Crusius, Christian August: Road to certainty and reliability – Corrupted understanding

We have reached a milestone in the logic of Crusius, since we are now about to turn to its practical part, where the question is not so much about the structure of the capacities and activities of human understanding, but of the proper way to use them. The first topic to be covered in this practical part, Crusius says, is that of the diseases of understanding, that is, not just temporary errors, but constant conditions hindering the understanding from its proper purpose of knowing what is true.

Crusius thinks it evident from experience that human understanding can have diseases in the sense just mentioned. Furthermore, he identifies three causes for these diseases. Firstly, because understanding is subservient to the will, the will can through a repeated bad use of understanding create harmful habitual dispositions. Secondly, Crusius continues, the body restricts the activities of thinking, and if it repeatedly makes thinking difficult, it can create constant bad qualities in understanding. Finally, the human soul is conceived through external causes, which can create many innate imperfections in understanding.

Despite admitting the possibility of human understanding becoming diseased or corrupted, Crusius denies vehemently that such a disease could affect its essence. After all, he argues, God created the essence of understanding, so that it must be good. This is no contradiction, Crusius assures the reader, since it is as true as eyes being by their essence the vehicle for seeing, but sometimes having maladies that impair the vision. Thus, Crusius concludes, the diseases of understanding can concern only its grade or relations to other things.

Crusius divides diseases of understanding into two classes: physical weakness of the fundamental forces of understanding, and faulty state of understanding in relation to its use. Starting from the first option, Crusius divides weakness of the force of understanding into absolute and relative weakness. Of the two kinds, absolute weakness is measured by the inability of the understanding (or one of its capacities) to fulfill its purpose. Relative weakness, on the other hand, describes a situation where two capacities of the understanding – usually what Crusius calls lower and higher faculties – reverse their customary roles, so that a lower faculty escapes the regulation given by the higher faculty of understanding.

Crusius divides the second class of diseases of understanding – those pertaining to the state of understanding in relation to its use – into further kinds. Firstly, there are all the faults pertaining to attention, such as the lack of external or internal attention, purposeless attention or attention for worthless causes – Crusius underlines that a conscious ignorance of things should not be included in this group, and indeed, is a fault only if what is ignored is something useful or something that we are obligated to know. Secondly, there is the incapacity to think many things at the same time, whether because one cannot represent many ideas at once or because one cannot make many abstractions at once. Thirdly, there’s the inability to continue mediation for a long period in a row. In the fourth place, Crusius mentions doubt and lack of constancy in assent, but also the opposite failures of carefree assent and stubborn adherence to an assent once given. Finally, there’s the too great dependency of the understanding on the heightened activities of will.

All the described diseases of understanding, Crusius thinks, have detrimental effects: they make our observations faulty and concepts obscure, they make us confuse objects with one another and imaginations with sensations, they hinder us from concluding our thoughts, and top it all, the more they affect us, the more habitual they become. No wonder then that Crusius gives a long list of means for curing these diseases, most of which are easy to comprehend, such as practicing continuous thinking. As a main cure Crusius recommends virtuous disciplining of understanding. He notices a potential circle – understanding cannot be improved without virtue, but virtue cannot be improved without understanding – but thinks this circle is not fatal, because even a small step towards better in one leads also to improvements in the other.

In addition to morality and virtue, Crusius connects his account also with religion, pointing out that even the Bible recognises the corruption of the human understanding and the beneficial effects of morality on it. He is also quick to emphasise that the Bible does not condemn reason and understanding as essentially faulty. Even further, Crusius suggests that the fear of error should make us eager to search for divine providence, especially in matters involving our own happiness. Still, he underlines, curing the corruption of understanding can never be forced upon anyone, but always requires internal activity of the person in question.

Crusius, Christian August: Road to certainty and reliability – Certainty and assent

Crusius defines certainty as a condition where a thinker has no more any fear that the opposite of something that they posit of an issue would hold. Such certainty can be true, so that what the thinker posits as true is true and is also held to be true due to such reasons that can be signs of truth. Then again, Crusius adds, certainty can also be just seeming, so that either the propositions posited are not true or that the reasons why we are certain of them are not valid – or even that neither holds. Crusius also distinguishes objective certainty – existence of a thing, insofar as we regard it as something that can be known certainly – from subjective certainty, that is, certain knowledge that an understanding person has of such a thing.

Crusius aims to find the answer to the question how it is possible that we can become certain of anything. He thinks that God knows all things by the infinite perfection of the divine essence, while it is still a conundrum how humans find subjective certainty and how such subjective certainty can be true. Crusius starts to resolve this conundrum by first noting that in some circumstances we are forced to take some propositions as certain. This compulsion is generated either immediately – he mentions as examples experiences and highest fundamental propositions of reason and immediately obvious axioms – or mediately through a perceived connection of a proposition with immediately certain propositions. The mediating connection, Crusius reminds us, can happen through demonstration or through infinite probability, that is, a state where each new evidence appears to inevitably point to a certain direction.

