From the general method of all research, Crusius moves on to the specific method of history. He thinks it evident that proofs in history can only use the method of probability: the links between the things in the world are so multifarious that we cannot discover the events from causes or causes from events through demonstration, and even where we could find the causes of some effects according to their essence, we could not find all circumstances of their existence. Furthermore, Crusius adds, the events of history are usually determined by the choices of free persons, while the method of demonstration can investigate only deterministic causes. Thus, he finds enough reasons to define a special historical probability, by which he means probability that helps us to distinguish justified accounts of the past from fabrications. Crusius believes that in innumerable examples of human life we have occasions of historical probability and that it often even changes into moral certainty. This means, he concludes, that we should be able to find ways to justify historical probability.
Crusius suggests several ultimate grounds of historical probability, starting with the assumption that especially fabrications, untruths and affectations reveal themselves quite easily, since it is not easy to create internally consistent stories, because fictional tales often clearly conflict with the known events of the real world and because our natural desire for truth makes it not easy for us to be fooled by deceptions. Indeed, he suggests that because of this natural desire for truth, people find credulity and deception shameful things and are therefore usually inclined to tell only such stories that they have judged to be true due to believable justifications. Thus, Crusius concludes, we should not presume that a historical account is groundless, as long as we know no particular causes that would weaken or even expressly refute the general presumption.
Of course, Crusius adds, this presumption has different degrees, depending on who is giving the account, and is especially strong in regard to public records. He notes that each person usually acts according to their status, for instance, a person who has been deceitful before is not to be trusted. Furthermore, Crusius continues, the easier it is to believe something to be possible or the more internal probability something has, the stronger is its trustworthiness. Here the particular method of historical probability points back to the general theory of probabilities: probability increases greatly, the more we have justifications and the more harmonious they are with one another. Even mere cognitive justifications might be enough for moral certainty, but links to purposes and obligations increases its strength, but no method of probability can be used further than its own justification allows, that is, when it is not weakened or even expressly refuted by opposed inferences.
Crusius notes that there are two things to evaluate with the historical justifications: firstly, the materials used as data for historical proofs, and secondly, their relation toward the suggested historical truth, the signs and grounds of which they should be. He points out that historical data can be of many types: not just history books and records, testimonies and accounts, but also memorials, coins, pictures, inscriptions, artifacts and even internal characteristics of the suggested events, that is, whether they are in themselves probable. Crusius states that first is to be investigated how certain the data are, sometimes through immediate sensations, sometimes through demonstrative grounds, but mostly through other probabilities.
Crusius reminds the reader that although we would have answered the question of the certainty of the data, we still wouldn’t have decided what the data can prove. This power of proof lies partly, he continues, in the existence and characteristic of testimonials of witnesses and in the characteristic of the things witnesses have told. Starting from the latter, Crusius explains that we should observe the possibility and the probability of things even before looking at the testimonials. Thus, he argues, we should consider the degree of possibility of the described event: for instance, are there many examples of similar things and are there clear causes that could have caused the thing at the context of that time. Furthermore, Crusius thinks, we should observe whether the suggested event has internal probability: whether it agrees with known physical and cultural circumstances or whether it contradicts them, whether the existence of such things is probable from general reasons etc. He also encourages to find any physical evidence corroborating what is told.
In addition to such internal characteristics of events, Crusius recognises testimonials as the other main source of historical proofs, whether they be testimonials of the experiences of the witnesses themselves or of someone else. He notes that we should observe whether the witness could have given a true testimonial. If they are speaking of something they have themselves supposedly experienced, do they have the required powers of sensation and attention, how much they could have actually sensed, what kind of obstacles their sensations might have had and how much time and attention the thing has required? On the other hand, Crusius adds, if we are speaking of something not directly experienced, but only inferred from something supposedly experienced by the witness (e.g. whether someone was angry), we must observe whether the witness has enough power of reasoning to do such inferences. Finally, he concludes, if the witness hasn’t personally encountered the thing they tell, the probability of their testimonials depends on the methods they have used to ascertin the truth of these tales and their capacities to use these methods.
Furthermore, Crusius continues, we should observe whether witnesses have wanted to tell the truth, that is, we should observe if for some reason it is easy to assume that they do not speak truth or whether some particular circumstances of the witnesses, such as their character, prevent this assumption. He also suggests considering whether witnesses could have deceived us, and if so, whether the deceptions have been done purposefully or due to witnesses themselves being deceived by others.
