by noting that they form the building blocks for further concepts, and later on, propositions and deductions. Starting from the building of further concepts, Crusius notes that this can happen through distinguishing or combining or a combination of both. He points out that distinctions have already been dealt with and therefore turns his attention to combination of concepts.

Combination of concepts, Crusius notes, can happen without purposeful use of powers of understanding through imagination, for instance, while dreaming. The combination can also happen purposefully, he points out and adds that such a purposeful combination presupposes a previous distinguishing of a concept into more abstract concepts and a consciousness of a new combination of such abstractions. Such a recombination requires, according to Crusius, a shifting of attention to a direction where the abstractions seem united by some circumstance.

Parts forming the combined concept, Crusius notes, might then all be regarded as subordinated to the combination, for example, when we think of a straight line drawn toward the Sun. In other cases, he adds, the combined concepts are opposed to one another and connected to a third concept which forms the ground of the division, for instance, when I think of a line that is either curved or straight. In the latter case, Crusius explains, the concept of line is undetermined and we want to think it determinately, thus, we think it with more than one determination, both of which are opposed to one another, but subordinated to the concept of line. The opposition of curved and straight does not prevent representing this as one concept, he insists, because we are not thinking of a single line, but the essence of line in general.

The combination of concepts, Crusius points out, can be more or less arbitrary. Firstly, the parts can hang together by their nature and only their boundary might be arbitrary. Secondly, even the boundary might be derived from the nature of the parts, so that we combine them only insofar as we have regarded one part after another and finally regarded them altogether as a whole. Finally, the combination can be fully arbitrary.

Moving on to propositions and deductions, both of which Crusius will go on to handle in more detail later, he merely mentions the latter, while of the former he notes that they differ from combined concepts only by their purpose. Thus, with a combined concept one thinks both its parts and considers them only as a combined whole – like when thinking of an immortal God), while with propositions one thinks the compared concepts precisely for the purpose of representing their relation, like when one thinks that God is immortal.

All effects of understanding, whether concepts, propositions or deductions, Crusius thinks, represent certain possible or actual things, which are the object of our representations outside our thinking. Furthermore, he argues, when we think things, we must think them through certain properties, by which we designate them and distinguish them from one another. Crusius suggests calling these properties designating things as the object of thinking within thinking or understanding itself. Whether we are discussing the object outside or within thinking, he notes, the representations can change without the object changing. Thus, Crusius concludes, this changing activity in our representations must be distinguished from the objects of representation: he calls it the mode of representation.

Crusius divided the modes of representation into external or contingent mode and internal mode. Internal mode of representation, he explains, can be changed without changing the object outside thinking, that is, without meaning another object outside thinking. External or contingent mode of representation, on the other hand, can be changed without changing the object within the understanding, that is, it can be changed in such a manner that one still thinks about the previous properties of the object. In other words, if one changes the internal mode of representation, one still thinks about the previous object, but represents it through other properties: for example, when one thinks of God once as an eternal cause of the world and then as an entity that constantly thinks about all possible worlds.

Crusius makes the remark that in defining the same thing in different ways, we have different modes of representation. If the modes of representation are external or contingent, the change of definition retains even the same object within understanding. Thus the difference might consist only in that the parts of the concept are at one time thought in a different order after one another than at the other time, without ascribing to them a different relation to one another, for instance, when I say that soul is no body and then that bodies are not souls.

We use concepts to think and designate objects, Crusius continues, but we also need signs to designate concepts. These signs are used, he explains, to transmit our thoughts, since when we are used to signs, they suggest concepts to us by the rules of imagination. Then again, Crusius adds, signs are also used for our own convenience, since we cannot think of many concepts at the same time and with combined concepts we easily forget what they mean, but designating them with signs makes it easier to distinguish them from one another.

