CHAPTER 8.
SYLLOGISM: DEFINITIONS.
We call inference the mental process of becoming aware of information
implicit in given information, be it concrete or abstract. When we draw ideas
from experience or generalities from particulars, we are involved in induction;
otherwise, it is deduction. In any case, the original data is called the
premises, and the logically derived proposition, the conclusion.
When the conclusion is already known to us, and we are considering its
validity in the context of other knowledge, we are said to argue. Furthermore,
if the motive of our argument was to arrive at the conclusion for its own sake,
we are said to be proving it; if on the other hand our motive was to show the
contradictory or a contrary of our conclusion to be false, we are said to be
engaged in a process of refutation.
The difference in connotation between inference and argument is merely
one of sequence: what was posited first, premise(s) or conclusion? The
distinction between proof and refutation lies in our motive. But the logical
form of all these processes is the same, so their names are used interchangeably
here.
The term deduction is sometimes used in a restricted sense which excludes
eduction. Eduction has already been defined as eliciting information from one
proposition (granting that the logical principles involved in this are not
regarded as premises too). The deductive process which concerns us here, in
contrast, is drawing information implicit in two or more propositions together,
and not separately. P and Q are true, ergo R is true.
This is called mediate inference, because it is found that the premises
must have some factor in common, which serves as the medium of inference, making
possible the eliciting of a conclusion. This might be thought of as
‘conduction’. The technical name for it is syllogism, from Greek, the language
of Aristotle.
It can be shown that arguments involving more than two categorical
propositions are reducible to a series of syllogisms and eductions. In this
analysis, we will concentrate on categorical syllogism, that involving only
categorical propositions. Argument involving noncategorical propositions will be
dealt with later.
Now, an argument may be valid or invalid. The science of Logic shows that
the validity of the method is independent of the truth or falsehood of the
premises or conclusion. A formal argument only claims that if the premises are
true, the conclusion must be true; if the conclusion is found false, then one or
more of the premises must be false. It may happen that the premises are false,
yet the conclusion is independently true; rejection of the premises does not
necessarily put the conclusion in doubt. The validity or invalidity of an
argument is a formal issue, irrespective of the content of the propositions
involved.
Logic analyses the variety of forms possible, and distinguishes the valid
from the invalid, by reference to the Laws of Thought. The results are analyzed,
in the search for general rules. Strictly speaking, only valid syllogisms are
ultimately so called; invalid syllogisms are mere fallacies. But at the outset,
Logic lists all possible combinations of propositions on an equal footing, to
ensure the exhaustiveness of its treatment; then it finds out which are good and
which bad.
Its ultimate aim is of course to draw the maximum consequent information
from any data. This allows us to correlate the different aspects of our
experience, and improve our knowledge of the world. By comparing and connecting
together all our beliefs, we can through logic discover inconsistencies, which
cause us to reassess our assumptions at some level, and correct our data banks.
In this way our beliefs are ‘proved’; at least until there is good reason to
think otherwise.
Scientific proof always depends on the context of knowledge. It is always
conceivable that some aspect of knowledge turns out to be open to doubt, even
after seeming fundamental and unassailable for ages. For instance, certain
axioms of Euclidean geometry. So proof never entirely frees a conclusion from
review, given some new motive. Finding an inconsistency does not in itself
guarantee that we will succeed in finding the source of the error, i.e. some
false premise. In such cases, we register that there is some doubt yet to
resolve, and either wait for new experience or search for an answer
imaginatively.
A syllogism, then, involves three propositions, two premises and a
conclusion. These together involve three, and only three, terms. They are: the
middle term, one common to both premises, but absent in the conclusion; the
minor term, which is the subject of the conclusion, and present in one of the
premises; and the major term, which is the predicate of the conclusion, and
present in the other premise. The minor and major term are also called the
extremes; the middle term acts as intermediary between them, to yield the
conclusion. The premise involving the minor term is called the minor premise,
that with the major term the major premise.