An important topic of investigation, according to Crusius, is whether testimonials agree with other testimonials – for instance, whether what the witness says here agrees with what they say elsewhere and with what other writers and historical records suggest. Even if a testimonial appears to be in contradiction with other testimonials, this seeming contradiction might be solved in other ways. If a testimonial cannot, for some reason, be compared with others, the events might still be remarkably probable for other reasons.
Crucius suggests some further rules to help in assessing historical probability of an account. Firstly, he notes, events that happen seldom or are in conflict with the natural characteristics of the causes in the world are internally improbable, thus, they require stronger historical justifications in order to become credible. Furthermore, Crusius points out, all justifications of historical probability can confirm each other reciprocally, that is, earlier events can confirm their consequences and consequences can confirm past events that caused them – we just have to know which of the two are more reliable and use them to justify the others. He also suggests that at least when dealing with events that could have been experiences, memorials of famous people provide stronger evidence for them than memorials of unknown people, while physical evidence, like coins, are generally more credible evidence than memorials.
Every testimonial has, Crusius reminds us, historical credibility, due to the presumption that people mostly speak truth, but this natural credibility can be weakened or even completely refuted by the circumstances or it can also be strengthened. Thus, historians should try to have as much information about the historical context, in order to better evaluate individual testimonies. Usually, Crusius notes, having several witnesses saying the same thing makes the account more credible, but if all the witnesses have heard the tale from the same source, their combined credibility is as great as the credibility of this source – unless, he adds, the witnesses have had more evidence, on which to base their belief in the original source. In any case, Crusius concludes, the character of the witnesses can weigh even more than their numbers.
Sometimes the credibility of testimonials is low, Crusius thinks. If a witness has not immediately experienced something, but merely makes a judgement that things have happened so and we cannot say what their judgement is based on, their testimony is as good as nothing. Also, if it seems quite possible that a witness could have erred or is speaking partially, they are to be deemed unreliable. Then again, Crusius states, if the witness gives an unforced account of a remarkably long, but still coherent series of events, this suggests that the tale is credible. Further indications of credibility, he suggests, are modest acknowledgements the witness makes of their own ignorance and sudden revelations of things the witness should have been quiet about (although the latter can also be, Crucius admits, a sign of a naive or a rash person).
Crusius warns that we should not confuse credibility of a single event and credibility of a historian in general. The latter can give credence to the former, but it is not the only possible justification for an event; besides, before becoming a credible historian, a person has usually established credibility of many historical events. Crusius also reminds the reader that they should distinguish between immediate and mediate witnesses. Immediate witnesses have themselves experienced something and then the question is, whether their experience has been complete enough and whether they have reported it faithfully. A mediate witness, on the other hand, has relied on the accounts of others, public records and other sources, and then the question is more about the credibility of these primary sources and about the ability of the mediate witness to use them without making things up on their own. Usually, Crusius thinks, immediate witnesses are to be preferred over mediate witnesses, although sometimes the immediate witnesses might not have had the opportunity to observe the event from all angles (for instance, a single soldier might understand less about the ongoings of a war than a researcher who has studied its course for a long time). Similarly, he points out, historians living closer to the time of an event are usually more reliable than later historians, but geographical distance, lack of understanding of the context (e.g. when a person of an upper class writes of the ongoings of the lower class) or partiality can weigh the balance on the side of the later historian.
Crusius thinks that historians relying on proofs lose their credibility, if we observe them using unwarranted sources or contradicting themselves. Then again, he states, mere unfortunate speculations about reasons of events do not destroy their credibility, if they just clearly distinguish these speculations from established historical events. If we are reading a work of an unreliable historian, Crusius continues, we should believe only such things, which seem in itself possible or probable or which are confirmed by other witnesses or justifications. He is also of the opinion that a single unfounded treatise should not make us suspect the historian in general, just like a single error should not make us suspect the whole treatise.
Crusius warns not to take a lack of mention of an event by historians as evidence of the event not happening. If we want to do so, he explains, we should show that there are no understandable reasons for their silence, such as a fear of state officials or religious beliefs, or we should show that being silent on a major event would contradict the character of the writers. Then again, much stronger evidence against the truth of some event than mere absence of mention, Crusius thinks, is provided by an account of a historian explicitly contradicting the supposed historical event.