If signs should be fit to represent thoughts, from the standpoint of Crusius, there must potentially be many different signs that cannot easily be confused with one another, because there are many concepts and they have many relations. Furthermore, they should be easy to generate, manipulate and make note of. Crusius thinks that sounds that form words have all these properties, hence, regards it natural that words are used as signs for thoughts

Crusius defines language as a capacity to use words as signs for thoughts, although he adds immediately that this is true only of human language – other beings with reason can have language without words and instead some other signs for thoughts. Indeed, Crusius suggests, if we understand by language the sum of all such signs that express the internal state of spirits, even beasts can be said to have a language. Then again, he says, language is usually thought to consist of signs of abstract concepts.

If we want to use something as a sign for a thought, Crusius goes on, we must first have an idea of it. Crusius calls the idea of a word, whether spoken or written, the material meaning of this word. He then distinguishes the material meaning from the formal meaning of the word, which is the idea of a thing it should signify. Thus, when one cannot distinguish a word from other words, because it is spoken or written indistinctly, one does not understand its material meaning, but if the word is of unknown language, its formal meaning is unknown.

Experience shows, Crusius thinks, that words should be first connected to concrete concepts, because it would be inconvenient to try to define all of them. According to him, this is especially true when words are used for transmission of our thoughts, because the aim of such a transmission is usually to inform others about known truths. Furthermore, even if it would be possible, it would be of no use to give definitions of every word, because this would fix the meaning of the words only from the standpoint of the person defining them.

Using a sign, like a word, presupposes that the designated object appears sometimes with the sign. Thus, Crusius suggests, if we are accustomed that words and designated concepts occur together, it is said that we understand a language. In other words, hearing or reading the words of a language should bring to our mind the respective concepts, and furthermore, in thinking a concept, we should know the appropriate words designating them: both implications can appear without the other, but both are required, if we are to properly know a language.

Crusius divides understanding of language into immediate understanding, where the words make us instantly think the designated concepts, and mediate understanding, where the words of one language make us think of words of another language. He thinks this difference is remarkable, because the meaning of the translated words might not exactly convey the same meaning as the translation, because different languages have not named the exact same concepts. Furthermore, Crusius points out, the mediate understanding takes far more time, because it involves translation of the words to another language.

Understanding words becomes easier, Crusius holds, the more sensuous are the concepts designated by them, because we are very used to thinking sensuous concepts. On the contrary, if we designate abstract ideas with words, we must first carefully analyse concrete concepts designated by individual words and thus gradually build abstract concepts out of them. If someone cannot do this, Crusius points out, they are said to understand the words and still not know what to do with them.

Because words are just signs of concepts and change nothing in these concepts, Crusius clarifies the reader, it requires no particular type of knowledge to connect words with their concepts: if we wanted to do that, it would be like classifying a flower in a garden according to a sign filled with numbers, attached to that flower. Still, he adds, words are useful, because without them, the variety of concepts would lead us to inevitable confusion. They are external aids for knowledge, and our knowledge grows, when we learn more characteristics of the same concepts.

Crusius argues that words do not affect the mode of representation, because we can think the same things in different languages, and indeed, because we can forget the words and still know the things, not knowing how to express ourselves or choosing other words. Thus he concludes, we can have concepts without words, particularly with immediate sensations, but also with some abstract concepts. Crusius also warns the reader not to say that we think things through words, but at most that we combine a concept of thing with a concept of a word as a sign.

Words are signs of thoughts and thus should express the content and the differences of the thoughts conveniently. Sometimes, Crusius continues, we express complete, sometimes incomplete things, sometimes absolute things, sometimes relations. Of these various divisions he picks out especially the one between categorematic and syncategorematic words, where the former refers to situations, where the word could be used both as a subject and a predicate in the same proposition.

Words follow concepts, thus, Crusius notes, humans face difficulties in understanding one another, when concepts are not naturally determined, but based on arbitrary customs and purposes. In other words, when we want to communicate our thoughts to others, it is possible that some people due to their different concepts see things with different eyes and from another viewpoint that changes their external mode of representation and they might even ignore some circumstances we deem to be important. The result is that people do not understand each other completely: even the wisest sayings might be turned upside down by people who think they understand these perfectly.