The certainty of both the immediately certain propositions and of the methods of demonstration and probability, Crusius argues, are ultimately based on the three fundamental propositions – or even on the highest fundamental proposition of contradiction. The proposition of contradiction is then, for Crusius, the form of all human knowledge, while its matter is provided by sensations of the objects of knowledge. Moving downwards from this pinnacle of human certainty, Crusius divides certainty into demonstrative certainty, based on the method of demonstration, and moral certainty, based on the method of probability. Demonstrative certainty divides further into geometric certainty, based merely on the proposition of contradiction, and disciplinary certainty, based also on the two other fundamental propositions: while demonstrative certainty is based on a principle allowing no exceptions, the principles of disciplinary certainty have their restrictions that we have seen earlier.

Crusius notes the sceptical worry that the just described certainty might be only a delusion. Yet, he points out, sceptics themselves must unavoidably think of certain things as true – they sense that they doubt things, and because doubt is a form of thinking, they sense themselves thinking, and they are aware of thinking certain issues. From this sensation of their own thinking, Crusius continues, they can abstract the three fundamental propositions of reason and they must find them and anything derived from them necessarily compelling. Now, a sceptic might answer that they do admit their own existence and perhaps even the proposition of contradiction, but they still doubt all the other fundamental propositions and sensations. Crusius accuses such a sceptic of partiality: the feeling of compulsion is the same in all these cases, so why prefer some over others?

Crusius also has some pragmatic arguments against scepticism. Since sceptics really do not want to admit the certainty of the methods of deciding what is true, he argues, they must act foolishly in their practical affairs – or more likely, they just forget their scepticism and use the methods to decide what is good for them. Similarly, Crusius sees sceptics as necessarily denying the validity of all legal and moral obligations and religion. Indeed, Crusius accuses, scepticism is often motivated by a godless fear of what their own conscience dictates, if it is not just a sign of laziness.

What the consideration of scepticism has shown, Crusius states, is that our certainty is ultimately based, on the one hand, on the physical inclination of our understanding to accept certain things as true, and on the other hand, on the obligation to prudently do what is good for oneself and thus to find out what truly is good. Both these routes, he suggests, point toward God as the original source of all truth: because God has created us in a certain manner, we are compelled and obligated to recognise something as true. Human knowledge, Crusius says, is just an image of divine understanding and is true insofar as it is similar to divine knowledge.

Crusius returns to the concepts of the form and the matter of human knowledge. We have seen, he states, that all the formal principles of human knowledge are certain, since its highest principle and all methods based on it are certain. Similarly, Crusius adds, its material principles, or experiences provided by our senses and axioms abstracted from these experiences, should also be certain. This is evidently clear of the axioms, he posits, because they are immediately based on the highest propositions, but the question of the certainty of sensations must be dealt with separately.

Crusius defines sensation as a condition of understanding where we are immediately forced to think something as existing and present. He divides it into external sensation, where we sense something outside our soul, and internal sensation, where we sense something within our soul. If the sensations are to be true, Crusius argues, we must, firstly, be able to distinguish sensations from other thoughts with certainty, secondly, it must be certain that if we sense, an object of sensation exists, and finally, it must be certain that what we sense of an object actually describes it. (An observant reader might notice that as is often the case in this book, Crusius is following his teacher, Hoffmann.)

Starting with the first problem, Crusius notes that a sensation is distinguished by a feeling of being compelled to admit the existence of something, and insofar as there is such a compulsion, it is certain that we sense. If the sensation is lively enough, the compulsion is so perfect that it is impossible to deny that we sense, while even a lesser grade of liveliness might make us morally certain, if it is backed up by other sensations and reflection of already known truths. Crusius admits that we sometimes confuse other mental states with sensations, such as vivid imaginations, dreams and hallucinations during illnesses. Still, he ensures the reader, all these states can be distinguished from true sensations, if they are just made distinct enough.

The next question is whether sensations have objects beyond the sensations themselves. In the case of internal sensations, Crusius thinks that they compel us so greatly and immediately that we cannot doubt that such a state of mind exists in our soul. He mentions that idealists doubt the existence of the objects of external sensations and accept as certain only the existence of either spirits in general or merely of their own spirit. Crusius relies again on the argument of partiality: why should we accept the existence of ourselves, but not of anything beyond ourselves, if the feeling of compulsion occurs with both internal and external sensations? He adds the pragmatic argument that an idealist is a fool if he argues with someone they don’t believe to exist.

All the arguments thus far presented for the existence of external objects do not rely on the existence of God, Crusius notes and adds that the case is even clearer if we do accept God. After all, if God has given us external sensations, they must be able to reveal something in correct circumstances. Indeed, Crusius adds, the existence of matter adds to the perfection of the world and thus reflects the perfection of its creator. He also finds here a weapon against the Leibnizian hypothesis of the pre-established harmony, since this hypothesis makes the creation of the material world seem useless, denying any possible interaction between what is sensed and the person sensing. Crusius even suggests that we can thus assume the action of some external object as a condition of external sensations.

The final question about the sensations is how much of what we sense actually pertains to the objects of the sensation. Crusius admits that even if sensations were true, what we sense need not always characterise the objects sensed, for instance, green colour might not be something in grass. Then again, he points out, when we say that something is green, we merely mean that it looks green. Thus, it doesn’t affect the truth of senses that things seem different in different circumstances, because circumstances affect the interaction of the object sensed and the sensory organs. According to Crusius, we can only say that the objects in certain circumstances are the causes of certain representations and that in the same circumstances they generate the same representations and thus corresponding sensations. He does also admit that especially visual sensations provide us with intuitive knowledge about issues pertaining to the sensed objects, namely, in case of their figure and motion.

