I am sure a majority of enthusiasts of classic German philosophy are just not so thrilled when they see yet another classification of proposition or judgement types rearing its head.Indeed, it might seem a rather peculiar obsession, but it makes some sense – after all, judgements are what reason is all about, so it should be pretty important to get its types right. Being familiar mostly with post-Kantian developments in the topic, getting to know the stance of judgement types in the pre-Kantian German philosophy has been rather revealing – some of the supposed innovations of Kant, like the addition of infinite and singular judgements, were actually quite widely accepted part of the discipline, some things Kant accepts without further ado, like modalities, are a rarity, and then there are judgement types Kant doesn't even mention. All this minutiae shows the richness and variety of the logical tradition before Kant, which was then trimmed down into the strict three-times-four division.
Before jumping onto Hoffmann's division of propositions, let's first take a look what he has to say about them in general. The psychological basis of logic comes to the fore very strongly in Hoffmann's idea of propositions. For Hoffmann, proposition is not just any ordinary combination of ideas, but reflects the order of actual thought or abstraction. Thus, one part of proposition, the subject, is the ground of abstraction, from which the predicate in then abstracted. A necessary consequence of this line of thought is that every proposition has a natural subject and a natural predicate, and it might be that e.g. the order in which the proposition is announced hides this, for instance, when we say that ”redness is the property of a rose” or ”world was created by God”.
Since Kant, we are accustomed to the dictate that only form of a proposition or judgement should matter in classifying it. In Hoffman's psychologistic view of propositions it is quite natural that matter of the propositions – or what objects the proposition refers to – should have something to say about classifying a proposition. This may sound rather anti-Kantian, but Hoffmann's material division has a Kantian twist. Hoffmann says that the proposition might refer to an idea and its name, several ideas or idea and its object – or then to some combination of the three. Thus, we get three types of propositions: nominal, ideal and real (and mixed). So, nominal proposition would be something like ”first emperor of Rome was called Augustus”, ideal proposition might be ”all triangles have three angles” and a real proposition could be ”God exists”.
Reason why this material division is important is that especially the difference between two latter types is quite important for defeating the Cartesian or ontological proof of the existence of God. This proof, Hoffmann insists, manages to show at most an ideal proposition that an idea of God is necessarily connected with an idea of existence. Yet, it cannot be a foundation for a real proposition, because a connection between ideas is not yet a connection with some actually existing object. Note how closely Hoffmann's reasoning resembles Kant's notion that mere positing of a combination of concepts does not yet mean absolute positing of the concept as existing. It is quite common knowledge that Kant had the idea even in his pre-critical period, but who knew someone else had had similar thoughts before Kant?
Moving on from the material side of propositions, we at first come to their qualities or the mode of combination of the subject and the predicate. Now, Hoffmann notes, even this combination has a material quality – it might be either existential or causal combination. Note how far we are going from what we understand as logical divisions. Of the two kinds of material quality, the existential combination is closer to what we would call a logical relation. Indeed, one type of existential combination Hoffmann calls logical: here predicate is an aspect that characterises all of subject, like in the proposition ”bodies are extended”.
Then again, existential propositions might be unlogical: the predicate might be a distinct part or aspect of the subject, like in a sentence ”humans have understanding” (note the different copula). Unlogical existential propositions then divide into various classes. We have metaphysical propositions, in which subject is the ground of the subsistence of the predicate, like in a proposition ”extended thing has a figure”. Then again, subject might be an essential whole and predicate its part: this is the case in qualitative existential propositions, exemplified by ”human soul has understanding”. In case of mathematical existential propositions, like ”triangle has three sides", the subject is mathematical whole for the predicate, while in case of proper quantitative propositions, like ”year has 365 days”, subject is an integral whole. Finally, proposition might be properly relative, in which subject and predicate are non-independent abstractions in comparison to one another – this is exemplified by proposition ”scientific discipline has an object”.
Causal propositions have also further classifications. The connection between subject and predicate might be physical (Sun makes us warm), moral (if you want this, you should do that) or mathematical (angle and sides determine triangle).
That accounts for the division of propositions according to their matter and the material aspect of its quality. The final three criteria are more formal and sufficiently similar to Kantian classification. For instance, we have the formal aspect of the quality – whether the combination between ideas is subordination or opposition – which leads to a natural division of propositions to affirmative and negative (unlike some Wolffians, Hoffmann doesn't really consider infinite judgements to be independent part of the classification of propositions, although he does mention them passingly).
Similarly Hoffmann divides propositions according to the quantity of things they refer to (we would call it extension), in quite predictable manner to universal, particular, singular and indefinite propositions. Hoffmann also mentions modalities, but merely to note that modal divisions reduce to combinations of divisions according to extension and quality in its formal and material sense.