Crusius turns next to speak of equivocity, where a word has more than one meaning. His general message is that equivocity or homonymy does not always imply obscurity of the meaning of the word or a confusion of concepts. Indeed, he points out, all languages have words that have more than one meaning without any confusion, because it is possible that in everyday use of the word the context provides the meaning. True, Crusius admits, sometimes there does arise obscurity of concept or even confusion, and therefore he separates mere grammatical equivocation from logical equivocation or ambiguity. In addition, he also mentions contingent or subjective equivocation where words are not actually equivocal, but their general concept just hasn’t been abstracted correctly from the examples.

Crusius starts to ponder the causes of equivocation. Sometimes, he says, it is based on a confusion of concepts, but often just giving a name of one thing to something else because of their greater or lesser similarity or connection. The reason for such a sharing of names might be that there are not enough words available and we still do not want to make up completely new and incomprehensible ones.

Crusius thinks that we should avoid ambiguity that is connected with obscurity and confusion. This means, he explains, that we should not use ambiguous words without adding determinations that highlight the uncertainty of their meanings in the context. Such determinations are either full nominal definitions of the words or mere auxiliary expressions, from which the meaning can be deduced. If it is nominal definitions that are used, we should pick a single distinct meaning of the ambiguous word or then distinguish all the common meanings of the word and retain the right to use all of them according to linguistic usage, but in such a manner that the obscurity is avoided through circumstances and additions.

In Crusius’s opinion, many philosophers are too strict when it comes to equivocity, demanding that a scholar should use a word constantly with the same meaning, although they cannot themselves apply this rule consistently. Indeed, Crusius emphasises that words are subservient to thoughts, thus, in common language we rarely meet a word, the meaning of which would not be a useful concept pointing to something real. Hence, in the determination of the meaning of words one should remain as much as possible with the common language and not deviate from it, if there is no danger of confusion and if there is no need to prevent inadequacies of knowledge. Otherwise other people wouldn’t understand what the scholar says, unless they took the arduous task of learning a new language. Still, Crusius concedes, because all concepts use words, it is allowed and required to give names for newly found concepts, but these novel names should be made as easy for the memory as possible, and concepts should be sufficiently significant, when making particular names for them.

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

It is in a sense logic, where one can best see that Crusius is not a part of Wolffian school: so different the manner he handles even this seemingly quite neutral discipline. Even with such concepts like distinctness of concepts, Crusius handles the topic in quite a different manner than Wolffians.

Before getting to the notion of distinctness, Crusius actually begins with the notions of truth and perfection of concept, which he emphasises to be two very different things. Concept is true, he says, if the (actual or possible) object supposedly corresponding to the concept has precisely that what is represented in the concept. Perfection of the concept, on the other hand, refers to the measure in which the concept represents its object. This perfection, Crusius adds, is also called the distinctness of the topic of the concept.

What does this perfection or distinctness then mean? Crusius explains that if we want to use concepts, we must be able to distinguish them in our understanding. Furthermore, he adds, if we are to make the most complete use of concepts, they must represent so many signs of a thing they are concepts of that we can through these signs recognise the corresponding thing outside our thought and distinguish it from other things. Crusius compares concepts here to a map: if it was completely black, we could not distinguish the countries at all, and if the borders would be drawn erroneously, we could not use the map as a criterion to distinguish countries in the world. The two types of perfection, he concludes, are essentially different, but the problem is that both are called distinctness. To make the difference of the two notions clear, Crusius calls the former or the capacity to distinguish a concept from other concepts in our understanding an ideal distinctness, while the latter or the capacity to use concept to distinguish objects outside thinking a characteristic distinctness.

