With syllogisms ends the theoretical
part of Wolff's Latin logic: we are not anymore just looking at the
various shapes human cognition can take, but actually think how to use
these various shapes. The practical part of logic begins then by
investigating truth, thus giving logic its purpose: it is true
judgements that we want to find, or at least truthlike or probable
propositions.

The investigation of truth began at
least with Aristotle's

*De Interpretatione*, where a judgement was said to be true, if what was said of the subject or topic of the judgement did hold of the topic: it is somewhat uncertain whether this is what nowadays is called a correspondence view or deflationary view of truth. This, of course, was just a definition of truth, which is not useful in telling when a judgement is true: this is work for the criterion of truth. Criterion was a particular interest of hellenistic thinkers, especially Stoics, who suggested that certain appearances were reliable basis for forming judgements, and their critics, Academicians and Sceptics, who noted that Stoics did not have a reliable criterion for recognizing these appearances.
Wolff makes this
distinction between definition and criterion of truth in terms of
nominal and real definitions: even if we can explain what truth is,
we still cannot reliably find truths. His nominal definition is at
first sight rather Aristotelian: proposition is true if and only if
its predicate applies to its subject. Yet, one might foresee some
difficulties: proposition should be linguistic entity, consisting of
words, is truth then nothing but a formal relation between words?

This question is
closely related to the supposed overreliance of Wolffian metaphysics
on logic, evidenced by his wish to base ontological law of sufficient
reason on logical law of contradiction. We have seen that this
overreliance has been just a misunderstanding, because Wolff viewed
even the law of contradiction in an ontological sense, as describing
the fight of incompatible possibilities over actuality.

Indeed, the
relation of the two disciplines is rather opposite, as Wolff thinks
logic to be an offshoot of metaphysics, particularly ontology and
psychology. Words are not just abstract marks with a peculiar syntax,
but produced by conscious beings and refer to possible thoughts of
those conscious beings – this is the link to psychology.
Furthermore, these thoughts are not just mental images, but represent
independent things – this is the link to ontology. Wolff can then
add another nominal definition of truth: judgement (or proposition
expressing it) is true, if and only if it coincides with the thing it
represents.

Now, it is clear
that this nominal definition cannot by itself tell whether a
proposition or judgement is true. Wolff's suggestion for the real
definition or criterion is at first sight rather perplexing: if
predicate is determined by subject, the proposition or judgement is
true. At first sight one might fail to see how Wolff's definition
makes sense. Consider an unconditional universal judgement, like
”humans are rational”. Here, Wolff continues, the subject or
humanity as such determines a set of predicates that apply to this
subject and one of these predicates happens to be rationality. The
problem appears to be whether this definition is then too strong, as
it seems to talk more of a conceptual, essential or necessary truth:
even if all actual humans would be rational, it might be that
humanity would still not imply rationality, because there could be
irrational humans. The problem is solved, if we consider universal
judgements as ranging over all possible worlds – or else, if we
suppose they have an implicit condition that we consider only the
actual world and its inhabitants.

The example above
accounts for how the criterion is about to be used for universal
propositions and judgements. Because affirmative and negative
propositions come always in pairs and one of them cannot be true,
while other is, negative propositions don't add anything new to the
equation. Same is true of particular propositions, because if some
rabbits are white, this just means that all rabbits under some
unspecified conditions compatible with being a rabbit are, that is, there are some properties such
that from the concept of a rabbit with these properties the concept
of whiteness can be deduced (and this combination of characteristics is not contradictory). If for some particular proposition or
judgement ”some Ps are Qs” no such conditions exist (that is, for
no M, such that ”Px and Mx” is possible, does "Px and Mx" essentially imply ”Qx”), then, because Q
itself would otherwise be one such M, Q and P cannot have any common elements or no P
is a Q.

The case is rather
different with singular propositions/judgements, which cannot just be
reduced to previous questions. The subject in question would be an
actual existent individual, which in Wolffian philosophy can exist
only within one possible world, actual or non-actual. The quest for
truth of a singular judgement, e.g. ”Peter writes a book” would
need to determine whether writing a book is something that is
currently happening with the complete concept of Peter, which in the
case of an individual boils down to seeing whether we could perceive
Peter writing something at the moment.

Wolff goes on to
note that this notion of truth is such that it is retained throughout
deductions, that is, if premisses are true, then conclusion must also
be true. As the starting points of a demonstration should be as true
as anything can be, demonstration appears to be relevant from an
epistemological viewpoint. Indeed, Wolff goes as far as to say that
demonstration is the only thing one requires for separating truth
from falsities – bold statement and apparently rationalistic, but
one must remember that Wolff does admit empirically verified
premisses in demonstration.