Crusius notes that we still have to consider the topic of assent, that is, we are not to merely discuss when we should take something as true and certain, but also when we do and can take something as true and certain. Assent, he explains, is not a matter of understanding, but is also dependent on our will. True, Crusius admits, it is not completely in our own power to decide what to assent to, since forceful enough reasons compel us to assent (he also points out that assent cannot be forced by external causes, but can only be compelled by reasons). Still, assent is also dependent on will in the sense that it decides where and in what measure we exert our understanding. Thus, we can hinder assenting to a truth through insufficient consideration of the grounds of knowledge. We can even generate an unreasonable assent by confusing inadequate with adequate grounds or by relying on very small probabilities due to our desires and decisions.

This concludes the theoretical part of the logic of Crusius. Next time, we shall begin tackling the practical part.

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

Until now, Crusius has dealt with demonstrations, where, he says, all alternatives are refuted as unthinkable, until only one remains. Now we are about to start the study of the method of probability, where a proposition is held to be more true than false or even fully certain, but alternatives or opposites can still be thought of. Crusius divides probability into three species: verisimilitude or what is more clearly possible and more to be assumed true than its opposite, reliability or what deserves to be taken as true in such a measure that one could act on it without further consideration, and moral certainty or what we consider to be undeniably certain, even though we can think of its opposite.

Crusius notes that reasons for taking something as probable can be cognitive in the sense of concerning just the characteristics of propositions and their relations toward other propositions, while some reasons concern also the connections of things with purposes. Starting with the merely cognitive reasons, Crusius considers the matter of probability, from which probable propositions are made, that is, logical possibilities or propositions that cannot be demonstrated true or false – he adds that actually even demonstrated propositions can be considered logical possibilities, if we ignore their demonstrations.

Crusius divides logical possibilities into perfect logical possibilities, where we understand how the predicate can be true of the subject, and imperfect logical possibilities, where we cannot understand this, but observe no contradiction in combining the predicate with the subject. Perfect logical possibilities have two levels, depending on whether we understand the possible connection of the subject and the predicate through an observation of an actual example or through mediation of other ideas. Crusius also distinguishes true logical possibilities from apparent or verbal possibilities, where at first sight the proposition seems to be irrefutable through demonstration, although further investigations show otherwise. Furthermore, he distinguishes logical possibility of propositions from metaphysical possibility of a thing that can be thought of, but might not exist.

How probable propositions can then come out of logical possibilities? Crusius notes that if we cannot prove a proposition, we are inclined to doubt its truth and even deny it. Then again, if the opposite of this proposition assumes even more without any proof, this makes us more inclined to reject the opposite. Then the original proposition is deemed probable. The fundamental essence of probability, Crusius says, is thus that a logical possibility assumes less without demonstration than its opposite. In other words, all probability is generated from the improbability of the opposite.

Crusius notes that sometimes the reason for assuming the probability of a proposition lies only in the subjective circumstances of the individual thinker: then we are dealing with subjective probability. Then again, the reason might also lie in the nature of things and the universal essence of reason and then we are dealing with objective probability. Thus, Crusius argues, subjective probability often vanishes with a more thorough investigation, for instance, when we find new alternatives we have not investigated, while an objective probability must remain constantly probable.

Crusius divides probability also to common and learned probability, depending on whether one only indistinctly feels the reasons for taking a proposition as probable or knows them distinctly. Furthermore, the learned probability has, he says, two different levels, depending on whether we can give the reasons of the probability only according to matter or whether we can evaluate it also according to form, that is, whether we can recognise the logical signs of probable and take them even to the highest grade of probability. By these logical signs of probable, Crusius appears to refer to rules, by which to determine whether something is probable. Just like with rules of deduction, I shall mostly just list them, using the six categories Crusius classifies them into.

Rules belonging to consideration of multifaceted possibility

1) The basic rule of this category: something that can occur in many different manners is more probable than something that can occur in less manners (e.g. because there are more ways to lose than to win a tournament, it is probable that our team will lose it)

2) If one of many possible alternatives must be true, the probability of one alternative is less, the greater the number of other possibilities (e.g. the more there are teams in a tournament, the less probable the win of our team is)

Crusius notes that both 1) and 2) work as stated, only if there are no other reasons that will change the scales between the alternatives, for instance, when a number of attempts is multiplied (e.g. if our team takes part in several tournaments, the probability it will win at least one of them increases).

Rule of consideration of chance coincidence of possibilities

3) A proposition that assumes the co-occurence of many possibilities by chance is improbable. Crusius notes that this rule does not work, if the proposition speaks of deliberately arranged coincidences. Furthermore, he admits that chance sometimes imitates foresight, if the number of attempts increases indefinitely.

Rules belonging to the consideration of more real possibility

4) The basic rule of this category: the more real possibility is probable. By a possibility being more real than another Crusius means that more of the causes and circumstances required for the existence of the possibility are already known to exist and can be presumed as existing. These causes and circumstances can also include signs of things, such as their effects, and partly even our thoughts of them, so that we can know at least their possibility through our understanding of them, and the more distinctly we understand the issues in question, the greater their possibility, which leads to further rules.