This leads us to the question what to do, when historians give conflicting accounts. Crusius suggests that in these cases we must observe the individual circumstances of the writers: for instance, whether they count the time differently or whether they speak only of similar events. Sometimes nothing more is needed than clearer definitions of words, he assures the reader. Whatever we suggest for explaining the seeming conflict, Crusius underlines, we have to consider whether we want to show that the suggestion is true – then we need to prove it – or whether we just try to justify the credibility of the historians – then it is enough that our suggestion is a real possibility. Crusius concludes by insisting that a conflict of historians requiring explanation does not necessarily weaken the credibility of their accounts and a good explanation might even strengthen their credibility.
Crusius concludes the chapter with the question whether the length of time that has passed from the event takes away from its credibility. His answer is essentially negative: the existence of triumvirate in Rome is as believable now as it was during the age of Charlemagne. True, he admits, we might have less justifications to believe an event to be true, especially if we find new evidence to refute earlier accounts. Then again, the credibility might, on the contrary, also increase through new evidence, he notes, so that what was earlier just a widely spread rumor, might in the new circumstances become credible history.
maanantai 13. heinäkuuta 2026
keskiviikko 8. heinäkuuta 2026
Crusius, Christian August: Road to certainty and reliability – Research and teaching
Like the logic textbooks of the time often did, the final few chapters of the work of Crusius treat the question how to apply everything previously said to the practices of scholarly work. Crusius speaks more precisely of meditation, by which he means a process of extending our knowledge further from some fundamental thoughts. In addition, he considers also the related problematic of how to transmit the internal meditation to others in a scholarly treatise, which requires accommodating the results of meditation to their needs. Crusius also ponders the practices of disputation, but has not that much new and interesting to say about the topic, so we’ll ignore it.
Quite traditionally, Crusius distinguishes two different types of meditation: analysis, where we try to make our knowledge of the fundamental thoughts more distinct, complete and certain, and synthesis, where we progress from fundamental thoughts to other truths that are not its part nor grounds, but are merely inferred from it. He notes that both actual meditation and scholarly treatises use both methods and that sometimes even individual pages in treatises can have many occasions of both methods.
In the synthetical method, Crusius thinks, the fundamental thoughts studied must always be concepts, but the analytical method can also have as its object words, the meaning of which is sought out. Thus, he argues, the analytical method is divided into analysis of things or concepts and analysis of words or terms. Starting with the analysis of concepts, Crusius divides it again into analysis of parts, which sets out distinctly all the parts and internal determinations of the fundamental thoughts, and analysis of reasons, which looks for proofs for the fundamental thoughts and evaluates proofs suggested by others. The difference of the latter from the synthetical method, he explains, is that we are usually convinced of the proof of the fundamental thoughts and we just want to make this conviction more secure.
Crusius divides the analysis of parts again into merely resolving analysis, which sets apart distinctly just what is already in the fundamental thought, and determining analysis, which adds further determinations to what is still indeterminate in the fundamental thought. He calls the latter also mixed analysis, because it often has to use also the synthetical method, although for an analytical purpose. This determining or mixed analysis, Crusius explains, adds either determinations that belong to the object all the time and thus are part of its essence or determinations that belong to the object disjunctively through divisions.
Crusius notes that the methods of analysis of parts and analysis of reasons can also be combined. This combined method is especially used, he explains, with problems, where we start from given data and progress to the grounds, on which the data depends, and generate from the characteristic or quantity of the grounds the required characteristic or quantity. In this method, Crucius points out, the first move toward grounds is analysis of reasons, while using the grounds to make the previously unknown determination distinct is determining analysis. He points out that this method is especially used in mathematics, under the name of algebraic method, when we are asked for a magnitude of something and we determine it through other magnitudes, on which the first one depends.
Analysis of words or texts Crusius divides into three types. Firstly, it may be about interpreting a text, it may be about outlining the order or disposition of the text or it may be about evaluating the worth of the text. The interpretation is something Crusius will return to in the final chapter of the book, so he in this point merely divides disposition of text into natural disposition, which follows the goal of the author, and artificial disposition, which follows any convenient general concept, and divides evaluation of the text into evaluation of the writing style and into evaluation of the thoughts in it.
Crusius lists three kinds of synthetical method, which he names after the sciences prominently using them. First of them is the geometric or mathematical method, which takes as its starting point the concept of a possible essence. The second, then, is the physical or experimental method, which starts from propositions involving physical existence. The final one is the moral method, which begins with propositions involving moral existence. Crusius notes that the physical and the moral method together can be called the philosophical method.