Wolff makes rather
curious connections between truth, possibility
(non-contradictoriness) and conceivability (capacity to form a
concept of something):he says that affirmative judgement corresponds
with a possible concept (negative judgement with an impossible
concept) and that one can conceive only true propositions. The first
connection is actually rather simple to understand. True affirmative
proposition, like ”gold is yellow” describes a possible complex
concept of yellow gold. Indeed, in the case of such a universal
proposition, the concept is possible in all circumstances, or the
combination of the two concepts is necessary, if we just have a
distinct enough concept of gold. Then again, a true particular
affirmative judgement, like ”some gold is pressed into coins”
describes a combination possible in some circumstances. True negative
universal proposition ”gold is not black” says that it is not
possible to think of black gold (even if we could think of a black
goldlike substance), while true negative particular proposition ”some
gold is not pressed into coins” tells that this combination is not
possible in some circumstances.

Conceivability
thesis then just follows from the definition that those propositions
are conceivable that one can form a notion of. In case of trying to
conceive yellow gold, the statement seems plausible, but what about
the proposition ”all gold is pressed into coins”, which is
clearly false, although one can think of gold pressed into coins?
Wolff's point appears to be that one cannot think of gold in itself,
without any further properties, as pressed into coins: gold coins is
gold under some circumstances and not generic gold.

Conceivability
forms a sort of transition from the objective notion of truth to more
subjective notion of certainty. No proposition is certain or uncertain in itself, but only in relation to some particular person:
if I know whether a proposition is true or false, I am certain of it,
but if not, I am uncertain of its truth. A certainty can be gained a
posteriori through observation or a priori through demonstration,
which can be either direct or indirect: we shall speak more of these
notions, when we discuss Wolffian methodology.

A notion closely
related to certainty is probability, which Wolff defines in terms of

*requisita ad veritatem*, which could be translated here as truth conditions: in effect, Wolff is discussing of those things on which to base affirmation of certain judgement. Thus, for a definition like ”triangle is a figure with three sides” the truth conditions are the various characteristic marks contained in the concept of triangle: definition must be based on these characteristic marks and account for all of them. Any other universal categorical judgement, on the other hand, has the definition of subject as its truth condition. Thus, the truth of Pythagorean theorem should be decided on the basis of the definition of triangles. Then again, in case of a hypothetical judgement, we also have to take the preconditions or the antecedent of the judgement into consideration. If we then follow Wolff's suggestion that particular judgements are hypothetical judgements with indeterminate conditions (for some unknown conditions and all X of certain species, if X fulfills these conditions, then X has a certain property), the truth of a particular judgement ”some bananas are rotten” would boil down to i) definition of a banana and ii) the possible existence of some conditions under which bananas would be rotten.
Now, if we can
account for all truth requirements or conditions of a judgement or
proposition, we would be certain of the truth of that judgement –
we would have all the reasons to believe in that proposition. Then
again, we might have only insufficient account of these conditions,
in which case the proposition would be only probable and not certain.
Wolff suggests some basic laws that hold for probable propositions,
such that syllogisms which have one certain and one probable
syllogism lead to just probable conclusions, and recommends the study
of probability as a future task of logic, because it is something
required in empirical studies, where full certainty is often
impossible to achieve.

The difference of probability and truth
leads us finally to the difference between the three levels of
certainty, which I have already discussed in another post. Actually, I failed to mention there that Wolff also considers a
fourth level, namely, the level of error, and indeed, in Latin logic
he uses considerable time to go through various forms of spurious
reasoning. I shall just mention the basic difference between sophism
and paralogism, the former of which is a hidden type of spurious
reasoning, while paralogism makes its mistakes explicit: we shall
later on see these concepts with Kant.

The notion of different levels of
truth-likeness raises a question far more serious than the supposed
logication of Wolffian ontology: how does Wolff account for the
normative element of logic, that is, for the fact that e.g. certain
forms of deduction are said to be better than others, and in general,
that methods for finding truth are to be followed more than methods
for finding erroneous views? Certainly Wolff could turn his logic
into hypothetical imperatives of the form ”if you want to find
truth, use these syllogisms”. Then again, one might ask if logic
even requires more than just hypothetical imperatives. The relevant
categorical imperative would be something like ”try to find truth
in all circumstances”, but logic itself does not appear to dictate
that one should attempt to find truths.

So much for truth, next time we shall
see Wolff's methodology for finding it.

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