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

Looking at the various classifications of propositions or judgements in the Classic German philosophers, it has become quite clear that while Wolffians were still rather distant from the classic Kantian division of judgements, Hoffmann’s classification resembled it more, while still having important differences. The classification of Crusius shares distinct similarities with Hoffman’s, but is still a bit different and perhaps a step closer to Kant’s.

Before introducing his classification, Crusius naturally explains what he means by a proposition: a representation of a relation between at least two concepts. This means, he argues, that all propositions have three essential parts: the concept to which the other concept is related (the subject), the concept related to the subject (the predicate) and the concept of their relation (the copula). Crusius makes the further remark that in the simplest form of a proposition “A is B”, the “is” is usually just partially an indication of copula (the relation between subject and predicate), while the implicit reference to the existence of B is actually part of the predicate. Still, he adds, we should not completely assimilate the notion of copula to that of predicate, since the idea of relation of concepts is so essential to that of proposition. Furthermore, he notes, in some propositions the copula might contain more than just this word “is”. Of the two other components of the proposition Crusius notes that the subject is by nature the concrete concept, from which the predicate is abstracted, but in actual propositions their roles might be reversed or at least reversible.

Crusius suggests eight divisions of propositions – quite a lot more than Kant will do. The first point of division, Crusius begins, is suggested by the fact that a proposition relates at least two concepts, which provide then the matter of the proposition. He implies that propositions could thus be divided according to disciplines they relate to, but adds that this does not concern logic. Still, he says, some divisions are necessary, firstly, between propositions expressing judgements of our understanding (e.g. rock is hard) and those expressing certain volition (e.g. I want you to come here). Crusius divided the first class or that of enunciative propositions in a manner reminiscent of Hoffmann to nominal propositions connecting concept to a name (e.g. first emperor was Augustus), ideal propositions representing conceptual connections (e.g. physical extension presupposes actual parts) and real propositions connecting concepts to existence or existent things to concepts (the example of the first case would be “there are immaterial substances” and of the second “my soul can reason”). Some of the ideal and real propositions concern concrete individuals – hence, they are called individual propositions, which are either simple individual propositions (e.g. Earth is round) or combined individual propositions, in which the subject represents a collection of several individuals (e.g. Athenians fought at Thermopylae). Propositions that are not individual concern then abstractions from individuals.

The next three points of divisions concern in some manner the copula of the proposition as the relation of two concepts. Firstly, Crusius begins, we must see what type of relations the concepts could have to one another and these correspond to types of subordinations. Thus, he first divides propositions into relative propositions, such as “the higher presupposes the lower”, and non-relative propositions that then divide into existential and causal propositions. Existential propositions divide into five subclasses: propositions of existential abstraction, which combine only externally connected concepts, such as sign and what they signify (“when my teeth hurt, it will rain”), propositions of metaphysical abstraction, where subject is a subject in a metaphysical sense and predicate is something subsisting in it (“a body has a shape”), propositions of mathematical abstraction, where one concept is an integral part of the other (“triangle has three sides”), propositions of qualitative part, where one is not a mathematical part, but a qualitative part of the other (“a reasoning soul has a capacity to speak”) and propositions of logical abstraction, indicated by the word “is” (“human is an animal”). Causal propositions, on the other hand, divide into propositions of ideal and real causality. Crusius notes that a proposition of ideal causality, such as “if two persons equal in their height a third person, they equal in their height also themselves”, differs from a proposition of external abstraction, because in the former the subject of the proposition (the first proposition) is the ground of the predicate (the second proposition), while in the latter the subject is only the sign of the predicate. He also divides propositions of real causality into physical propositions stating efficient causes (“Sun warms the Earth”), moral propositions stating means (“willingness to learn from others is a means to wisdom”) and mathematical causal propositions stating relations of determination between magnitudes (“two sides of a triangle and an angle inscribed by them determine the rest of the sides and the angles”).

The second point of division related to copula concerns the question whether the relation between subject and predicate exists or not, which Crusius calls, as Kant later, the quality of the proposition. It is not surprising that Crusius divides propositions in this sense to affirmative and negative, but a more peculiar is his point that both affirmative and negative propositions can be such contingently or in themselves: for instance, “God is not mortal” is in itself a negative proposition, because it expresses the non-relation of God to a concept of mortality, while proposition saying exactly same, namely, “God is immortal”, is contingently positive proposition, because it expresses the relation of God to a negated concept of mortality. Crusius explains that such contingently affirmative or negative propositions are possible only with logical propositions, with mere “is” as a copula. With other types of propositions, he says, a similar transformation would change the truth of the proposition: for example, it is a completely different thing to say that a good conscience makes one joyful and that a good conscience makes one nothing more but joyful. Furthermore, Crusius notes that in common speech a contingently negative proposition implies that the predicate belongs to the subject only in a mediocre grade, for instance, saying that someone is not unskilled implies that they are only mediately skilled.

