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

After propositions, Crusius naturally progresses in his applied logic to proving, where a proposition (the conclusion) is held to be true because of its relation to other propositions assumed to be true (the premisses). This relation, he explains, is formed by a chain of deductions, and while the premisses could be called the matter of the proof, the deductive chains are similarly its form. Crusius points out that there is a clear hierarchy what can be proven from different kinds of propositions: thus, a nominal proposition about mere words cannot be used to derive ideal conclusions about possibilities, let alone real conclusions about the existence of things, while ideal propositions cannot be used to back up real conclusions. He also notes that proofs can have different purposes: sometimes we just want to see what follows from assuming some premisses as true – this could be called a hypothetical proof – while at other times we truly want to establish the truth of the conclusion – this is then an absolute proof.

Crusius goes through several ways to classify proofs, starting with whether the proofs use only the proposition of contradiction or whether they rely also on the two other fundamental propositions. Furthermore, he adds, proofs can be divided according to whether the method used is the demonstration or the method of probability. The first kind – demonstrative proofs – can then be combined with the classification of the first sentence, so that we gain the concepts of geometrical demonstration, which uses only the highest fundamental proposition, and disciplinary demonstration, which takes advantage also of the two other fundamental propositions.

Crusius also divides proofs in a priori, a posteriori and mixed proofs. Of these, he explains, a priori proof establishes not just that the conclusion is true, but also why it is true. A priori proof can also be what Crusius calls a hypothetical a priori proof, which tries to develop a conclusion implicitly contained in some premisses, or an absolute a priori proof, where the conclusion is intrinsically connected, but not implicitly connected with the premisses. The names of these subtypes is explained by hypothetical a priori proof being also hypothetical in the sense of merely explicating the premisses, while the absolute proof should establish truths through the mere fundamental propositions and axioms immediately dependent on them, such as those involving causal powers of things.

A posteriori proof, then, means for Crusius a proof which establishes only the truth of the conclusion without explaining it. As is to be expected, he includes all proofs dependent on experience in this class, but somewhat surprisingly also the so-called proofs ad absurdum, where a conclusion is derived by showing that the supposition of its falsity leads to absurd conclusions (of course, the latter do not explain why something is the case).

Crusius includes also a third kind of or mixed proof, which should be in some sense a priori and in another a posteriori. His paradigmatic example of such a proof is those found in geometry, where objects according to some defined concepts are postulated to exist and then the existence or characteristic of some objects is established. Such proofs are first and foremost a posteriori, since they do not really explain the conclusion – that’s why Crusius calls them mixed a posteriori proofs – but the method is still a priori in the sense that the justifying ground of the proof is comprehended from the mere idea of the proposition to be proved.

All proofs should prove the truth of their conclusions, Crusius says, but not all of them establish the necessity of the conclusion. A priori proofs, he states, always do this, but the degree of necessity depends on the necessity of their grounds: thus, Crusius notes, if we want to prove the existence of something absolutely necessary, it must be proven a priori from the properties of God. When it comes to other kinds of proof, he states, deductions ad absurdum and mixed proofs prove the necessity of their conclusions, while proofs from experiences prove only the truth of their conclusions.

Observing the purpose of proofs, Crusius notes that they either prove something from the standpoint of truth and try to establish some conclusion as true, or then they prove from the standpoint of humans, that is, indicate what a person must admit, if they accept something as true. Another point of division concerns the question whether the proof uses only the tools of understanding or whether it aims to justify some course of action and is thus dependent also on moral issues.

With these divisions out of the way. Crusius goes on to explicate some rules on how proving is to be effected. Thus, he says, we should begin with the preliminaries of making all the concepts distinct and analysing the required conclusion. If we want to prove the existence of something, Crusius underlines, we have to base the proof ultimately on experience, which is our only criterion of existence. This does not mean that we can use only a posteriori proofs for this, since we can also use an a priori proof to justify the existence of something from the existence of something else, for instance, through causal connections.

Proofs are based on premisses, but should the premisses then in turn be justified? Crusius notes that all true scholars are committed to linking all conclusions that we want to proof with the highest grounds of all thinking. Yet, he admits, in individual scholarly treatises such long chains of proof are cumbersome and we should, in case of proofs aimed for convincing certain persons, not go further than what our opponents consider acceptable, and in case of proofs aimed for establishing some truth, not go further than to certain postulates that require no further proof and to lemmas from other sciences.