Final criteria of division concerns then the quantity of ideas within a proposition. The basic classification here is a division to simple propositions, with at most two ideas (if there is only one idea, the proposition is also identical), and to complex propositions, with more than two ideas. Hoffmann then divides complex propositions depending on whether the complexity occurs in subject or predicate – that is, remembering Hoffmann's psychologistic notion of propositions, whether we abstract from a complex of ideas a single idea or whether we abstract from a single idea many different ideas. This description leads Hoffmann to many original directions.
Let's start from the case in which the subject side of the proposition is complex. This might mean, firstly, that the subject or the ground of abstraction is a complex of propositions – this happens in a hypothetical proposition. Here, we might have as a ground a proposition ”A is B” and the idea of C and abstract from C and the precondition ”A is B” a predicate D – that is, announce that if A is B, then C is D. What if instead of different subjects in the propositions, we would have only one subject common to the two propositions? If the connection between A and B is uncertain, then, Hoffmann says, the complex forms a hypothetical, but if A certainly is B, then there's no hypothesis or assumption and proposition sounds more like ”A, as a B, is C”, in which subject side of the proposition consists of a complex of ideas.
More precisely, a proposition of the type ”A, as a B, is C” is one in which B is subordinated to the A, which is supposed to be its ground. An extreme case is such where the subject term is merely repeated twice, like in a reduplicative proposition ”humans as humans are able to speak”, which emphasises that is just their humanity that makes humans able to speak, not just their animal nature. Then again, the second subject term might be an essential or natural attribute of the first subject term, like in an explicative proposition ”actions as caused by free will are either good or bad”. The second subject term might also be an actual or possible accident of the first term, like in a specifying proposition ”all actions, when based on free will, are judged through moral law”, or it might be an external abstract of the latter, like in a determinative proposition ”sense organs, when near a certain object, sense it”.
Of course, it might be that the two subject terms are not subordinated. They might instead be coordinated. This is true, for instance, when A and B are correlatives in a relation – we might, say, picture the relation of whole and part and note a certain feature of that relation. An important subspecies of such complex relational propositions are comparative propositions of the form ”A is better than B”: Hoffmann is probably thinking that we should analyse these propositions as saying ”A and B are such that first is better than second”. This is all actually well in line with how relations are handled nowadays – a relation is a predicate for several objects.
In addition to relations, coordinated subjects appear in copulative propositions like ”reason and free will make human beings capable of morality”. Hoffmann's psychologistic notion of judgements makes it actually impossible that copulations or conjunctions would appear at predicate side of the proposition – either it is a case of a proposition with the correct form hidden (that is, the true subject or the two grounds of abstraction are said after the true predicate or their common abstract) or then we have just two propositions externally connected (because mere ”and” implies no intrinsic reason for connecting two predicates of the same subject). Similar restriction applies also to e.g. comparisons, because apparent exceptions, like ”Alexander conquered more of Asia than of Europe”, implicitly have a converse structure ”Asia and Europe are such that Alexander conquered more of first than the other”.
The two ideas in subject side could be subordinated or coordinated, but they also might be opposed or have no particular relation. In the first case, we get exclusive propositions, like ”all propositions of science, except axioms, must be proved”. In the second case, we get extensive propositions, in which the second subject appears at first sight to break the relation to predicate, but then actually doesn't – a good example might be ”all sinners, even the most sinful, are capable of salvation”. Since the two subject terms cannot have any other relation to one another, this concludes the account of all the possible complex propositions, in which complexity resides in subject side.
Hoffmann's clear desire of completeness leads him to fill his account with division of complex propositions, in which complexity lies in predicates. While in case of a complex subject side, the terms might have been equally essential, of the predicates one must be more primary than the other, or otherwise we do not have one case of abstraction, but of two completely unrelated abstractions. Thus, in these complex propositions, one at first abstracts one predicate from subject and then abstracts another predicate from the connection of subject and first predicate. Here the first predicate might only be implicit, like in the famous question ”have you stopped beating your mother”, in which the predicate ”stopped beating your mother” presupposes an implicit predicate ”have beaten your mother”.
In case of both predicates being explicit, there must be some relation beyond mere coordination, in order that the two predicates form one instead of two propositions. One of these possible relations is subordination, and here we get same reduplicative (”universities make scholars, as scholars”), explicative (”discipline is good for a human being, as having free will”) and determinative propositions (”it rained yesterday”), as in case of complex subjects. The other possible relation is opposition, which forms an essential ingredient of disjunctions of the form ”A is B or C”. Just like conjunctions couldn't occur in the predicate side, Hoffmann thinks that disjunctions cannot occur in subject side, because subject as the ground of abstraction cannot be more indeterminate than the predicate.
This concludes Hoffmann's division of propositions. Next time we see what he has to say about proofs.