The position of the middle term in the premises, that is, whether it is
subject or predicate in each, determines what is called the ‘figure’ of the
syllogism. (The colloquial expression for thought, ‘to figure’ or ‘to figure
out’ may derive from this usage.) There are four possible figures of the
syllogism. They are shown in the following
table, with S, M, P symbolizing the minor, middle and major terms, respectively:
Table
8.1
Figures of the Syllogism.
| Figure | First | Second | Third | Fourth |
Major | M-P | P-M | M-P | P-M |
Minor | S-M | S-M | M-S | M-S |
Conclusion: | S-P | S-P | S-P | S-P |
Note well the variety in the position of the terms. The order of the
propositions in Logic is conventionally set as major-minor-conclusion, so that
symbolic references can always be understood. But of course in actual thought
any order of appearance may occur. Thus it is seen that syllogism is mediate
inference; from their respective relationships to a middle term, a relationship
may be found to follow between the extremes.
Each figure of the syllogism
reflects a structure of our thinking. In practise, the Fourth figure is not
regarded by many logicians as very significant. Aristotle, though aware of its
existence, had this viewpoint. Galen, however, introduced it as a formal
alternative for the sake of completeness.
We previously identified six categorical forms, A,
E. I,
O, R and G, which can be
involved in such syllogism. Each of the propositions in each figure might at
first glance have any of these six forms. So there are 6X6X6 = 216 possibilities
per group of proposition in each figure. Each of these combinations is called a
mood of the syllogism. Altogether, in the four figures, there are 216X4 = 864
imaginable syllogistic forms. Each such form can be designated clearly by
mentioning its figure and mood; for example, ‘mood EAA
in the first figure’, or more briefly, ‘1/EAA‘.
Our task is differentiate the valid from the invalid, in this
multiplicity of theoretical constructs. It will be seen that very few actually
pass the test. The valid moods per figure should be justified, and the invalid
ones shown wrong. This will enable us to know when a conclusion can be drawn
from given premises, and when not.
Note that each of the propositions may be positive (+)
or negative (–), so that there are
2X2X2 = 8 possible combinations of polarity in each figure; they are: +++,
++-, +-+,+–,
-++, -+-,
–+, —.
Likewise, as three quantities exist, viz. universal (u),
particular (p), and singular (s),
there are 3X3X3 = 27 possible combinations of quantity in each figure; which
are: uuu, uup, uus,
upu, upp, ups,
puu, pup, pus,
ppu, ppp, pps,
and so on. It will be seen that many of these combinations are nonsensical, and
rules concerning polarity and quantity can be formulated. Some rules are general
to all figures, some are specific to each. In any case, the conclusion sought is
always the maximal one; if a universal can be concluded, the subaltern
conclusion is not of interest, though it follows a-fortiori.
A more traditional way to express the task of logic with respect to
syllogism is as follows. In each figure, which of the 6X6 = 36 combination(s) of
premises yield a conclusion? Or which of the 2X2 = 4 combination(s) of polarity:
++, +-, -+, —? And which 3X3 =
9 combination(s) of quantity: uu, up,
pu, pp, us,
su, sp, ps,
ss?
Some critics of Logic have accused it of puerility, arguing that the
syllogism is too simple in form, and yields no new information, whereas actual
thinking is somehow a more creative and complex process. But the ‘event’ of
syllogistic reasoning is not as mechanical and automatic as it is made to appear
on paper. Logic presents a static picture of what is psychologically a very
dynamic and often difficult process.
There is a mental effort in bringing together the concepts which form the
separate propositions involved; this requires complex differential perceptions
and insights. We also have to think of bringing together the propositions which
constitute our premises; they are not always joined and compared automatically,
sometimes a veritable inspiration is required to achieve this. And even then,
actual drawing of the conclusion is not mechanically inevitable; honesty, will,
and intelligence are needed.
Thus, Logic merely establishes standards of proper reasoning, identifying
common aspects of thought and justifying its sequences. But mentally, in
practise, the processes are complexes of differentiation and integration.
Sometimes such events are easy to produce, but often years of study and even
genius are necessary to produce even a single result. Virtues such as
open-mindedness, reality-orientation, perceptiveness, intuition, will-power are
involved.