With such basic rules established, Crusius moves on to discuss fallacies, which he quickly admits is a topic, the various types of which need not be learned – and although he then proceeds to list various types of fallacies, this listing shows almost nothing of interest, so we can skip it over. What is more interesting is the notion of colliding or conflicting proofs, which Crusius has inherited from Hoffman and which bears striking resemblance with the so-called antinomies of Kant. In effect, Crusius defines colliding proofs as a case where we have various proofs that seem trustworthy by their form and matter and have the necessary signs for truth, but these proofs also lead to conclusions that cannot all be true at the same time. The colliding proofs are not fallacies as such, because proofs with similar properties are reliable in some contexts, but not just in this particular case.

The first question is, Crusius notes, how colliding proofs are possible: how can a proof have all the signs of being true, without being so always? One problem here is, Crusius explains, that something cannot be both true and false at the same time. His answer is to distinguish objective from subjective truth: objectively considered, nothing can be both true and false at the same time, but what is objectively false can still be subjectively true, that is, have signs of truth, but only in a restricted sense. Another problem is that colliding proofs seem to refute our capacity to know what is true, if we cannot rely on signs of truth. Crusius points out that these signs of truth do work, but with restrictions.

What then are the particular reasons for the appearance of colliding proofs? One special reason Crusius picks out are the latter two of his fundamental principles and all propositions based on them, which are reliable within their limits, but lack the completely universal validity of the law of contradiction. Thus, he explains in more detail, although these principles hold of finite things, they might have exceptions with infinite, which is not just different from finite things by some quantitative degree, but by its essence. Furthermore, Crusius adds, even if these principles hold of things in the known parts of the world, we do not know whether things are different in other parts of this world or at least in another possible world. Crusius concludes by assuring the reader that God must have had a good reason for making these principles work only within these restrictions, and any errors are just an unavoidable side effect. Besides, he adds, the collisions are a clear criterion, by which we know we have overreached the limits of our knowledge.

Crusius adds that not all collisions indicate fundamental restrictions of our knowledge, but some of them are generated by following principles that are not yet fully determined, so that we are not aware of all restrictions for their application. This happens, he suggests, when we are dealing with complex cases, where it is too hard to think all details at once and we have to just take the most usual details and abstract a universal rule from them, for instance, when in moral questions we cannot evaluate all factors, but have to assume a universal rule to decide at least something. Furthermore, Crusius notes, we might also just not have ever dealt earlier with cases where the restrictions of these principles become obvious: he gives as an example the development of Christian philosophy, where tenets of the religion have required the introduction of new restrictions to old principles followed universally by pre-Christian philosophers. Finally, Crusius points out the particular case of causal deduction, where we might still lack the full knowledge of some object and its influence, so that we are forced to be satisfied with what we have experienced and presume that things will follow the same course in the future.

Moving on to the collisions themselves, Crusius notes that they can involve formal principles used as signs for possibility, existence or connection of things. Such formal collisions happen especially in metaphysics, he adds, and they are the closest to the later Kantian antinomies. Crusius reminds the reader that these collisions always involve something more than just the law of contradiction, which allows no exceptions. Thus, the colliding proofs use principles that show something to be incomprehensible for us, although this incomprehensibility might just reveal the restrictions of the human mind. Crusius especially emphasises the force of obligation to decide, which of two seemingly equal proofs is to be accepted: for instance, he suggests, although the notion of freedom involves much that goes beyond our comprehension, we should accept it, because only freedom can explain the existence of divine law and moral guilt.

Crusius also thinks that the law of sufficient cause can never contradict the law of contradiction and proofs based on the first law are thus to be preferred over other proofs. For example, he explains, although the notion of creation of the world seems incomprehensible to us, we must accept it, because the world is such that it requires some ultimate causes.The final case of formal collision Crusius investigates involves using an otherwise reliable principle that in a particular context would force us to remove certain features of a thing, without which it could not be thought. For instance, he exemplifies, if we assume that a thing A can be divided infinitely, an actual infinite division would mean removing such intrinsic features of A, like its extension.