Whatever the distinctness we are talking about, Crusius says, it depends partly on the characteristics of the concept itself, partly on the measure of liveliness, with which it is thought. The first aspect, he explains further, depends partly on whether the concept endures in the understanding constantly in the same manner and does not change anymore, since if it does not remain constantly similar, it cannot have any constant similarity or dissimilarity with other concepts. Partly it depends on the measure of the perfection of the content of the concept, that is, on whether the concept contains so many properties and signs that it enables distinguishing the concept constantly from other concepts – or even its object from other objects. The second aspect or the grade of liveliness, by which understanding thinks the concept, is important for distinctness of the concept, Crusius thinks, because without forceful enough activity understanding cannot use the concept for its purposes

Moving on specifically to the ideal distinctness, Crusius notes that it can be divided from the viewpoint of the method, by which one arrives at distinct concepts, and from the viewpoint of the type of knowledge, by which they are thought. Regarding the first type of division, he continues, distinct concepts can be reached through a good concrete idea – then we talk of common distinctness – or through an appropriate abstraction – then we talk of abstract or scholarly distinctness. Crusius notes as one type of abstract distinctness the logical distinctness, in which concept is distinguished from others through the specific method of abstraction used for reaching it. The other type of abstract distinctness, he adds, is the distinctness of essential content, where a concept is distinguished from others through the parts contained in it or through other circumstances connected to it.

Crusius turns his attention first to common distinctness, giving as an example our concept of sour, which we distinguish from the concept of sweet through our concrete idea of what both taste like. With many concepts, he notes, common distinctness is the only possible form of distinctness for us. It is adequate, Crusius thinks, only for such things that are immediately sensed or which are known through sensuous properties, that is, properties that we can think without scientific abstraction. Thus, common distinctness is enough for common practices in human life, but more intricate objects require also scholarly distinctness. Still, Crusius adds, common distinctness of concrete ideas provides us the matter to think about and the guiding thread of our thoughts. Furthermore, he notes, it is not just external sensations where common distinctness is available for us, since drive of conscience provides us a natural feeling of right and wrong that could have common distinctness, if the activity of conscience is not hindered.

Crusius turns his attention to logical distinctness, where one represents, firstly, something concrete, from which the abstract concept in question is to be found. Starting from this concrete, one starts to think away characteristics, until only the desired abstract concept remains and becomes apparent in its separation from other concepts. Crusius underlines that this kind of representation, based on the generation of concept, should not be confused with defining a thing through its manner of generation, since the latter is a form of distinctness of essential content. Logical distinctness, he continues, is especially important for simple concepts, since they cannot have common distinctness, which concerns only individuals, nor distinctness of essential content, since simple concepts cannot have parts required for it.

Moving then to the distinctness of essential content, Crusius points out that the parts used for it are not meant to be real parts, but conceptual or ideal parts, separated through scholarly abstraction. This form of distinctness, he says, is used in definitions, and therefore many scholars ignore other forms of distinctness (Crusius is possibly referring here to Wolffians). This type of distinctness has grades, since it can be made more perfect by dividing the parts of the concept further, but it must finally end with logical or common distinctness. Thus, Crusius concludes, distinctness does not end in obscurity, but in another type of distinctness. Furthermore, he adds, the division of concept does not provide distinctness, if the parts cannot be distinguished from one another, hence, the highest concepts of ontology must be the most logically distinct.

Crusius emphasises that ideal distinctness of concepts differs from distinctness of words, which means the capacity to use a word appropriately for distinguishing the corresponding concrete idea from others. He also distinguishes the ideal distinctness of a concept from the ease, by which it can be understood without great effort and subtle abstraction.

Distinctness, Crusius tells the reader, is opposed to obscurity, which thus has as many types as distinctness. Particularly, obscurity can concern concepts or words. Furthermore, Crusius adds, we can speak of the obscurity of things, which means simply imperfection of knowledge. Obscurity of things should not be confused with obscurity of concepts, he emphasises, because while a thing is obscure to us only if we do not know its whole nature, concepts of the aspects we do know of it can still be distinct. Indeed, although we would have a distinct concept, this distinctness might be based only on a few properties, so that the full nature of the thing might still remain obscure, because we do not know its other properties.