Crusius goes through the different types of synthetical method in more detail, starting with the mathematical or geometrical method, where the possible essence it begins with is such that the existence of which is not yet posited or at least not yet considered. This method then proceeds to find out more about the relations and consequences of the essence and discusses problems following from these. Crusius notes that the specialty of the geometrical method is that it does not prove its definitions, but just postulates them as possible. Thus, he argues, propositions shown by it have only a hypothetical reality, which is enough for pure mathematics. Then again, Crusius points out, the geometrical method is used elsewhere, for instance, in studying the relations of possible essences.
The physical method, Crusius continues, starts from experiences or real propositions deduced from experiences – he notes that all existences must in the end be justified from experiences. The method then proceeds to other propositions involving physical existence or real possibilities. In other words, Crusius explains, the physical method moves from effects and properties of things, known by experience, to their causes, further effects and relations. The method is used, naturally, in physics and also in medicine, which Crusius takes to be a special subspecies of physics. He notes that this method is used also elsewhere, for instance, in revealed theology, where the Bible takes the place of experiences.
Moral method, finally, proceeds from fundamental thoughts to the purposes of things or from posited purposes to other purposes, whether these purposes concern human happiness or moral laws. In case of moral laws, Crusius thinks that we know them sometimes through sensation – when we are speaking of written or announced laws – and if we are speaking of natural laws, we can know them by deducing from experience, although he warns the reader not to confuse inferences from what makes us happy for a proof of moral law. Crusius also points out that studies of moral existence or possibility should not be confused with studies of efficient causes and means that make certain conditions of mind possible or actual, because the latter demand the physical method. Then again, he adds, most moral topics also require these physical investigations.
Crusius states that the synthetical method cannot be applied before the fundamental thoughts are distinct and known to be real or at least possible, which presupposes that we know definitions, experiences and other propositions. Definitions in particular, he says, should at least be resolved into axioms, and if this is not enough, determining analysis is required. Thus, Crusius argues, both analysis and synthesis are required in meditation, but synthesis presupposes analysis. Furthermore, he continues, each thing must be studied according to its nature. For instance, existence must be studied analytically and especially through determining analysis or synthetically with physical or moral method or often by both means, while study of essence requires mathematical method or analysis.
Crusius also gives some general guidelines on how to go about in meditation of things. A central concept here is the theme of meditation, by which he means its main or objective purpose. The theme is either simple – a concept, a proposition or a problem – or composed of many simple themes. If the theme is something arbitrarily made by humans, Crusius says, we should check whether it is useful to investigate it. With naturally generated things this check is not required, he thinks, because knowledge of such things enriches the sciences and influences many truths.
In order that meditation will be useful, Crusius explains, we should already have some capacities for meditation, which requires a diligent and thorough study of logic. In addition, he notes, meditation requires materials, which are supplied by preliminary knowledge that helps to form concrete ideas, both on the general structure of all sciences and particularly on sciences close to the theme investigated. Crusius also instructs the reader to learn about history, because historical knowledge can provide experiences and understanding on causes of many possibilities.
After gathering this preliminary knowledge, Crusius explains, the meditation starts by directing attention to the fundamental thoughts and trying to think them lively and ever more perfectly. This means, he adds, reflecting on and analysing examples that fit the concrete ideas, together with the opposites of these examples and the predicates that are ascribed to the examples through the concrete ideas. In addition, we should recollect what we have heard and read about the topic and perhaps collect more experiences about it. When all of this is done, Crusius suggests, we should draw an outline of the meditation to guide our imagination, by determining the main points in the theme, to which meditation should be directed.
Once we have fixed the purpose of meditation, Crusius insists, we should make a special theme about the requirements of the method. This means, firstly, he explains, planning a good order for the meditation or the treatise made through it. The general rule, Crusius says, is to start with that without which the following cannot be understood, at least not as conveniently. This does not mean, he clarifies, that nature would determine the place for each thought so precisely that they could not change their places, because there’s much arbitrary in the order of meditation and scholarly treatises.
Something peculiar to treatises, in opposition to meditation, Crusius suggests, is that although in meditation scholars should be ready to reduce everything to first grounds of all sciences, it would be too difficult to do that for every proposition and often superfluous in the eyes of the reader. Still, he adds, we should not assume as familiar what is doubtful and we should try to find justifications even for familiar truths, especially if this is a key to finding desired truths, or to shying away from difficulties.