Contingently affirmative and negative propositions are infinite propositions – another term Crusius shares with Kant – that is, propositions with negative concepts as predicates. Then again, Crusius appears to imply that there can be infinite propositions beyond contingently affirmative and negative ones (and unlike Kant, he does not treat infinite propositions as forming an independent class besides affirmative and negative propositions). Indeed, he adds, it is sometimes unclear and even dependent on context whether a proposition is infinite or not: “cows cannot learn to speak” seems like a regular negative proposition, but if it is used in a deduction with a premiss “that which cannot learn to speak, although having means for it, has no reason”, it works like an affirmative infinite proposition.

Crusius divides negative propositions further into incomplete and complete negations, depending on whether the negation is still taken as doubtful or assumed to be certain. The distinction is useful, he explains, because only complete negations demand proving. Furthermore, he adds, sometimes further obligations might force us to act according to incomplete negations, as if they were complete negations: for instance, if we could not with utmost certainty prove that there is only one God, but we did have some grounds to suspect it, we would still be obligated to believe that this is so and worship only one God. Just like negations, Crusius suggests, affirmations can also be incomplete or complete, which he deems to an especially important distinction in case of propositions concerning possibilities: for example, when we say that it is possible that some stars move and do not seem to move because of their distance, this is an incomplete affirmation, but when we say that it is possible that affections make people furious, this is a complete affirmation.

The final point of division regarding copula, Crusius states, concerns the grade of the relation between subject and predicate. Crusius calls this division one of modality – this is another term shared by Kant. We have already seen earlier that Crusius recognises six forms of modality: essential relation, natural relation, contingent relation, merely possible relation, unnatural relation and impossible relation. Interestingly, Crusius regards the division of properties into universal and particular – what he calls a division according to the extension of propositions – as a mere imperfect expression of the division according to modality: a universal affirmative proposition is either an essential or natural proposition, while a universal negative proposition is unnatural or impossible.

The next real point of division – fifth, if you haven’t been counting – concerns the possibility that a proposition might consist of more than two concepts, which occurs, Crusius suggests, if a proposition is a combination of several propositions. This combination might be just rhetorical, for instance, made just because of shortening the expression (“gold is heavy and yellow”). Then again, the combination might be necessary in the sense that the constituent propositions alone would not say the same thing and might even contradict their combination: these combinations Crusius calls logical. The logical combinations require then two concrete concepts, from which something is abstracted.

Following Hoffmann, Crusius suggests that this double abstraction can happen in such a manner that both of the concrete concepts are contained in the subject, from which the predicate is abstracted: both Hoffmann and Crusius call these composite propositions according to subject. This class includes, Crusius explains, hypothetical propositions, where the subject is of a form “A, if a proposition x holds” and thus connected only conditionally to the predicate (“the price of grain, if the harvest is good, will fall”). Then again, he adds, it also contains cases where the subject is a combination of coordinated concepts, of opposed concepts, of seemingly, but not truly opposed concepts and of subordinated concepts. In the case of coordinated concepts, we might be dealing with copulative propositions where the predicate is an absolute concept (“heat and oxygen cause eruption of fire”) or with composite relative propositions where the predicate is some kind of relation (“two plus two equals four”). If the concepts are opposed, Crusius calls the proposition exceptive (“no one but God is omniscient”), and if they are just seemingly opposed, extensive (“all bodies, even the thickest, have pores”). Finally, if the concepts are subordinated, this subordination concerns the whole essence in reduplicative proposition (“law as a law differs from a mere rule”), an essential part in explicative proposition (“human beings, regarding their souls, are immortal”), a contingent circumstance distinguishing a particular species of the more universal concept in specificative proposition (“reasoning souls, even without bodies, retain distinct concepts”) or a contingent circumstance forming a mere external abstraction in determinative propositions (“humans, when getting older, become weaker”).

Needless to say, the double abstraction can also happen according to predicate, Crusius explains, when we first abstract or at least try to abstract something from a subject and then again abstract something from the relation of the first abstraction to the original concrete concept. This double abstraction, he continues, might result in a disjunctive proposition saying that only one of two predicates will belong to a concept. Then again, it might also merely serve to determine original predicate further, in the already familiar reduplicative propositions (“electors choose the emperor as the emperor”), explicative propositions (“sciences improve soul, when it comes to understanding”) and determinative propositions (“Christians were persecuted, during the first three centuries”) – specificative propositions do not occur with predicates, Crusius insists, because the seeming examples of such are mere rhetorical combinations.

The final three points of division can be dealt with quickly. First of them concerns the certainty of the propositions: a proposition can be certain (its opposite cannot be true), merely probable (there are more reasons for it than for its opposite), reliable (it is safe to act according to the proposition) or merely possible (there are no grounds for or against the proposition). The second point of division concerns the expression of the proposition: the expression agrees with the sense in a regular proposition or not in a cryptic proposition. The final point of division concerns a relation between different propositions: they can be equivalent (perfectly or imperfectly, that is, in some context, but not in others), subordinated (one can be deduced from the other), opposed (either contrary or contradictory) or completely unrelated.