Crusius divides obscurity also according to causes generating it. Thus, obscurity might be subjective, if it is based on the circumstances of the person in question, so that other persons do not share these circumstances or at least they are not based on their essential facilities. The other type of obscurity, on the other hand, depends on the essential facilities of the persons of the same kind and is thus shared by all of them: Crusius calls this objective obscurity. So, words can be subjectively obscure, if a person is not familiar with the language, but they can also be objectively obscure, if they are not used so determinately that their meaning could be fixed with normal rules of interpretation. Similarly, a scholarly concept is subjectively obscure, if a person trying to learn that concept is weak of understanding, but objectively obscure, if there’s not enough signs to distinguish it from others. Finally, a thing is objectively obscure, if human understanding does not have capacities required for knowing what remains unknown about it.

Crusius offers some rules for making concepts more ideally distinct. Firstly, he begins, each concept that should be used constantly must be distinctly thinkable at least in some sense, thus, we should see what kind of distinctness a concept is capable of and how far the distinctness can be taken. Crusius divides concepts in this sense to three types: unanalysable concepts allow only common distinctness, the simple or fully analysed concepts allow only logical distinctness, while those in between allow all three kinds of distinctness. When deciding what kind of distinctness we want, we must know for what purpose they are required: for instance, for the purposes of human life the common distinctness is enough. Even with most of the scholarly things, Crusius thinks, it is enough to combine common distinctness with  the capacity to analyse things and thus the distinctness of essential content. Still, it is very useful for understanding, if a scholar tries to have all three forms of distinctness, wherever possible.

Crusius notes that we should try to think all the parts of a concept together at the same time, because in the combination of many partial properties lie the most beautiful points of distinction. Thus, when all these parts are represented together, the concept is more easily distinguished from others and so more distinct, just like a face is easier to recognise, when you look at all the parts all at once and not one after another.

Crusius suggests that we should try to apply abstract concepts to a corresponding concrete case, as if one would abstract them from this anew. He thinks this application is a means to make concepts more distinct, because this is the method by which we discover abstract concepts, and the more we use it, the more perfect our abstract concepts are. Crusius considers this application also a sign of distinctness, because just as we can reach abstract concepts from a corresponding concrete case, similarly we must be able to imagine the concrete case, when we think of the corresponding abstract concepts in a remarkably perfect manner. This means also that general abstractions should be applied to examples, from which they could be abstracted by removing the individuality of the examples and all the concepts not belonging to these abstractions.

Crusius notes particularly of causal abstractions that for their perfect distinctness it is not enough just to give an specific case corresponding to this abstraction. Instead, one should also make comprehensible the manner in which the causal abstraction connects to a given causal relation, so that one could distinguish the dependence of this particular effect from this particular cause from the dependence of another particular effect from another particular cause. Furthermore, Crusius adds, the link between the cause and any of its effects should be drawn through immediate links between a cause and an effect. Still, he admits, all of this is demanded only if our causal abstractions should be perfectly distinct, whereas we can be convinced of certain causal relations and even know them distinctly in the sense of distinguishing them from other causal relations, even if the structure of this particular causal relation is not yet known in a fully distinct manner.

Even if we don’t know an actual concrete case, to which we could apply the abstraction and thus prove its distinctness, Crusius suggests, we could also just merely imagine a possible case or at least find some analogical case to consider. Of course, he warns the reader, we should not be deceived by analogies, but distinctly abstract the point of similarity that should make apparent what is compared with the analogy, for instance, when we compare the human body to a hydraulic machine. If we do not fully understand the analogy, we should at least try to use our capacity of abstraction to provide two cases similar to one another where admitting the possibility or actuality of the first makes it necessary to admit also the other case. In other words, Crusius exemplifies, if a person wanted to make the idea of a generation of the soul of children from the souls of the parents distinct and for this reason compared it to the case of light or fire being lit by another light or fire, this comparison would help nothing for distinctness, because the compared circumstances are not similar in the important sense: the fire lighting the others does not generate the substance of the lighted fire.

Crusius states that thinking a magnitude distinctly requires measuring it and gaining a distinct concept of the unity we use for measuring. Thus, he explains, while extensive magnitudes are measured with other extensive magnitudes, what Crusius calls magnitudes of quality, such as force or action, should be measured through their known effects. Yet, he asks the reader also to be cautious when they choose the effect for measurement. For instance, if the magnitude of some quality is represented through an effect that it generates after a certain period of time, this does not mean that waiting for double amount of time would double the effect, because some forces lose their capacity through action – if I can learn something in an hour, I cannot learn twice as much by increasing the time.