Crusius suggests that the working of themes is easier, when their main points are classified and ordered under a few titles – he calls this classification by the Aristotelian term topics. I shall skip this part of the chapter, because it consists mostly of titles of the treatise to be made.
Quite traditionally, Crusius distinguishes two different types of meditation: analysis, where we try to make our knowledge of the fundamental thoughts more distinct, complete and certain, and synthesis, where we progress from fundamental thoughts to other truths that are not its part nor grounds, but are merely inferred from it. He notes that both actual meditation and scholarly treatises use both methods and that sometimes even individual pages in treatises can have many occasions of both methods.
In the synthetical method, Crusius thinks, the fundamental thoughts studied must always be concepts, but the analytical method can also have as its object words, the meaning of which is sought out. Thus, he argues, the analytical method is divided into analysis of things or concepts and analysis of words or terms. Starting with the analysis of concepts, Crusius divides it again into analysis of parts, which sets out distinctly all the parts and internal determinations of the fundamental thoughts, and analysis of reasons, which looks for proofs for the fundamental thoughts and evaluates proofs suggested by others. The difference of the latter from the synthetical method, he explains, is that we are usually convinced of the proof of the fundamental thoughts and we just want to make this conviction more secure.
Crusius divides the analysis of parts again into merely resolving analysis, which sets apart distinctly just what is already in the fundamental thought, and determining analysis, which adds further determinations to what is still indeterminate in the fundamental thought. He calls the latter also mixed analysis, because it often has to use also the synthetical method, although for an analytical purpose. This determining or mixed analysis, Crusius explains, adds either determinations that belong to the object all the time and thus are part of its essence or determinations that belong to the object disjunctively through divisions.
Crusius notes that the methods of analysis of parts and analysis of reasons can also be combined. This combined method is especially used, he explains, with problems, where we start from given data and progress to the grounds, on which the data depends, and generate from the characteristic or quantity of the grounds the required characteristic or quantity. In this method, Crucius points out, the first move toward grounds is analysis of reasons, while using the grounds to make the previously unknown determination distinct is determining analysis. He points out that this method is especially used in mathematics, under the name of algebraic method, when we are asked for a magnitude of something and we determine it through other magnitudes, on which the first one depends.
Analysis of words or texts Crusius divides into three types. Firstly, it may be about interpreting a text, it may be about outlining the order or disposition of the text or it may be about evaluating the worth of the text. The interpretation is something Crusius will return to in the final chapter of the book, so he in this point merely divides disposition of text into natural disposition, which follows the goal of the author, and artificial disposition, which follows any convenient general concept, and divides evaluation of the text into evaluation of the writing style and into evaluation of the thoughts in it.
Crusius lists three kinds of synthetical method, which he names after the sciences prominently using them. First of them is the geometric or mathematical method, which takes as its starting point the concept of a possible essence. The second, then, is the physical or experimental method, which starts from propositions involving physical existence. The final one is the moral method, which begins with propositions involving moral existence. Crusius notes that the physical and the moral method together can be called the philosophical method.
Crusius goes through the different types of synthetical method in more detail, starting with the mathematical or geometrical method, where the possible essence it begins with is such that the existence of which is not yet posited or at least not yet considered. This method then proceeds to find out more about the relations and consequences of the essence and discusses problems following from these. Crusius notes that the specialty of the geometrical method is that it does not prove its definitions, but just postulates them as possible. Thus, he argues, propositions shown by it have only a hypothetical reality, which is enough for pure mathematics. Then again, Crusius points out, the geometrical method is used elsewhere, for instance, in studying the relations of possible essences.
The physical method, Crusius continues, starts from experiences or real propositions deduced from experiences – he notes that all existences must in the end be justified from experiences. The method then proceeds to other propositions involving physical existence or real possibilities. In other words, Crusius explains, the physical method moves from effects and properties of things, known by experience, to their causes, further effects and relations. The method is used, naturally, in physics and also in medicine, which Crusius takes to be a special subspecies of physics. He notes that this method is used also elsewhere, for instance, in revealed theology, where the Bible takes the place of experiences.