5) If we distinctly understand the way in which a predicate belongs to a subject in a possible proposition, the proposition is more probable than if we do understand this (e.g. a mechanical explanation of a physical phenomenon is more probable than an explanation through unknown forces).

6) If we already know an example where the possible proposition is actualised, but the same is not true of any of its alternatives, this proposition is more probable (e.g. if we know how a phrase is to be interpreted in one passage, it is probable that it will be interpreted in a similar manner in another passage).

7) The more we already know of the parts of what is assumed in a proposition or of the existence of their cause, the more probable this proposition is (e.g. if we can explain a phenomenon through known causes like air and salt, it is probable that no hidden causes are required to explain it).

8) If we know of only one alternative possibility and if it is improbable that we would have missed a possibility, then this possibility is probable. Crusius underlines that this rule leads to objective probability, only if we have so much experience of the issue or so much practice for this type of thinking that we can presuppose that it would be too great of a coincidence that only a single possibility would occur to us (thus, if we are not doctors, we should not say that the only cause of sickness we can come up with is the probable one).

9) If two things seem to be similar or dissimilar and it is improbable that we should find no reasons to suppose otherwise, their apparent similarity or dissimilarity is probably true.

Rules belonging to the expectation of similar cases or analogy

10) The basic rule of this category: what has been constantly encountered is also probable in all other and future cases, insofar as it is probably based on a common essence or a constant external cause. Crusius notes that the restriction of the conditional clause to probabilities is important, because otherwise we would be dealing with a demonstration. Furthermore, he adds, the rule is also based on another probability, that is, that we have experienced enough examples to draw the probable conclusion. Finally, Crusius notes, the conclusion cannot be made without the assumption of common essence or constant external cause (e.g. although I would have won all the poker games thus far, there is no guarantee that I will win the next one, since winning poker games is not part of my essence nor guaranteed by some constant cause).

11) If we have encountered something often, it is probable that we will encounter it many times in the future, as long as we cannot state any reason why it would be at least as possible that it would happen otherwise in other cases. Crusius notes that this probability is at least subjective, but it can be also objective, if there are good reasons to assume that it would be highly improbable that we would have experienced only examples justifying the probability.

12) What we have most often encountered in earlier examples is to be expected more than its alternative in any individual case.

13) What we have perceived to occur in one exemplary case occurs probably at least most times also in other cases of the same kind, insofar as it is probable that the similar cases have similar sufficient causes. Crusius notes again that if the conditioning clause would not be probable, we would be dealing with a demonstration. Furthermore, he points out that this rule presupposes the use of two other rules: we must use rule 8) to conclude that the sufficient cause we have envisioned is probably the only possible explanation, and we must use rule 9) to conclude that the cases are probably similar.

Rule or the consideration of conflict with known causes

14) What conflicts with existing sufficient causes is improbable.

Rules belonging to the correspondence with phenomena or circumstances

15) If a possible proposition corresponds with already known phenomena better than its alternatives, it is thereby probable. Crusius defines phenomena as something that is already otherwise known demonstratively or probably and that has a possible causal connection with what is assumed in a possible proposition, which is then called a hypothesis. Crusius divides phenomena into two kinds: mere phenomena that just possibly corresponds with the hypothesis and harmonious phenomena that agree also with one another and must therefore be derived from a single hypothesis.

16) Hypothesis based on two harmonic phenomena is more probable than alternative hypotheses based merely on a number of mere phenomena.

17) If we must count the phenomena backing the hypothesis up, we must divide the phenomena into smaller phenomena that can exist without other phenomena (thus, phenomena that are intrinsically linked to one another must be thought as a single phenomenon).

18) When counting harmonic phenomena, the correspondence of the phenomena creates a new phenomenon backing up the hypothesis (in other words, adding another harmonic phenomenon to a known phenomenon already raises the sum of the phenomena into three, because we have a) the original phenomenon, b) the new phenomenon and c) the correspondence between the phenomena).

Crusius points out that not all phenomena are of equal strength, because some of them may have internal weaknesses that cancel their power to prove things. He identifies three possibilities that can create weaknesses: the matter of a phenomenon might be uncertain, the possible causal connection between the hypothesis and the phenomenon might be uncertain, and the phenomenon might concur as well with other possible hypotheses.  Hypotheses, Crusius continues, can also have their weaknesses or difficulties, if they conflict with actual circumstances. In order to avoid difficulties, he explains, we can sometimes add subsidiary hypotheses. Such an addition makes the hypothesis a more complex possibility and thus sometimes also more difficult to prove.

Having gone through the various rules for deciding that something is probable, Crusius notes that they can be applied either to individual or to universal propositions: in the latter case, the probable proposition is called a presumption. Thus, Crusius divides all probabilities into presumption probabilities, which are proven by subsumption to a presumption that has been proved earlier, simple correspondence probabilities, which are known through a correspondence with the phenomena, and mixed cases involving both kinds of proofs.