After presenting the previous rules, Crusius goes on to divide ideal distinctness in regard to the type of knowledge that one has of things in thinking them distinctly. Firstly, he begins, when we think of something, we may designate it positively, that is, assign to this thing something that could also be separated from it, like when we think that sun (a thing) shines (the additional thought). Then again, we could also designate the thing negatively, that is, separate an undetermined concept from something that does not belong to it, like when we think that God has no organs.

A positive concept, Crusius continues, is either absolute, representing abstraction from a single thing, or relative, representing abstraction from several things at the same time. He notes that relative concept presupposes that we represent at least two things with an absolute concept, and indeed, the better we understand what absolute lies on the basis of a relative concept, the more distinct the relative concept becomes. This explains, Crusius notes, why we desire knowledge of absolute matters, but this does not mean that knowledge of relative matters could not be certain.

When we represent something, Crusius goes on, we think it through what it is in itself or through concepts acting as signs representing its existence: the former he calls intuitive and the latter symbolic knowledge. This does not mean, he immediately adds, that in intuitive knowledge we would think without words and in symbolic knowledge with words. Instead, examples of symbolic knowledge, as Crusius conceives it, would be representing causes through their effects, effects through their causes, or things through their relations or through what they are not. Intuitive and symbolic knowledge have their own kind of distinctness, he adds, so that our knowledge of triangles is intuitively distinct, but our knowledge of the soul mostly just symbolically distinct. Although it might seem natural to favour intuitive over symbolic knowledge, Crusius insists that sometimes symbolic knowledge is the more important one: for instance, in geography it is not important whether we have experienced some lands, but it is essential to know their relations and connections with other lands.

Crusius tells the reader that the ability to recognise intuitive knowledge is based on assuming a completely correct and distinct internal sensation: as long as we are distinctly conscious that we have to to think a thing to be something in itself, our knowledge is to be regarded as intuitive. For instance, he explains, we have intuitive knowledge of triangles, since we are aware that we must think of them in a certain manner, that is, as a figure closed by three lines. If such a compulsion is not perceived, Crusius adds, but instead we observe that something else must be presupposed for thinking a thing, this knowledge is symbolic. Hence, he argues, the common concept of a curved line is symbolic, since we know that the curved line must be described in a certain manner, because it constantly deviates from its direction, but since we do not know how great the deviation is, we have to think the curve through its sensuous image.

Crusius points out that we cannot have complete intuitive knowledge of things, but must often satisfy ourselves with symbolic knowledge. Then again, he adds, we could not think at all, if we would have no intuitive knowledge of anything. Still, he concludes, even our best knowledge is at least partially undetermined, and in place of these unknown determinations we put symbolic knowledge. Knowledge of simple concepts, Crusius continues, is intuitive, but because we cannot think of simple concepts themselves without great difficulties, we are used to representing them symbolically through a concrete idea.

Crusius notes that when we abstract incomplete things and consider them in isolation, we can have intuitive knowledge of them: for instance, we have intuitive knowledge of straight-lined figures, of motion in general and of numbers determined by their own units. He emphasises that incomplete knowledge can be intuitive, since intuitiveness does not mean the same as completeness.

The more we have intuitive knowledge, Crusius suggests, the more perfect and appropriate this knowledge becomes, because it makes it easier to distinguish a concept from all others: a thing is best distinguished by what it is, since a sign might have defects that prevent it from completely corresponding to the thing it is supposed to signify. Thus, he concludes, what makes our knowledge more intuitive makes concepts more distinct for us. Then again, anything that does not make our knowledge more intuitive, like circular definitions, does not make it more distinct.

