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of one of the three ' Figures' of the syllogism, which we are about to discuss. Most logicians say that there are four of these figures; but Aristotle gave only three, and as the fourth is easily derived from the others by a purely mechanical process, has no special function as distinguished from the others, and is seldom or never used in ordinary reasoning, it may easily be omitted.
THE FIRST FIGURE OF THE SYLLOGISM.
In the first figure the reasoning is of this sort. One premise, called the Major, asserts something about a certain
object or certain objects; the other premise, General
called the Minor, points out that one or more
specified individuals are identical with some or all of these objects; and on the strength of this the Conclusion makes the statement contained in the major premise with direct reference to the individuals specified in the minor. Examples:
None of the apostles were Gentiles;
Peter was an apostle; .:. Peter was not a Gentile.
Every one who has consumption has tubercular bacilli;
This patient has consumption; .'. This patient has tubercular bacilli.
No Anglo-Saxon likes mob rule;
Most Americans are Anglo-Saxons; .:. Most Americans do not like mob rule.
It should be noticed that the major premise (which in each of these examples is written first) can affirm or deny any sort of relation whatever, while the minor always keeps saying: 'This is he', 'This is one of them ', ‘These are some of them '. We may say if we like that in all typical examples of the first figure the major gives a rule, and the minor points out that a certain case comes under it.
In this figure the conclusion merely makes a specific or more specific application of what was said in the major premise to the objects specially mentioned in the minor. To do this, it substitutes the more specific term which occurs in the minor premise for the less specific term which occurred in the major; but in the conclusion the general sense of the major premise and its general arrangement of terms is preserved. This is not true of any other figure.
In the two other figures the distinction between major and minor premise is purely arbitrary, for both premises deal with the same kind of relations; the conclusion does not preserve the general sense of either; and one arrangement of terms in the conclusion is just as natural as the other.
It should not be overlooked that when the major premise points out a relation of any sort between two objects or sets of objects the minor can specify any or all of the objects in question, and the specification is carried into the conclusion regardless of whether these objects were denoted by the subject or by the predicate of the major. The following, for example, are perfectly valid syllogisms in the first figure:
All Slavs hate all Semites;
The Russians are Slavs and the Jews are Semites; ... The Russians hate the Jews.
Oil and water will never mix;
This is oil and that is water; .:. This and that will not mix.
John is beating Thomas;
Thomas is John's son; .: John is beating his son.
John and Thomas are quarreling;
Thomas is John's son; ... John and his son are quarreling.
If we use an arrow to indicate any dynamic or non-dynamic relation between two different objects and three horizontal lines to indicate identity and a bar across the symbol to indicate the absence of the relation, these four syllogisms would be represented in this way: Major:
All Slavs → all Semites. Minors:
Every Russian = a Slav.
Every Jew = a Semite. Conclusion: .'. All Russians → all Jews. Major:
This = oil.
That = water. Conclusion: This that. Major:
→ Thomas. Minor:
Thomas = John's son.
John ++ James.
Thomas = John's son. Conclusion: John + his son.
Inference in the first figure amounts, as has been said, merely to this: Some or all of the individuals about which a
statement has been made in the major premise Is there
are pointed out more specifically in the minor, inference ?
and then in the conclusion the statement is made over again with specific reference to these individuals. The interesting question about it is whether in such a process
* When we recognize that propositions expressing relations between different objects can be treated by the syllogism we must abandon, for such cases at least, the old rule that the major premise contains the predicate of the conclusion. In the third of these examples this rule would make what I have called the minor premise--Thomas is John's son—the major, though it is perfectly obvious that it is the other premise—John is beating Thomas, whose general sense is preserved in the conclusion. It is infinitely better to judge by the meaning than by the outward form.
there is any inference at all. Does not the conclusion merely repeat in other words a part of what has been already stated in the major premise ? And if so can this be called inference ? Mill and others have maintained that it cannot. To get a fair view of the subject we must consider three slightly different sets of cases. Let us take an example of each.
Peter, James, and John were all Jews;
Peter is one of these; ... Peter was a Jew.
All of the apostles were Jews;
Peter was an apostle; ... Peter was a Jew.
Whoever has consumption has tubercular bacilli;
This patient has consumption;
In the first of these examples no one would maintain that there is any inference. The conclusion merely repeats what has been said just as explicitly in the major premise.
In the second example the case is somewhat different. No one who investigated the matter could be sure that all the apostles were Jews unless he were first sure about Peter and each of the others individually, but it would be possible, nevertheless, to make a statement about all of the apostles without thinking about Peter and each of the others individually. If there is inference in this case it rests upon the curious fact that, by using such words as 'all' and 'every',
we can speak of each of a large number of individuals, y though we do not, and cannot, have at once separate mental images of more than a very few of them. Such inference as there is consists in pointing out that the statement made applies to certain individuals that we may never have thought of when the statement was made—in realizing to some
extent whom or what it was that was spoken about. i adhere to our definition of inference as the recognition of a
new relation of things without which the relations asserted