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.

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