Crusius notes that some words we use are not connected to any concepts, while some concepts are found to be impossible, when we try to make them distinct. Sometimes such words and concepts are regarded as true and even sublime thoughts and confused with symbolic knowledge, which is then defined as what is left when all intuitive knowledge is taken away. Such a confusion can occur, Crusius explains, when these concepts are supposedly defined, but the definition is circular or parts of definition are again words without concepts or mere impossible concepts. Furthermore, he adds, we might not even really try to think the parts of concepts as really combined, as the words seem to indicate, but merely think them one after another, while further consideration would show that these parts contradict and cancel one another or at least nothing unsymbolic and absolute would be left, but merely relative symbols and figments of imagination. Finally, we might forget to provide an example for such concepts or words, but use them thoughtlessly or at least against the usual meaning of them.

In addition to using words without concepts and impossible concepts, Crusius finds another reason why the relation of intuitive and symbolic knowledge might be confused: it is not uncommon that we desire only intuitive knowledge in an incorrect place and are not satisfied with symbolic knowledge. For instance, he says, many atheists do not want to believe in God nor in any immaterial substance, because they cannot have intuitive knowledge of them. Indeed, Crusius insists it is an error to think that symbolic knowledge could not be certain, because certainty is not dependent on intuitiveness.

Crusius has looked at ideal distinctness from many different perspectives, but his account of characteristic distinctness is relatively short. Most important to recognise, he insists, is that characteristic distinctness differs from ideal distinctness: if characteristic distinctness is lacking, even ideally distinct concepts can be used only abstractly, but we cannot advance to application.

Since there are, Crusius thinks, two kinds of existence – physical existence that something is and moral existence that something should be – characteristic distinctness can concern either of them. In other words, if a concept is characteristically distinct according to physical existence, we can give an example of an existing object corresponding to that concept. Similarly, if a concept is characteristically distinct according to moral existence, we can always use the concept to determine, where we should, should not or are allowed to act in a certain manner.

Crusius divides characteristic distinctness into common and abstract or scholarly distinctness. A common distinction is caused by a good concrete idea, which can be both ideally and characteristically distinct. On the other hand, abstract or scholarly distinction is caused by an abstract idea, that is, criteria for the existence of something are given in abstract concepts, or in case of moral existence, abstract concepts can be used to define reasons why something should or may happen.

Crusius opposes the correct distinguishing of concepts, involving both ideal and characteristic distinctness, to three incorrect states: merely lacking distinction, false distinction and confusion. Starting with the first incorrect state, where some or all types of distinctness are lacking, Crusius emphasises that a reasonable person should not judge a thing or decide an action, if the required type of distinction is lacking, since if no judgement or decision is made, no error can occur. If all types of ideal distinctness are absent, he continues, the concept is completely obscure. Then again, if common distinctness is enough for recognising a thing and abstract distinctness is lacking, the concept is not obscure, but just unanalysed. If a concept is ideally distinct, it all depends on what type of distinction is lacking, for instance, if the concept has common distinction and lacks only the abstract distinction, while common distinction is enough for the purpose, then no error occurs, but greater perfection will not be reached.

By false distinction Crusius means supposed distinction, which is actually no distinction at all: the things that should be distinguished are not distinct, at least not in the manner indicated. Such false distinctions occur, he exemplifies, when we distinguish things through words which can actually refer to the same idea, or when we distinguish things through imagined abstractions that do not point to any real distinction in the objects. Another example Crusius provides happens when we try to use contingent properties to make stable distinctions, like when we use gradual distinctions to indicate essential differences.

Another prominent instance of false distinction, Crusius suggests, occurs when we indicate a point of distinction that does not differentiate the things we want to, even if it is based on a true property of one of the things. Thus, he explains, when someone distinguishes physical and moral necessity by saying that in the former the effect is generated according to laws of movement, while in the latter it is generated by acting through ideas, this distinction is false, because the important point of difference is actually that moral necessity leaves open the real possibility that things could go otherwise.

All the previous types of false distinction still allow the possibility that the falsely distinguished things still are really distinguished (just not in the sense indicated by the false distinction). Yet, it can also happen, Crusius clarifies, that the things are not distinguished, for instance, when one considers ideally distinguished objects, like perspectives to the same object, as objectively distinguished. Another example occurs when things that are externally connected are held as subsisting in each other, for instance, when soul is regarded as a form of body.

