Crusius finally begins the proper study of logic, after the introductory chapters, from the theoretical part, studying powers and activities of understanding (Verstand) that make the knowledge of truth possible. By truth he refers to the correspondence of thoughts with their objects, or to put it more precisely, such a relation between an understanding that thinks and the object it thinks, so that if the former thinks that the something about the object is, is not, is possible or impossible, this something respectively is, is not, is possible or is impossible also independent of this thought. Crusius emphasises that in this definition one should not speak of the object being something independently of the understanding, since the definition should apply also in cases where the object handled is understanding itself.
Crusius notes that truth must be distinguished from both error and ignorance, where error means a lack of correspondence between thought and its object, while ignorance means a lack of any thought about a topic. In other words, we cannot speak of truth if there is no thought that has ideally exactly that which object has really. Crusius underlines that we are speaking here only of truth in its logical meaning, and in addition, there is also a notion of truth in moral or ethical sense, that is, truthfulness, which means correspondence of a state of mind with the intended meaning of external signs that are used for communicating this state of mind. Finally, Crusius also points out that sometimes we speak simply of truth, when we actually mean some true proposition.
Crusius notes that when an object is compared to an understanding, this understanding can be either a possible understanding or an actual understanding that has some knowledge of the object. In the former case, he clarifies, we are speaking of objective or metaphysical truth, which means thus truth or possibility of an object itself, insofar as it is regarded as something that could be known by any understanding, while the latter is then subjective or logical truth, which means truth in an actually existing understanding or such a relation between a representation and its object, where the representation and the object correspond and thus some truth is known. Furthermore, Crusius notes, all objective truth is subjective in relation to divine understanding.
In human understanding, Crusius continues, all subjective truth is generated by the impossibility to think opposite of what one is conscious of, where the impossibility can happen in all cases or only in the current conditions. He notes that our first thoughts are always sensations, while other thoughts are then abstracted from sensations, so that we become thus conscious of relations between our thoughts or propositions and can attend to them. Furthermore, Crusius says, when we attend to what we can and cannot think, we generate a very special kind of propositions or rules indicating awareness of deductive relations: if certain propositions are connected in certain manner through the ideas they contain, we are bound to take one as true, if we take the other as true. With such rules, we receive a capacity to make deductions with such rules. Now, Crusius argues, since we know the truth of every proposition from the falsity of its opposite, all knowledge of truth in human understanding happens through deduction, although we are usually not aware of these deductions, because they happen so easily.
On the basis of the previous considerations, Crusius states that subjective knowledge of truth in human understanding is dependent on the capacities of sensation, abstraction and deduction. According to him, these capacities are physical, hence, we can abstract physical laws from their use. In a similar vein, since these capacities are under the control of our free will, the laws of free will can also be abstracted from their use. Thus, Crusius concludes, the human understanding can find truths concerning the whole created world (both the physical bodies and the free will), if it just follows its own nature.
Conclusion that Crusius thinks he has proven is that human understanding works just fine by its own nature, even without any further education. Then again, he at once admits, errors are in this case possible, because our representations of the rules of deduction are obscure. Logic is thus required to make understanding more capable of knowing truth. In its abstract sense, Crusius explains, logic is a science that represents distinctly and exactly the effects and laws of understanding and thus shows its correct use. Logic has also, he adds, a concrete sense, according to which it is a capacity of a subject to know fundamentally the effects and the laws of understanding and its correct use.
Crusius considers the capacity of our understanding to work and thus to know truth without logical education and calls it natural logic, which means thus an inherent feeling of true and false that generates a capacity to evaluate grounds for and against something. A person with good understanding can thus recognise through this natural feeling, if some suggested laws and rules of understanding are untrue, which Crusius takes as a justification that incorrectness of suggested logical laws can be shown also a posteriori from experience, just like in arithmetics. Yet, he adds, there are more differences of opinion in logic than in arithmetics, since reflection on kinds of abstraction and on grounds of truth is more difficult than thinking about more concrete topics. This difficulty makes humans ignore the investigation of their understanding and thus rely too much on their natural logical capacity, which has a tendency to error. The wilful ignorance is furthered, according to Crusius, because treatises of logic seem to be so far removed from the use of understanding in practical life.
Logic teaches the kinds of abstraction and methods of knowledge, thus, Crusius thinks, it is the only means to make cognition sharp. He even calls logic the soul of philosophy and scholarship, because it makes them correct and distinct. Because of logic, he underlines, knowledge is fruitful, and logic gives understanding the ability to know truth and evaluate judgements, hence, it strengthens our capacity to study. In effect, Crusius concludes, logic is the subjective foundational science, just like metaphysics is the objective foundational science.
Crusius identifies two weaknesses in natural logic, which the proper logic can fix. Firstly, he says, when we are dealing with complex topics, natural logic is not enough for distinguishing true from false and for arranging our studies in a suitable order. In other words, he explains further, when we use natural logic for dealing with a complex topic, we might find material for justifications or grounds, but we still cannot give them the proper form, that is, place them in such relations that would make them justifications of something. The result would then be, Crusius insists, that we may end up suggesting many grounds or justifications that in their current state do not justify anything. He thinks that this is especially true with probable proofs, where recognising true and false is more difficult. The conclusion of Crusius about the first weakness is that the natural logic is applicable only, on the one hand, in common tasks of human life, where object is characterised with sensuous properties, and on the other hand, in distinguishing moral good and bad, because our understanding of good and bad is supported by conscience and a feeling of guilt. The second weakness Crusius finds in natural logic is that the lack of proper logic often leads to errors and even outright scepticism.
Crusius goes on to divide the parts of logic. First of these parts is, according to him, the theoretical part that handles grounds that make the knowledge possible in the human understanding, and in addition, must also consider the powers of human understanding and its effects or concepts, propositions and deductions. The study of the powers of human understanding Crusius calls noology, necessary truths of which belong also to metaphysics. Crusius also emphasises that noology needs to investigate only what lies in the soul, together with the general features of the dependence of certain effects of understanding from the body. Then again, external conditions of sensations in bodies belong to the study of nature.
The other or practical part of logic, Crusius says, explains how the powers and effects of understanding should be used for the purpose of truth. It also deals with the illnesses of these powers, the experience as a modification of the power of sensation, use of concepts in divisions and definitions, use of propositions in judgements, and use of deductions in proving, recognition of seeming proofs and decision over colliding proofs. All the effects in unison, Crusius adds, are handled by the study of method and also in some special topics, such as interpretations, special kinds of probability and disputation.
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