An important type of presumptions are logical presumptions, which are the most general types of presumptions related to the first five of the six rules of probability:

1. presumption or rarity (we presume improbable what happens only in rare cases),
2. presumption of miraculous chance (we presume improbable what involves a chance coincidence of many possibilities)
3. presumption of more real possibility (we presume probable what is most real) and its subtypes, presumption of sufficient cause (we presume that an effect will follow an unhindered sufficient cause), presumption of unapparent cause (in issues we are experts, we presume improbable what has no causes) and presumption of deficient power in given cause (we presume improbable what the well-known given causes have no power to produce)
4. presumption of analogy of perpetual and frequent (we presume probable what we have encountered perpetually or frequently) and the presumption of uncommon, divided into presumption of fully uncommon (we presume improbable what we have never witnessed) and the presumption of rare (we presume improbable what we have rarely witnessed), and 
5. presumption of repugnant or unnatural (we presume improbable what is opposed to existent and sufficient causes).

Crusius still goes through methods for deciding what to choose when different rules of probability contradict one another – in essence, these methods rely ultimately on the very notion of probability. I shall already move on to the next subject, that is, the additional weight of non-cognitive issues or purposes and goals in deciding what is probable. Crusius notes that this new weight might be derived either from obligations involving prudence (do this if you want to achieve that) or from obligations of moral law (do this in order to follow the will of your ruler). In the first case, he explains, it might be prudent for us to act according to what is probable, while in the second case, we might be obligated to act according to what is probable. This is especially true when the probability is what Crusius calls infinitely large, when we can be certain that any future evidence will just reveal examples justifying its probability.

Crusius suggests that God specifically intended the humans to have only probable knowledge of certain key truths. Firstly, he explains, this is due to essential limitations of human nature, but secondly, God also wanted us to fulfil the duty of trusting God with less than perfect knowledge of the things. Indeed, Crusius thinks, even our belief in the veracity of demonstrations is often based on probability, especially if the demonstrations are very complex: we might have made an error following the demonstration once, but it is improbable that we have gone through its details many times and always found it convincing. In fact, he concludes, we often find probable arguments more convincing than demonstrations, since a single fault in our line of reasoning will make demonstration faulty, while probable arguments depend on an accumulation of many facts speaking for the intended conclusion, so that even if one supposed fact is revealed to be faulty, the whole argument does not stand on it alone.

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

Listing all the possible rules of deduction, Crusius thinks, is the only systematisation of the doctrine of deduction needed. Still, he will go through some prominent types of deduction, often just to note their name, but sometimes also to point out some interesting features of this type of deduction. He begins by dividing the whole field of deductions into existential and casual deductions, depending on the type of connection of ideas on which the deduction is based. Furthermore, he notes that many of the actual deductions we make are cryptic in the sense that the order in which we go through it in our thoughts differs from the order of the listed rule of deduction used in that deduction. I shall again mainly list out the types of deduction Crusius introduces and give further details only when he himself considers it important.

Verbal deductions

• Deduction of equivalence uses rule 3) to derive from the truth of falsity of a proposition the truth or falsity of a proposition differing from the first only by some contingent formality (e.g. order of the words: justice is a condition of healthy state, thus, healthy state has justice as its condition).
• Deduction of external abstraction uses rule 4) to derive from an essential relation of two concepts that the concepts can be applied in same contexts when adding some external abstraction (e.g. being learned implies being intelligent, thus, a learned person is an intelligent person).
• Objective deduction is a subspecies of the deduction of external abstraction, where the concept mentioned in premiss is regarded as an object of another thing (e.g. wisdom is useful => a person who despises wisdom despises something useful).

Hypothetical deduction

Two propositions called antecedent and consequent are connected to one another and it is deduced either that when one is true, the other is also, or that when the latter is false, the former is also. Crusius notes that hypothetical deduction is actually just a combination of two types of deduction:

• The first type is, Crusius thinks, actually one form of the deduction of external abstraction: one thing is a sign of another thing, thus, the existence of one thing signifies the existence of this other thing.
• In the other type, the connection is based on an ideal or even real causality between antecedent and consequent (e.g. if God is just, evil is not unpunished, but God is just, thus, evil is punished).
• Crusius notes that both types of hypothetical deduction divide again into two subspecies, depending on whether truth is derived from truth or falsity from falsity. The latter kind uses the rule 40): from a true proposition cannot follow anything false.

Some deductions using rules for logical subordination of concepts

• Deduction by induction uses the rule 21) to argue that something, which belongs to all individuals or species, belongs universally also to the genus. Induction divides into induction from species and induction from individuals.
• Dilemma uses the rule 20) to argue from the denial of all species or individuals to the denial of genus (e.g. if God would be variable in their decisions, they would not have known everything from eternity or they would not have considered many things correctly or they would have changed something against the rules of wisdom, but all three possibilities are absurd, thus, God is never variable in their decisions).