Crusius also suggests a few reasons why we might have false distinctions, first of them being that we humans are not attentive nor industrious enough. Indeed, he adds, many of us do not reflect ourselves nor our concepts and then get distracted by mere primary or material abstractions, hastily progressing from one to the other, without first making concrete concepts distinct and judging them appropriately. Crusius notes that with scholars this error is connected with the habit of always using the same patterns of thought without caution. Final cause he mentions is the inadequate subtility, where one does divide the concept again and again, but regards only some series of divisions necessary, disregarding others.

Confusion of concepts, in the sense Crusius means it, is in a sense opposite to false distinction: in it different things are considered similar or even same. The causes of confusion can be same as with false distinction, he explains, but we can go further, for instance, we might be deluded by common name, by which both are called, or by certain common concept belonging to both, which is still not sufficient enough for posited similarity. Thus, Crusius states, venereal love and friendly love are often thought as species of the same closest genus, but actually they are connected merely by the word “love”.

If the cause of confusion is a certain common concept belonging to the two things confused, Crusius adds, the blame for confusion might lie in that the same common concept is thought concretely, whatever it is in its kind, like when the true and false virtue are often confused, leading to people regarding every action or passion that they regard as worthy of admiration and even calling them virtue. The confusion is even easier, he notes, if the common concept is dissimilar or impure genus, for example, many believe that they remain free, even if they ascribe all their actions to a determining ground, because the opposite of their actions remains possible, confusing the ideal and real possibility. In the final example, Crusius continues, the common concept confusing two things is represented in a distinct abstract idea and lacking only in the application. Even so, he points out, the distinction in question might still not be sufficient for the search for similarity or sameness, because then one ignores a subtle, but significant circumstance forming the distinction.

Crusius, Christian August: Road to certainty and reliability – Modalities of subordination

Before moving on from the topic of subordination and distinction of concepts, Crusius takes some time to consider two related questions. Firstly, he entertains the possibility of presenting the various types of subordination and distinction as a kind of algebra, with symbols chosen to represent the different types. He seems optimistic about the possibility of such an endeavour, although it is not evident what he considers its benefits – at least the amount of symbols required is rather extensive.

The more interesting question concerns different grades or modalities of subordination and distinction. In effect, Crusius supposes there to be three kinds of modalities for both subordination and distinction. The first of these he calls essential subordination, which connects concepts all the time. The sum of everything subordinated essentially to a thing forms then, Crusius says, the logical essence of that thing. Furthermore, he adds, this logical essence can be divided into contingent properties, essential to the thing only with the supposition of God having freely created the current world, and necessary properties, essential whatever God might choose to create.

The second modality of subordination, according to Crusius, is natural subordination. This means, he says, that two kinds of things are regularly connected, although the essence of the thing allows that in an extraordinary case this connection would be lacking. Crusius calls such naturally subordinated properties naturalia, an example of which would be five fingers of a human. He notes that naturalia can be based in the essence of a thing, like the human capacity to speak. Then again, Crusius thinks, it might also be generated by a regular connection to an external cause, like the tanned skin colour in areas with more sunlight.

The final modality of subordination, Crusius continues, is contingent subordination. Here, a thing is connected to some property only occasionally or accidentally. Crusius also points out that while a property might be just accidental, capacity for it could still be natural or even essential: for instance, while wisdom is an accidental property of human beings, capacity for wisdom is natural or even essential property of humans.

Distinction, Crusius suggests, comes also in three modalities. The first of these is the necessity of distinction, that is, the impossibility of subordination, where no possibility of combining concepts is possible, without contradicting their essence. Similarly, the second modality is the natural distinction or the unnatural subordination, where the combination of concepts can occur only in extraordinary cases, where some naturalia have been cancelled. The final modality is then the accidental distinction or the mere possibility of subordination, where nothing essential or natural prevents the combination of concepts, but in this particular case the concepts just have not been combined.

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

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

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

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

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

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

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

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

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

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