Ever since Aristotle's Posterior
analytics, syllogistic logic had
been a crucial part of philosophical methodology and at times
methodology consisted of little else. There are at least two reasons
why Aristotle thought syllogistic so important. Firstly, syllogistic
was an improvement over Platonic dialectics, because it replaced
individual arguments with a group of general schemes for constructing
incontrovertible arguments. Secondly, the science most developed at
the time, geometry, was easily converted into a syllogistic shape.
From Aristotle, the
enthusiasism over syllogistic logic was transferred from one
generation to another, and even when the fame of Aristotle dwindled,
the syllogistic was still the core of the logic, and the only thing
that truly threatened its position in methodology was the relatively
young notion of experimental science. Thus, it is no wonder that
Wolff is also obliged to give an account of syllogistic in his logic.
Because the issue will undoubtedly appear in the future – Hegel at
least loves the syllogism as a symbol – I shall expound in the
following two blog texts syllogistic logic in more detail. Those who
know the syllogistic by heart and those who are bored to death by
formal logic can skip ahead.
Before going into
syllogisms themselves, I shall say in this text something about their
constituents. We have discussed concepts and words in previous texts,
but the things between – that is, judgements – are still missing.
Now, Wolff – and probably also many other logicians of the time –
defines judgements in two manners. Firstly, in judging we supposedly
think that a thing has or has not or could or couldn't have some
characteristic: the thing is represented by the subject term and its
characteristic by the predicate term, which Wolff calls respectively
front and back terms (Förder – und Hinterglied). Secondly,
the judgement is regarded as a combination of concepts, namely, the
subject and the predicate.
The identification
of these two definitions is problematic, because on a closer look
they define two completely different things. As Husserl noted,
thinking a combination of redness and ball or red ball is something
else than thinking or considering the possibility or the fact that a
ball is red – and as Frege would add, both are different from
asserting that a ball is red. It is somewhat disturbing to think that
quite a number of people had not noticed these what seem to be
obvious platitudes.
A reasonable
explanation for this apparent confusion is that Wolff and his fellow
logicians had a different paradigm of judgement in mind. While the
modern mathematical logic has taught to us to start from sentences
like ”Mickey is a mouse”, where an individual is characterised in
some manner, the Aristotelian tradition begun from sentences like
”Gold is malleable”. This is a case of a lawlike unification of
two universal terms, and because of the lawlikeness, the assertion of
their connection appears inevitable.
At least in case of
Wolff, the explanation is made even more plausible by two facts.
First fact is connected to a difference between universal and
particular judgements, which Wolff equates with the difference
between necessary or essential and contingent or accidental
judgements. The equation itself is interesting, because it tells us
something about Wolff's notion of alethic modalities: if all Xs are
Ys then an X is essentially an Y, but if the connection between Xs
and Ys is accidental, only some Xs can be Ys. Now, Wolff suggests
that all the particular judgements can be turned into universal
judgements by stating the conditions in which the particular
connection of concepts is true: that is, if some Xs are Ys, then all
Xs filling suitable conditions are Ys. What is important here is that
Wolff clearly accepts that universal/necessary judgements are the
norm to which all the other sort of judgements should be transformed.
Secondly, Wolff
suggests that we are able to think or judge something through a given
sentence only if the concepts combined in the sentence are distinctly
known to conform with one another, while we are unable to think the
sentence if the concepts are distinctly known to be contradictory;
otherwise, we do not know whether we can think it or not. This might
in itself sound completely harmless, but Wolff defines the conformity
as the necessity of thinking one concept, when you think the other
concept. In other words, in a true judgement two concepts must be
necessarily or in a lawlike manner connected with one another – an
accidental connection of characteristics is then not a true
judgement.
A word on the
classification of judgements. We have already seen Wolff divide
judgements into universal or absolutely valid and particular or
contextually valid. In addition, he mentions the division into
affirmative (bekräftigende) and negative (verneinende)
judgements. These two classifications are actually all that we need
in syllogistics. Not only is Wolff then unaware of what Kant called
infinite and singular judgements, but he and probably many other
logicians fail to think the possibility of dividing judgements
according to relation or modalities. Hypothetical and disjunctive
judgements appear only in a place where Wolff shows how other
deductions can be transformed into syllogistical form, while
modalities are discussed in Wolff's ontology. When scholars then say
that Kant merely assumed his category system from the logic of his
time without any arguments, we might suspect that he actually just
assumed the system, which was not based even in logic.
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