Moral method, finally, proceeds from fundamental thoughts to the purposes of things or from posited purposes to other purposes, whether these purposes concern human happiness or moral laws. In case of moral laws, Crusius thinks that we know them sometimes through sensation – when we are speaking of written or announced laws – and if we are speaking of natural laws, we can know them by deducing from experience, although he warns the reader not to confuse inferences from what makes us happy for a proof of moral law. Crusius also points out that studies of moral existence or possibility should not be confused with studies of efficient causes and means that make certain conditions of mind possible or actual, because the latter demand the physical method. Then again, he adds, most moral topics also require these physical investigations.
Crusius states that the synthetical method cannot be applied before the fundamental thoughts are distinct and known to be real or at least possible, which presupposes that we know definitions, experiences and other propositions. Definitions in particular, he says, should at least be resolved into axioms, and if this is not enough, determining analysis is required. Thus, Crusius argues, both analysis and synthesis are required in meditation, but synthesis presupposes analysis. Furthermore, he continues, each thing must be studied according to its nature. For instance, existence must be studied analytically and especially through determining analysis or synthetically with physical or moral method or often by both means, while study of essence requires mathematical method or analysis.
Crusius also gives some general guidelines on how to go about in meditation of things. A central concept here is the theme of meditation, by which he means its main or objective purpose. The theme is either simple – a concept, a proposition or a problem – or composed of many simple themes. If the theme is something arbitrarily made by humans, Crusius says, we should check whether it is useful to investigate it. With naturally generated things this check is not required, he thinks, because knowledge of such things enriches the sciences and influences many truths.
In order that meditation will be useful, Crusius explains, we should already have some capacities for meditation, which requires a diligent and thorough study of logic. In addition, he notes, meditation requires materials, which are supplied by preliminary knowledge that helps to form concrete ideas, both on the general structure of all sciences and particularly on sciences close to the theme investigated. Crusius also instructs the reader to learn about history, because historical knowledge can provide experiences and understanding on causes of many possibilities.
After gathering this preliminary knowledge, Crusius explains, the meditation starts by directing attention to the fundamental thoughts and trying to think them lively and ever more perfectly. This means, he adds, reflecting on and analysing examples that fit the concrete ideas, together with the opposites of these examples and the predicates that are ascribed to the examples through the concrete ideas. In addition, we should recollect what we have heard and read about the topic and perhaps collect more experiences about it. When all of this is done, Crusius suggests, we should draw an outline of the meditation to guide our imagination, by determining the main points in the theme, to which meditation should be directed.
Once we have fixed the purpose of meditation, Crusius insists, we should make a special theme about the requirements of the method. This means, firstly, he explains, planning a good order for the meditation or the treatise made through it. The general rule, Crusius says, is to start with that without which the following cannot be understood, at least not as conveniently. This does not mean, he clarifies, that nature would determine the place for each thought so precisely that they could not change their places, because there’s much arbitrary in the order of meditation and scholarly treatises.
Something peculiar to treatises, in opposition to meditation, Crusius suggests, is that although in meditation scholars should be ready to reduce everything to first grounds of all sciences, it would be too difficult to do that for every proposition and often superfluous in the eyes of the reader. Still, he adds, we should not assume as familiar what is doubtful and we should try to find justifications even for familiar truths, especially if this is a key to finding desired truths, or to shying away from difficulties.
Crusius suggests that the working of themes is easier, when their main points are classified and ordered under a few titles – he calls this classification by the Aristotelian term topics. I shall skip this part of the chapter, because it consists mostly of titles of the treatise to be made.
perjantai 26. kesäkuuta 2026
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 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.
sunnuntai 14. kesäkuuta 2026
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.
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.
perjantai 5. kesäkuuta 2026
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.
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.
keskiviikko 3. kesäkuuta 2026
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 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.
perjantai 29. toukokuuta 2026
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.
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.
perjantai 15. toukokuuta 2026
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 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.
torstai 7. toukokuuta 2026
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.
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.
torstai 30. huhtikuuta 2026
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.
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).
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.
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.
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.
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:
- presumption or rarity (we presume improbable what happens only in rare cases),
- presumption of miraculous chance (we presume improbable what involves a chance coincidence of many possibilities)
- 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)
- 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
- 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 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.
lauantai 18. huhtikuuta 2026
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.
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:
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:
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.
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
- 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.
- 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).
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:
- transform illogical abstractions into logical abstractions with relative deductions
- use other deductions, like deductions of conversion, equivalence and external abstraction, to transform the propositions into an appropriate form
- if necessary, add identical propositions and transform them into logical propositions
- make the rule used in the original deduction into the first premiss of the new subsumption deduction.
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.
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