Just like some collisions involve just formal principles, Crusius explains, other collisions concern only the material propositions used in the proofs. Such collisions, he notes, occur when investigating efficient causes, especially in questions of morality. Crusius goes to great lengths to establish how to solve such moral dilemmas. To put it short, it all hinges on first analysing what justification each of the colliding proofs is based on and then finding out some principles of higher kind, on which to test the justifications of each proof. Even with this method, Crusius admits, moral collisions are often left undecided, because no satisfactory higher ground can be found.

Crusius, Christian August: Road to certainty and reliability – Analysing obscure propositions

Having investigated how to define and divide concepts, Crusius turns next to the question what applied logic has to say about propositions. He notes that most perfections and imperfections that propositions could have do not require specific rules, since they would concern the whole logic. The only topics left to consider in this regard, Crusius says, are rules for avoiding obscurity in propositions and rules for analysing propositions into their constituent propositions.

Starting with obscurities in propositions, Crusius notes the most prominent reasons why a proposition is obscure. These reasons include ambiguity of words and concepts belonging to two different genera. Crusius exemplifies the latter with one of his pet peeves: when we speak of grounds of something, we might be talking of causes or of existential grounds.

A specific case of obscurity Crusius mentions involves words indicating some quantity, like great or best. Such words create obscurities, he explains, if we do not have any clear measure to which to compare them (thus, if I say that this is the best world, this is still obscure, since we do not know on what scale this goodness is measured on). Even more obscure the case becomes, if instead of one quantity we have several and we do not know what it is we are talking about (for instance, if someone is said to have good memory, it is unclear whether e.g. they are quick to memorise things or whether they retain for a long time what they have memorised).

Moving on to the second topic or logical analysis or exposition of propositions, Crusius means by this showing what other propositions are thought at the same time when a certain proposition is thought distinctly. He notices at once that logical analysis does not mean going through all propositions that can be deduced from the proposition-to-be-analysed, if they cannot be thought with this original proposition. This does not mean that the propositions found through analysis need to be explicitly observable in the analysed proposition, Crusius adds: for example, although it is not evident from the form of the proposition, all real definitions include an implicit statement that the subject of the proposition exists or is at least possible. Similarly imperatives include also implicit propositions about the will of the speaker and often even indications of moral necessity.

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

After definitions, Crusius moves on to divisions, in which a more extensive logical concept (genus) is separated into narrower logical concepts contained in it (species and in rare cases even individuals) adequately, in other words, in such a manner that all individuals of the genus belong to one and only one of the divided species. Crusius is clear to distinguish division from mere distinction of concepts in general, which could be applied also to concepts that are not logical (say, when distinguishing cause from effect). He also points out the obvious fact that the divided concept is more undetermined and the narrower concepts go through all the possible determinations that could be attached to the divided concept.

Just like definitions, Crusius divides divisions into nominal and real kinds. By nominal division, he means an account of different meanings an ambiguous word has. In addition to this definition, nominal divisions are not of that much interest to Crusius, who deals more with real divisions, where species or individuals contained in an abstract concept are separated from one another. Crusius notes that real divisions come with four important elements: firstly, we have divided and undetermined general concept, secondly, the narrower concepts, into which the general concept is divided or determined, thirdly, the difference between the different members of the division or the narrower concepts, and finally, the point of division in the undetermined concept, to which the narrower concepts or separated species relate as further determinations. Crusius states that this point of division can be an existential or causal abstraction, and in the former case, an external or internal abstraction.

Crusius points out many reasons why we need to make divisions, first of them being that division brings abstract concepts closer to practical applications. Furthermore, he adds, if we did not have a clear idea of a hierarchy of a general concept dividing into many species, we would have to make do with mere individuals, with no idea of their commonalities, thus being deprived of many important truths. Yet, the main use Crusius envisions for divisions lies in their application in disjunctive deductions.

Crusius goes through the most prominent classifications of real divisions. Thus, real divisions are either divisions of logical oppositions or divisions of real oppositions and also either divisions of contraries or divisions of contradictories. Furthermore, Crusius notes that if we compare divisions applied to the same general concept, these alternative divisions can be subordinated – one division applies the other division and then divides its members further – or coordinated, that is, made according to completely different schema.

