After propositions Crusius proceeds in a rather conventional manner to deductions or arguments, where the truth of a conclusion is based on the assumed truth of premisses. He underlines that the conclusion of a deduction is not held to be true because of its content, but because of the specific relation it has to these premisses. Thus, Crusius suggests distinguishing this relation as the form of the deduction from its individual propositions (that is, premisses and the conclusion), which then work as the matter of this deduction, while the form provides the rule that the deduction follows. He also emphasises that although we can express deductions in words and usually communicate them to others through this medium, this use of words changes nothing essential in the proceedings and can therefore safely be ignored.
Before going on to classify the rules followed by different deductions, Crusius suggests investigating the first principles on which all these deductions are based on. He begins from the capacity of human understanding to think, combine and separate concepts, but notes that it has its natural limits: there are certain seeming concepts or their combinations or separations that we cannot think of. Since human souls strive naturally toward perfection, Crusius argues, and in case of understanding this implies a natural drive to truth, we should follow this natural disposition and accept as true (and respectively as false) what we cannot think as anything but true (and respectively as anything but false).
All our thoughts originally derive from external sensation, Crusius begins his study of these natural dispositions. External sensation provides us with concepts of objects, and as long as a distinct sensation continues, he underlines, we are forced to think of these objects as existing and present. Such an external sensation also makes our internal sensation active, and through this internal sensation, Crusius explains, we become conscious of characteristics, parts and circumstances of external sensations. Then again, he adds, such external sensations induce in us also other concepts that are not externally sensuous and that lead us to universal propositions that we should think as true.
It is no surprise that the first of these universal propositions Crusius mentions is the so-called principle of (non-)contradiction. He at once adds that this proposition as such is just identical, saying nothing more than that what is, is, and what is not, is not. Thus, Crusius argues, the principle of contradiction requires the establishment of further concepts, to which it can be applied, in order to make any use of it. The established concepts might not refer to anything real, he states, and then the applied principle of contradiction has a merely hypothetical reality. Hence, Crusius insists, we must know from elsewhere that the concept in question refers to something real.
Crusius suggests as a further rule for the establishment of concepts following the essence of our understanding: combining concepts that the sensations represent as combined or that we are necessitated to think as combined, because disappearance of one makes the other one vanish also, and similarly separating concepts that sensations represent as separated. Concepts established in this manner generate propositions that are not identical and form the positive core in our knowledge, Crusius thinks: every force is in some subject, all that is generated is generated by a sufficient cause, every substance exists somewhere and at some point in time etc.
Crusius insists that these propositions are not merely derived from the principle of contradiction, but adds that this does not mean that these propositions are not certainties: it is merely a question of how they are generated in our understanding and how we thus come to know them. Furthermore, it does not mean that we could not deny the opposites of these propositions through the principle of contradiction, but only that this principle is not sufficient for establishing the concepts involved. Finally, it does not mean that the principle of contradiction itself would be uncertain, but only that it is empty and thus not the only principle of human certainty. For example, Crusius explains, the principle of contradiction easily explains that every effect presupposes a cause, but only because by an effect is meant something generated by a cause and thus the concept of effect involves the concept of cause. Furthermore, he adds, the concept of effect still refers only to a hypothetical reality, since we do not know what things are effects: even seeing something being generated doesn’t tell us that it is an effect, since causeless generation is just absurd, but not contradictory.
The argument of the emptiness of the principle of contradiction is probably targeted against the Wolffian school, who were famous of basing intricate ontological truths on it (of course, it might well be, and I’d argue that it is so, that especially Wolff himself referred by the principle of contradiction to a stronger principle that is not identical, but this is beside the point here). Crusius still finds some reasons why anyone would hold the principle of contradiction to be the only principle of our knowledge. Firstly, he says, demonstration from the principle of contradiction seems comparatively easy, since otherwise we would have to use internal sensation and attention to account for the physical possibility or impossibility of our thoughts. Furthermore, Crusius thinks, the principle is the only fundamental proposition required for pure mathematics, and someone might want to extend the indubitable certainty of that discipline to the whole of knowledge. Finally, he concludes, we are more used to deducing from already presupposed concepts than searching for the ground of reality in the establishment of concepts.
The true fundamentals of all our deductions, for Crusius, are then three propositions: the principle of contradiction (nothing can both be and not be at the same time and in the same sense), the principle of inseparability (things that cannot be thought without one another cannot exist without one another) and the principle of incompatibility (things that cannot be thought together cannot exist together). He adds at once the cautionary remark that while the first principle is indubitable – no understanding could think of any contradictions – the two others might mislead us, since due to our finite nature, we are sometimes incapable of thinking things that an infinite understanding can think. Especially if the two principles are used to contradict the very principle of contradiction, Crusius underlines, we should reject this use as unfounded. Furthermore, he adds, revelation by a higher form of understanding can show us truths we cannot comprehend: thus, we should accept such a revelation, especially if we can have at least a symbolic concept of what is described by the revelation. Crusius gives as an example the case of limits: we can never think anything existent without the notion of limit, but this does not mean that something unlimited couldn’t exist, just that we are too limited to think about it. Similarly, although we cannot think of two pieces of matter existing in the same place, this does not mean that God could not be omnipresent in every part of the universe.
Crusius proceeds to explain how the other true propositions can be generated from the three principles. Firstly, he begins, we can apply these highest principles to propositions discussing certain characteristics of objects that we cannot think without these characteristics: the connection between the object and the characteristic forms then an axiom. Then again, Crusius continues, we can also apply the three principles to such relations between propositions, where one proposition must be true if the other propositions are assumed to be true: this relation is inscribed in some rule of deduction or argumentation. Just like axioms are immediately connected to the three principles, the rules of deduction connect all the other true propositions to them, he concludes.
The justification of axioms and rules of deduction, Crusius insists, is an example of what he calls a subsumptive deduction, where the conclusion concerns a concept or an individual or a set of individuals contained in a concept that is the topic of the premisses. Yet, he clarifies, this does not mean that all deductions should be subsumptive, unlike the Aristotelian tradition had assumed. Indeed, he separates primary or formal deductions, which justify axioms and rules of deduction and are always subsumptive, from secondary or material deductions, which concern more specific topics and which might not be subsumptive. Thus, Crusius exemplifies, while we can subsumptively deduce from the principles the rule that if a cause brings about a whole, it brings about its essential parts, when the rule itself is used, the resulting deduction is not subsumptive. True, he admits, all deductions can be transformed into a subsumptive form, but this is just jugglery that hides the essential manifoldness of types of deduction.
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