Disjunctive deduction

Crusius is careful to distinguish dilemma from disjunctive deduction, where the rules of contradiction are applied to a disjunctive premiss by denying one or several disjuncts. Crusius distinguishes three possible types of disjunctive deduction:

• Using rule 1) to argue from positing of one disjunct to the denial of others
• Using rule 2) to argue from denial of one disjunct to indeterminate positing of one of the remaining disjuncts
• Using rule 2) to argue from denial of all disjuncts, but one, to the positing of the remaining disjunct

Crusius notes that the disjunctive premiss can also be implicit, especially when the disjunction is obvious: then we are dealing with an immediate deduction of opposition. Crusius outlines two subtypes of it:

• Deduction of immediate opposition in predicate, where the implicit disjunctive premiss opposes a proposition to its contradictory opposite and the deduction goes straight from the truth of one to the falsity of the other, without even mentioning the quantity in the proposition (e.g. the world is finite, thus, it is not infinite).
• Immediate deduction of opposition of copula, where the implicit disjunctive premiss posits the possible determinations of copula against one another in regard to their quantity and quality, in other words, the premiss says that a predicate must hold of all, of none or only of some individuals of the subject.

Crusius distinguishes disjunctive deduction from deduction by force of opposition, which uses the rule 7) and starting from two adequate opposites, where one knows the definition one opposite and the commonalities of both, argues that in denying the differentiating element of one the differentiating element of the other subsists (e.g. truth and error are adequately opposed, truth is the relation of correspondence between thought and its object and error is also a relation of thought and its object, thus, in error thought and object do not correspond with one another). Crusius notes that this deduction has some preconditions:

• The two concepts must be adequate opposites, that is, there must be no other possibilities in their proximate genus, so that either they two opposites are contradictorily opposed, or if they are contraries, one must otherwise know or postulate that there are no other possibilities.
• We should know how much in common both things have and what belongs to their proximate genus.
• We should know the complete definition of the one opposite.

Conversions and contrapositions

Crusius defines conversion as a deduction where the place of the subject and the predicate is swapped in such a manner that because of the truth of the original proposition, the truth of the converted proposition must be admitted. Crusius notes the following types of conversion:

• Pure conversion, where the quality of the proposition (i.e. being affirmative or negative) is not changed and which uses the rule 25) to deduce from the relation of the subject to the predicate to the opposite relation of the predicate toward the subject. Crusius notes that the possibility of pure conversion is determined by the logical relation between the ideas. If the predicate belongs universally to the subject, it must be a genus or a proprium, and in the former case, the predicate is more extensive, and in the latter case, their extension is identical, and since the original proposition does not reveal which case we have, the converted proposition can have only uncertain particularity (e.g. all virtues are laudable, thus, at least something laudable is a virtue). One exception, Crusius insists, is formed of quantitative propositions where a magnitude is determined by another, where the predicate must be a proprium of the subject (e.g. if a line cuts another one perpendicularly, a right angle is generated, thus, if lines cross in right angles, they are perpendicular to one another). Crusius adds also the familiar rules that a particularly affirmative proposition can be converted particularly, a universally negative proposition can be converted universally and a particularly negative proposition cannot be converted.
• Pure conversion divides into conversion simpliciter, where the proposition is converted without a change of quantity, and conversion by accident, where the proposition is converted with change of quantity.
• Crusius divides conversion of quantitative propositions into simple conversion, where the subject remains as it is, and separating conversion, where the subject of the original proposition is composed of several characteristics, only of some of which convert to the predicate. For example, knowing that if two triangles fit in same apex and have parallel bases, they are similar, we can deduce by simple conversion that if two triangles are similar, they fit in the same apex so that they have parallel bases, or by separating conversion that if two triangles are similar and their bases are placed in parallel, they fit somewhere in one apex.
• Contraposition is, for Crusius, a conversion where the quality of the original proposition changes. Contrapositions of universal affirmative propositions, where the predicate is essential to the subject, use rule 11), (e.g. all humans have a reason, thus, what has no reason is not human). Then again, Crusius adds, negative propositions, whether universal or particular, can be contraposed into particular affirmative propositions by combining deduction of immediate opposition in predicate with a deduction of pure conversion, if the negative proposition is first turned into a contingently affirmative proposition (e.g. a swindler does not act correctly, thus, a swindler acts incorrectly, thus, some incorrectly acting people are swindlers).
• Crusius points out that contrapositions of universal affirmative propositions can in some cases, like conversion of quantitative propositions, be divided into a simple contraposition or a separating contraposition. Thus, from the proposition that with all humans, insofar as their mind is not too distracted or malicious, conscience has occasionally regrets, we can deduce with simple contraposition that if the conscience of some person has never regrets, they are too distracted or malicious, but also with separating contraposition that if the conscience of an unmalicious person never has regrets, they are too distracted.

Relative deductions

Relative deductions, Crusius says, use some of the rules 24)–27) and differ from conversions in that they involve more than merely the change of the places of subject and predicate. Crusius divides relative deduction into the following subtypes:

• Deduction by rule 24) from a relatum to the positing of its correlate (e.g. order that the God has created in the world is a means, thus, it has a purpose). Crusius notes this deduction presupposes first justifying that the relatum is truly a relatum.
• Deduction by rule 25 from a relation to an opposed relation, which involves more than just conversion (e.g. God is the creator of the world, thus, the world is created by God). Crusius notes that this type could also be seen a one form of the deduction of equivalence.
• Deduction by rule 26) that if an idea presupposes another and this other a third, the first presupposes the third (e.g. guilt presupposes law and law presupposes lawgiver, thus, guilt presupposes a lawgiver.
• Deduction by rule 27) from the similarity of a relation between A and B and between B and C to a relation between A and C, ignoring the grade of distance (e.g. the effect is later than the nearest cause and the nearest cause is later than the more distant, thus, effect is later than the more distant cause).

