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in the premises could not exist, this process is not inference, for the relation realized in the conclusion is not a new one; there is no new fact. But if we broaden our definition so as to include this realization of what has been said, though perhaps not realized, then of course there is inference; there is a new thought. Logicians who are mainly interested in their own mental processes are likely to admit this broader definition; those who are mainly interested in the relations of things are likely not to.
In the third example the case is still different. one says that all of the apostles were Jews he means to include each member of a certain definite number of individuals determined beforehand. He speaks demonstratively of certain individuals as such. The only question is, whether or not he realizes as he should the identity of all the individuals that he speaks about. But when any one says that whoever has consumption is suffering from the presence of tubercular bacilli, he is not pointing to certain definite individuals determined beforehand. Rather he is speaking descriptively of any individual who happens to have consumption, no matter who he may be or how many there
may be of them. To know that whoever has consumption has tubercular bacilli, one does not have to know first about each individual patient as such; he needs only to know that these bacilli are the sole cause of the disease. When, therefore, he puts the two premises together and concludes that some particular patient has tubercular bacilli he has gained some knowledge that could not possibly have been derived from a mere analysis of the major premise. He has reached a new aspect of things—found a relation not previously mentioned—and has undoubtedly made an inference.
Looking back at the three kinds of cases, we can see that in the first, where objects are individually specified in the major premise, the minor is superfluous, and in the conclusion there is no real inference. In the second, where a certain definite number of objects are mentioned in general
terms in the major, the minor would be superfluous if we realized all that is said, and such inference as there is consists in realizing what is said. In the third, where the major expresses a general law applicable to every individual of a certain kind, the minor is not superfluous, and in the conclusion there is real inierence.
From all that has been said it is evident that the principle upon which we reason in the first figure is as follows: What is true of an object specified in one way is true of
Principle the same object specified in any other way. If we and omit the case in which the major premise is a singular proposition, the principle amounts to this: What is stated in a universal proposition is stated of every object to which the subject term is applicable; or, less technically, What is said to be true of every member of a group (or of every object which possesses a given relation) is said about each one of them, even though each is not 'separately thought of when the statement is made.
So much for the principle. In applying it we must observe certain cautions. In the first place, if the major premise speaks only of certain unspecified members of a group -i.e., if the major is particular—we cannot be sure that any of the objects named in the minor, though members of the group, are objects spoken of in the major; and consequently no conclusion can be drawn.
It is true that some animals are fierce, and it is also true that all mice are animals; but it is not true that mice are fierce. If such a conclusion did happen to be true in any one case, that would not make it follow from the premises; for a conclusion does not follow unless we can be absolutely certain that whenever premises of that kind are true that kind of conclusion must be true also.
If we use a number of small circles to represent animals of various kinds, and let a plain stroke drawn through a circle, 0, indicate that the animal is fierce, and a stroke with a bar across it, 0, indicate that it is not fierce, the major
premise gives this picture: oφoρφο Some are said to be fierce, and of some nothing is said; so some of the circles are marked with a plain stroke and some are left unmarked.
If now we indicate mice by thickened dots, we must put all the dots within the circles to indicate what is stated in the minor premise, that each mouse is identical with some animal; but as there may be animals which are not mice, we must leave some circles without dots, thus:
If it afterwards turns out that every animal is a mouse, we can fill in the remaining circles.
Now if we indicate in a single set of figures everything which has been asserted and remember this rule: Do not put more marks than you have to in any one circle, we get such a diagram as the following: 0 0 0 0 0 0
Here dots and plain strokes do not coincide, but there is nothing in the diagram to indicate that they cannot. That would be indicated by drawing a crossed stroke (meaning not-fierce) through every dot, thus: 0 0 0 0 0 0 The figure as it stands merely means that there is no evidence to show that any dot (mouse) must possess a plain stroke (fierceness). Whenever the major premise is particular it is possible to construct such a diagram.
If in the example given the major premise had been universal, every circle would have been marked, so that it would have been impossible to avoid putting the dots where they would also be marked; and so the diagrams would have indicated the conclusion that all mice are fierce: $ $ $ $
If the major premise is not particular, but the minor is, that is, if the minor says that some members of a second group belong to the group spoken of in the major but does not say which members of the second group these are, then we can conclude that what was said in the major premise was said of some members of the group named in the minor, but we cannot possibly say which members they are. The objects cannot be designated any more definitely in the conclusion than they were designated in the premise.
young animals like play and some mice are young animals, we can conclude that some mice like play, 0 0 0
but we cannot conclude that all mice like play or that any particular mouse likes it.
In other words, if the minor premise is particular, the conclusion must be particular also. have no definite information to begin with, syllogistic manipulation will not supply it.
Putting together what has been said about the two premises, our FIRST CAUTION is this: In the first figure if the major premise is particular, no conclusion can be drawn; if the minor is particular, the conclusion must be particular. This caution can be stated less mechanically and without regard to figure or distinction of premises as follows:
1) A relation can belong to some members of a group without belonging to all the members, to any given member, or to any one of a given group of members.
The phrase "to all the members' is really superfluous; for no relation could belong to each member without belonging to a given member. What is true of all mice must be true of this mouse.
The last words of the caution—"or to any one of a given group of members ''—are necessary in order to exclude a particular conclusion as well as a singular or universal when the major premise is particular.
The principle on which we reason in the first figure is quite as applicable when the major premise is negative as when it is affirmative. The proposition ‘No men are perfect ' states something about every man, not about no man. It means that every man is without perfection, and if we know Socrates to be a man, it is applicable to Socrates. If we represent the proposition by a diagram, we may cross our strokes to indicate that the objects represented have not the quality in question; but the strokes must be drawn through every circle, to indicate that every man is described,
$$$, and the circle that stands for Socrates must be is marked with the rest. 1 But when the minor premise in the first figure is negative it
does not come under the principle, and no conclusion can be drawn. If we know that all the apostles were Jews, it will not tell us anything about Job's race to say that he was not an apostle. The function of a minor premise in this figyre is to point out particularly some of the things spoken about in the major, and if an object is not one of those spoken about in the major, then nothing has been said about it one way or the other.
Clear as this is, there is a strong tendency in such cases to draw a negative conclusion, e.g., The apostles were Jews; Job was not an apostle; therefore Job was not a Jew. The caution against yielding to this tendency might run as follows:
2) To say that something is true of certain objects does not imply that it is false of others.
The same tendency to draw negative conclusions where no conclusion at all should be drawn is found—though it is not so strong—where the minor premise is particular. If we are told that no men are perfect and that some rational beings are men, we have a right to conclude that some rational beings-namely, those that are men—are not perfect; but we have no right to conclude that some rational beings -namely, those that are not men—are perfect. To do so is to ignore the caution just given, It also involves the other blunder of interpreting some are' to mean some are and some are not'. The statement that some rational beings are men gives us no valid reason for believing that they are not all men. Both blunders are covered by the caution. *
Here is a set of diagrams for the benefit of any one who may wish to compare them with his own. If we wish to include negative minors, we may draw a short stroke through one side of the circles to indicate something outside of the
* The first caution covers fallacies of illicit minor and undistributed middle as they occur in the first figure ; the second caution covers fallacies of illicit major in the same figure,