Besides these classifications, Crusius hands out some rules, such that the point of division should optimally be essential to the divided general concept and that in choosing from different alternative divisions, we should consider what is the most useful of them. Finally, he shares some methods for finding divisions, such as following experiences of differences or going through possible determinations and causal connections of the general concept to be divided.

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

If in the previous chapter Crusius dealt with the application of sensations and experience, he now turns his attention toward abstract ideas, which due to their non-concreteness are prone to confusion and might even not correspond to anything existent. Thus, he argues, abstract concepts should always be defined. By definition Crusius means a method of making objects of an abstract concept distinguishable from other objects. Definition needs therefore not reveal the fundamental essence of a thing. Still, it is something more than mere description, which just collects some distinctly abstracted predicates of a thing, which still are not sufficient to distinguish the thing from others, except perhaps in some limited context.

Crusius goes on to indicate some basic rules about definitions. Definition, he says, should contain only concepts that belong to the defined object always and are thus logically essential to it. This means that the concepts contained in a definition are either genera or propria, which in case of definitions are usually called specific differences. Furthermore, Crusius continues, these logically essential concepts can be either essential as such to the object defined or just natural, which then have to be used sparingly and always with the appropriate restriction that they belong to the object regularly and are lacking only in extraordinary cases. Some of the logically essential concepts, he adds, are essential to the object in themselves, but others only when we suppose the existence of the world.

Parts of a definition, Crusius explains, must be more distinct than the defined object, in other words, obscure concepts should not be defined by other obscure concepts. Especially metaphors and circular definitions should be avoided. Even so, he admits, the parts of the definition need not be fully distinct, just more distinct than the object defined. Crusius adds also that a definition must be adequate in the sense that it contains all the same individuals as the defined concept and nothing more.

Crusius divides definitions according to their purpose: the purpose of a nominal definition is to explain what a word means through an abstract idea separated into its constituents, while the purpose of real definition is to transform an obscure or at least concrete concept into an abstractly distinct and adequate concept. A clear consequence of these explanations is that the same definition can be nominal and real, depending on its purpose.

Starting with nominal definitions, Crusius notes that they should be used to define something possible, because it would be of no use to have a word that refers to something that could not be thought. Indeed, he adds, nominal definitions should in general be useful, which implies that they should not give occasion to error and confusion and should conform as much as possible to ordinary language Crusius emphasises also that nominal definitions can be used only to deduce nominal conclusions, how a word can or must be used.

Crusius divides real definitions into ideal definitions, which define only something possible that need not exist, and real definitions in the strict sense, which transform a concrete idea of an existing thing into an abstract and adequate idea. Beginning with ideal definitions, he notes that they are not to be confused with nominal definitions, which define only a name of something. Still, they are also not yet real definitions in the strict sense, because they cannot be used to deduce what really is or is not, but only hypothetical conclusions: what must be affirmed or denied when we presuppose the existence of objects corresponding to this concept. Of course, if we show that there exists something agreeing with the ideal definition, we have made it a real definition. Crusius also notes that in pure mathematics ideal definitions are always real definitions, since this discipline investigates abstract possible magnitudes with their properties and relations.

Real definitions in the strict sense, finally, are divided by Crusius into fundamental or first concepts and deduced or further definitions. By a first concept he means a definition that we can know without presupposing a proof from another definition. Crusius emphasises that a first concept is thus first only for us and need not be a natural ground for all other properties of a thing. Indeed, he adds, there could well be many first concepts, depending on what characteristics is our starting point for abstractions.

It depends on the thing in question where we should find their first concepts, Crusius explains. With physical, non-artificial entities (e.g. natural bodies and souls), the crucial question, according to him, is whether they are sensuous or not: with the former, the sensations provide us enough first concepts, while with the latter, we must just begin with the most undetermined idea. With artificial entities, the first concept is provided by their method of generation, and if they particularly are mechanical entities, the first concept is given by their immediate purpose and the structure required for this purpose. With moral entities (e.g. obligations and rights), Crusius notes, their first concept is defined by their purpose. Finally, he concludes, God and their activities can be defined only by symbolical concepts, indicating negatively what they are not, or pointing positively to their effects and to very indeterminate abstractions common to all things.

