”That which
belongs to all things of a kind must also belong to this that is of
the same kind.”
”What is denied
of a whole kind must also be denied of anyone of the same kind.”
These somewhat
complex sentences Wolff calls the principles of syllogisms. They are
supposedly not the final axioms of syllogistic, because Wolff thinks
they are themselves based on the so-called principle of
contradiction: a thing cannot both have and not have a
characteristic.
The two principles
could also be stated through three statements:
”A property C
belongs or does not belong to all things of a kind B.”
”A is a thing of
kind B.”
”Thus, the
property C belongs or does not belong to A.”
or in a symbolic
form:
B – C
A – B
Thus, A – C
Such a combination
of three sentences is what has been traditionally called a syllogism.
Actually all the sentences in a syllogism have their own traditional
names. The first statement is known as a major proposition, or as
Wolff calls it, an upper proposition (Ober-Satz), while the
second statement is known as a minor proposition (in Wolff,
Unter-Satz or lower proposition). A major proposition here
characterises a certain kind or species and it often does describe a
general law connecting two concepts. The minor proposition here
states that a certain thing belongs to a certain kind and it often
presents an example of a general species. The major and minor
proposition together are called premises (in Wolff, Förder-Sätze
or front propositions), while the third proposition is then the
conclusion of the syllogism (in Wolff, Hinter-Satz or back
proposition).
In the previous
text I noted that syllogistic logic required only two divisions of
judgements: to universal and particular and to affirmative and
negative. Clearly then there are four different judgement types to
consider: universal-affirmative (all As are Bs),
particular-affirmative (some As are Bs), universal-negative (no As
are Bs) and particular-negative (some As are not Bs). Now, Aristotle
had painstaikingly investigated all the different possible
combinations of two premisses and noted which combinations could be
used as premisses of syllogisms. We need not bother with the details, but
we may note that at least one premiss must be universal and
affirmative.
Besides the
judgements, the words or concepts in the syllogism have also
traditional names. The subject of the conclusion, which in the
example is also the subject of the minor proposition, is called the
minor term (in Wolff, Förder-Glied or front term), and
similarly predicate of the conclusion, which in the example is the
predicate of the major proposition, is called the major term (in
Wolff, Hinter-Glied or back term). The third concept, which,
as it were, connects the minor and the major term, but vanishes when
we come to the conclusion of the syllogism, is then called the middle
term (Mittel-Glied).
In the example
above, the middle term is in the middle of the syllogism in a very
concrete sense, as it is the predicate of one and the subject of the
other premiss. But we could also change the places of the three
terms. For instance, we could place the middle term as the subject of
both premisses:
B – C
B – A
Thus, A – C
Now, in this case
the premisses tell that a certain species of objects is a common
subspecies for two other species – and nothing else. Hence, the
conclusion can at most be a particular judgement, some As (those that
are Bs) are Cs. For instance, because bats are both mammals and
flying animals, some mammals can fly.
We could also place
the middle term as the predicate of both premisses:
C – B
A – B
Thus, A – C
In this case two
affirmative premisses would tell that A and C share some predicate or
are subspecies of the same genus. This does not by itself tell us
anything new: two species of the same genus might have no common
elements (like tigers and lions), but they also can have common
elements (like teachers and writers, because a person can be both).
More results are gained when one of the premisses is negative – one
things has a predicate, the other does not, therefore, we cannot
identify these things or even connect them in a judgement. Thus,
because apples are plants, but bats are not, apples cannot be bats.
Aristotle
classified the different syllogisms into three figures according to
the three different positions the middle term could take. After
Aristotle, people noted that there is actually a fourth possible
figure. That is, we could reverse the positions of the minor and
major terms in the first figure like this:
C – B
B – A
Thus, A – C.
Logicians quickly
noted that the syllogisms of the fourth figure were not very helpful.
It is then no wonder that some philosophers, like Wolff and even
Aristotle himself, simply ignored it, and that Hegel mentioned it
merely to make ridicule of the unnecessary complexity of syllogistic.
Another piece of complexity one might also want to make fun of is the
medieval invention of giving all the individual syllogisms a name of
their own. Each of the four possible types of judgements was assigned
its own vowel, and as every syllogism comes with three judgements, a
name with just these three vowels was given to each syllogism. A
famous example is Baroco, that is, a syllogism of the sort:
All gold is
malleable,
But some people are
not malleable,
So some people are
not golden.
It seems
unbelievable that one would try to argue for such an insignifanct
conclusion with such complexities. And indeed, the name Baroco, or
its modification, baroque, acquired later a meaning of unnecessary
extravagancies. Indeed, as even Aristotle noted, all the other syllogisms could actually be based on the
syllogisms of the first figure – and with his pragmatic nature
Wolff instructs his students to ignore the other figures.
Despite the
extravagant and unnecessary intricacy of syllogistic, we should not
disvalue syllogistic completely. Syllogisms were the one form of
argumentation by which from premisses known to be true one could
infallibly deduce further truths. Of course, this infallibility is
also based on knowing some truths beforehand: from false premisses
syllogisms can produce both true and false conclusions. In the
traditional terms, the truth of the premisses is what makes
syllogisms into demonstrations. There have been various suggestions
as to how one can find true premisses – we shall see how Wolff
answers the question in the next text.
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