Crusius notes that we could define deductions from whole to parts and from parts to whole, which would use some of the rules 10), 12)–15), 18), 19), 22), 23), 41) and 42), but sees no benefit in classifying these deductions under one name.

Syllogisms

Crusius begins his study of syllogisms by again emphasising the need to respect the manifoldness of deductions instead of just reducing all of them into syllogisms. In fact, he is even against placing all syllogisms into one mold, stating that when logicians usually describe the characteristics of syllogisms, they often concentrate on just the syllogisms of the first figure, believing that it is enough to transform the other figures to the first figure.

Crusius himself distinguishes the first figure of syllogisms by calling them subsumption deductions: the meaning of the name is provided by the fact that they use the rule 16), based on the relation of subsumption between the subjects and the predicates of the various propositions. He does understand why subsumption deductions have been preferred over other types, since the basis of our reasoning or all the primary or formal deductions are subsumption deductions, and furthermore, all other deductions can be brought into the form of a subsumption deduction through the following steps:

1. transform illogical abstractions into logical abstractions with relative deductions
2. use other deductions, like deductions of conversion, equivalence and external abstraction, to transform the propositions into an appropriate form
3. if necessary, add identical propositions and transform them into logical propositions
4. make the rule used in the original deduction into the first premiss of the new subsumption deduction.

Despite this possibility, Crusius still thinks that other types of deduction are of value, because they reveal other types of abstraction beyond the logical one. If our understanding could make only subsumption deductions, he argues, our deductions would have a mere hypothetical validity, since we wouldn’t have in our possession the real grounds implicit in the rules of other deductions.

Unlike subsumption deductions, Crusius insists, other syllogistic figures use the rule 17). His account of these figures follows, for the most part, the usual routes. The most important differences lie in his treatment of the fourth figure. Crusius rejects the so-called Galenic syllogisms, since he thinks they provide nothing useful for us, because they are so complicated that our understanding never really uses them. Instead, Crusius includes in the fourth syllogistic figure deductions from the first premiss that concept B is a predicate with a relation of subordination to concept A and the second premiss that the concept C can be affirmed or denied of the concept B universally to the conclusion that C must be affirmed or denied of A with the same universality. One might think that this type of deduction differs not so much from subsumption deductions, requiring only the swapping of the places of the premisses for its reduction. Crusius explains his choice by noting that this fourth figure, unlike subsumption deductions, can be always applied to disjunctive propositions. Crusius mentions two types of such applications:

• We can abstract from all the disjuncts together a common concept and predicate it of the subject of the other premiss (e.g futile desires reach their object or not, and when they do, they make us lose our piece of mind, because the achievement of one desire leads to further desires, but if they do not, they also make us lose our piece of mind, because the inability to achieve what we desire generates pain, thus, futile desires always make us lose our piece of mind).
• We can abstract from each disjunct particularly something and predicate disjunctively these abstractions from the subject of the other premiss (e.g. if the futile desires make us act, they either reach their object or not, and if they do, they produce more futile desires, and if they don’t, they cause pain, thus, if futile desires make us act, they cause either further futile desires or they cause pain). This type of fourth figure, Crusius thinks, cannot be reduced to a subsumption figure, because these cannot have disjunctive subjects in their premisses.

Comparative deductions

Comparative deductions use rules 28) and 39), and often also rule 30), determining magnitude of something from the magnitude of its essence or sufficient reason. Crusius specifies following types of comparative deduction:

• Simple comparative deduction argues that because a concept forms the essence or the sufficient cause of another, their magnitudes are also proportional (e.g. the essence of virtue consists in the correspondence of a moral state of a person with the law, thus, the greater the correspondence, the greater the virtue; or another example: the sufficient cause of the magnitude of angle of reflection is the magnitude of angle of incidence, thus, the greater the one, the greater the other).
• In complex or applied comparative deduction, the magnitude used as an epistemic foundation for another magnitude is determined more precisely and from this is deduced the determination of the other. This can happen in two ways, first of which is to determine the magnitudes only by their relation to a third thing (e.g. the stronger the motivation, the more certain are the actions based on them; motivations are stronger in in true virtue, based on an obedience to God, than in mere apparent virtue, based only on self-love; thus, actions based on true virtue happen more certainly than those based on mere apparent virtue).
• In second kind of applied comparative deduction, which Crusius calls deduction from greater to smaller or from smaller to greater, or in some cases, from equal to equal (e.g. healthy person has greater capacity to avoid being tired than an one afflicted with sickness; even a healthy person will feel tired when putting an effort to meditation; a sick person will be even more certainly tired in meditating).