An important point for Crusius is that we should always demonstrate that a first concept does really refer to objects beyond our thought (if we couldn’t do that, it wouldn’t be a real definition, but only nominal or ideal). He does explain that in some cases we might not be speaking of physical, but of moral existence, in other words, that something should be the case (this is evidently what we should prove of moral entities). In any case, the proof can happen a posteriori from experience or a priori from connections between concepts or grounds.

The final type of real definition – that of further or deduced definitions – includes, Crusius says, many useless explanations that really add nothing to the first concept and even confuse what is meant with them. He delineates two useful kinds of deduced definitions, namely explanations of the essence of things, which serve to uncover the fundamental nature of the thing defined, and characteristic definitions, which help to distinguish individuals belonging to the defined class from others.

Starting with the explanations of the essence of things, Crusius notes that they might provide the physical ground – fundamental forces that constitute the defined thing – or the moral ground – explanation why the defined thing should or is allowed to exist (the traditional explanation why God allows the existence of sin is of this kind). In searching for these explanations, he adds, we might either start from a sensuously given first concept and then move to the grounds explaining these sensuous properties, or then we can start from an undetermined first concept of a non-sensuous or a moral thing and determine it in more detail.

Ending his discussion with characteristic definitions, Crusius explains that they are required, whenever the first concepts do not give us enough criteria for deciding how to apply these concepts. Examples of such characteristic definitions are criteria for deciding when something is true or false, criteria for deciding when some law applies, or criteria for recognising the existence of non-sensuous entities from their effects.

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

Crusius sets out as the aim of the practical part of his logic to show how to apply the capacities of understanding for knowing the truth. In order to do this, he explains, we must investigate, on the one hand, sensations or experiences, and on the other hand, judicious use of abstract ideas (memory and ingenuity, he thinks, require no rules). Starting from experience, Crusius notes that the word can refer to two things: to a certain kind of proposition and to an act of experiencing. He mostly deals with the propositions of experience, having only few things to say about the act of experiencing, and I will also focus on the former.

As a proposition, Crusius continues, experience means an immediately sensed connection of subject and predicate. Depending on the kind of sensation, the experience can then be either external or internal. Crusius underlines that internal experience should not be confused with axioms or immediate propositions. We are conscious of all propositions through internal sensation, he explains, but only such propositions are axioms, where we immediately sense an essential connection between the subject and the predicate, so that when the predicate is denied, the concept of subject must also disappear. On the other hand, a mere internal experience is a proposition where the subject and the predicate are internally sensed as existentially connected.

Although it would be natural to assume that in all experiences both the subject and the predicate would have to be sensuous, that is, ideas generated through sensation, without the aid of any abstraction, Crusius notes that we can sense also a mere existential connection of such objects that are thought through abstract ideas. Thus, he divides experiences into common and reflecting experience, based on whether the subject and the predicate of the experience are sensuous or abstract.

Crusius states that the certainty of the propositions of experience are shown by his earlier demonstrations about the certainty of our sensations. Of course, he adds, it is still a possibility that what we think is a proposition of experience contains something else, for instance, imaginations and even outright impossibilities, connected to obscure and incomplete sensations. Thus, Crusius concludes, we need some rules to decide when we have a true proposition of experience in front of us. Thus, while experience teaches us that in certain circumstances certain representations are generated in us, a proposition stating that something existing is connected with these representations is already dependent on further deduction. Other clear instances of propositions that cannot be propositions of experience, according to Crusius, are negative propositions (experience can only tell that we do not sense something), causal propositions (experience can only show connections between representations) and universal propositions (abstractions cannot be sensed as abstractions).

Crusius continues by noting that, according to experience, we do not sense simple substances nor their fundamental forces. This means, he explains, that we cannot sense the fundamental essence of anything, since things are divided into abstractions, simple substances and complex substances, out of which we can sense only the last one, and even in their case we cannot sense how they consist of simple substances, which we would have to do, in order to sense their essence. Many of seeming propositions of experience, Crusius concludes, are then only mixed experiences, that is, they require something added to sensations through proofs.

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.