Some mathematical deductions

• Arithmetical deduction uses the rule 29) to argue that an integral whole increases or decreases just like the number of similar parts increases or decreases (e.g. 2 + 3 = 5, 5 + 4 = 9, thus, 2 + 3 + 4 = 9). Crusius notes that this deduction cannot be presented as a syllogism, because there is no subsumption, but all three propositions are complex relative propositions and the idea of equality is their predicate.
• Common algebraic deduction uses the rule 30) arguing from two magnitudes increasing or decreasing in the same proportion that their previous relation remains. The name of the deduction, Crusius explains, is chosen because in algebra this deduction is used in finding the unknown in equations (e.g. it is known that x + 1= 2y – 2 – subtracting 1 from both sides gives x = 2y – 3; furthermore, it is known that x – 1 = y + 1, thus, adding 1 to both sides, x = y + 2 => 2y – 3 = y + 2 = x; adding 3, 2y = y + 5, subtracting y, y = 5 => x = y + 2 = 7).

Causal deductions

Causal deductions argue according to rules handling causes and effects to a combination between a cause and its effect. Crusius notes that comparative judgements are no causal deductions, although they use one of the rules for causes and effects, because comparative deductions are used only for determining magnitude and they merely assume the causal connection of things. The ultimate foundation of all causal deductions, he thinks, are the principles of sufficient cause and contradiction, the latter insofar as it is applied to causes and effects. Crusius finds the following kinds of causal deduction:

• In a deduction of perfect causal abstraction, effect is understood from its cause through mere immediate propositions. These divide into further subtypes, first of which is causal deduction of perfect possibility that shows using the rule 34) that certain effects are possible, when assuming certain causes. This type of deduction, Crusius explains, is applicable in cases where the effect depends fully or partly on freely acting causes, whereby one can only search for sufficient motives and other grounds of possibility.
• The second subtype of the deduction of perfect causal abstraction are causal deductions from determining causes, using rules 33) or 35), where the effect is inevitable with the presupposed causes. This subtype divides further into hypothetical causal deductions from determining causes, where the effect must follow if the posited causes are present and no new causes or obstructions appear, and absolute causal deductions from determining cause, where it is presupposed that nothing can obstruct the causes.
• Another way to divide causal deductions of perfect causal abstraction, Crusius adds, is their simplicity or complexity. Simple deduction of causal abstraction abstracts through immediate propositions from the only represented acting cause of a substance its consequences (e.g. in a compressed elastic substance there is a striving to expand that is obstructed, thus, if the obstacle is taken away, the substance actually expands).
• Complex causal deduction explains an effect from the nature of several causes taken together. In order to be valid, it requires a distinct concept of the effect to be explained, description of one or several causes together with their activities, explanation of the nature of the object and its influence, and if necessary, the derivation of the nearest consequences of each through axioms and the rule of causal deduction. In addition, the effect to be explained should be able to be abstracted from all of these together as an immediate consequence in the final proposition of the deduction (e.g. the effect to be explained is how writing with feather happens; by writing one understands drawing certain lines on the paper that are after this distinguished by their colour from the other parts of the paper; the efficient causes are ink that is liquid and heavy, and feather that has certain shape and that is directed by the hand of the writer; the paper as the object must be level and have enough glue, so that it won’t break down; deduction: if the feather is put down and the fissures are pressed slightly from one another, a part of ink flows to the paper underneath, and since the paper is unbroken, the outdrawn ink remains on it, thus, in the very same order as the feather is moved are generated certain lines on the paper, which due to the outdrawn ink differ by their colour from the rest of the surface).
• Crusius also divides deductions of perfect causal abstraction into affirmative and negative. Affirmative deductions of perfect causal abstraction show that a certain effect is understandable from certain causes, while negative deductions of perfect causal abstraction show that this is not so. Negative deductions might argue that the given circumstances do not yet explain the effect as possible or unavoidable or they might even argue that the effect is not even possible in the given circumstances.
• In addition to deductions of perfect causal abstraction, there are also deductions of imperfect causal abstraction, where effect is not understood from its causes through mere immediate propositions, but a combination between cause and effect is still shown. Such a deduction can again be either affirmative or negative. In an affirmative imperfect causal deduction one argues from effect in general to the existence of a cause, or one argues something that belongs to possibility of an effect and judges that such is present in the cause by rule (human thinks, thus, there is a power to think in the human), or one argues that where precisely this cause is again present, precisely this effect must also follow.
• A negative deduction of imperfect causal abstraction either argues according to rule 37) from the dissimilarity of sufficient causes to dissimilarity of effects or conversely according to rule 36) from dissimilarity of effects to dissimilarity in their sufficient causes, or one argues according to rule 38) from the contrariness of causes to the contrariness of their adequate effects (e.g. fear and courage conflict one another, and courage makes one accustomed to adventure thus fear hinders the tendency to adventure).

Practical deduction

Practical deductions evaluate whether given means are in fact means for the given goal. Crusius points out that practical deductions do not use particular rules and are not distinguished from other deductions by their form, but only by their matter. Still, they need to be mentioned separately in logic, he argues, because if they are not particularly explained, certain common errors concerning them do not become evident.

Crusius notes that in speaking of practical deductions we should especially study the mediating causes, which are used by a person for reaching their goal and are equipped with capacities that can wholly or partly generate the goal. These mediating causes or means should be real grounds for the goal and they must be in the power of the acting person, at least so far that the person can direct the means to generate the goal. Sometimes the direction of the means requires the constant activity of the person (for instance, when a person reads books to become learned in a subject), but in other cases the person needs to just trigger the means, but not sustain them.

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.