CHAPTER IV.. Of Syllogism.

OF SYLLOGISM.

1. The definition of syllogism.—2. In a syllogism there are but three terms.—3. Major, minor, and middle term; also major and minor proposition, what they are.—4. The middle term in every syllogism ought to be determined in both the propositions to one and the same thing.—5. From two particular propositions nothing can be concluded.—6. A syllogism is the collection of two propositions into one sum.—7. The figure of a syllogism, what it is.—8. What is in the mind answering to a syllogism.—9. The first indirect figure, how it is made.—10. The second indirect figure, how made.—11. How the third indirect figure is made.—12. There are many moods in every figure, but most of them useless in philosophy.—13. An hypothetical syllogism when equipollent to a categorical.

1. A SPEECH, consisting of three propositions, from two of which the third follows, is called a SYLLOGISM; and that which follows is called the conclusion; the other two premises. For example, this speech, every man is a living creature, every living creature is a body, therefore, every man is a body, is a syllogism, because the third proposition follows from the two first; that is, if those be granted to be true, this must also be granted to be true.

2. From two propositions which have not one term common, no conclusion can follow; and therefore no syllogism can be made of them. For let any two premises, a man is a living creature, a tree is a plant, be both of them true, yet because it cannot be collected from them that plant is the name of a man, or man the name of a plant, it is not necessary that this conclusion, a man is a plant, should be true. Corollary: therefore, in the premises of a syllogism there can be but three terms.

Besides, there can be no term in the conclusion, which was not in the premises. For let any two premises be, a man is a living creature, a living creature is a body, yet if any other term be put in the conclusion, as man is two-footed; though it be true, it cannot follow from the premises, because from them it cannot be collected, that the name two-footed belongs to a man; and therefore, again, in every syllogism there can be but three terms.

3. Of these terms, that which is the predicate in the conclusion, is commonly called the major; that which is the subject in the conclusion, the minor, and the other is the middle term; as in this syllogism, a man is a living creature, a living creature is a body, therefore, a man is a body, body is the major, man the minor, and living creature the middle term. Also of the premises, that in which the major term is found, is called the major proposition, and that which has the minor term, the minor proposition.

4. If the middle term be not in both the premises determined to one and the same singular thing, no conclusion will follow, nor syllogism be made. For let the minor term be man, the middle term living creature, and the major term lion; and let the premises be, man is a living creature, some living creature is a lion, yet it will not follow that every or any man is a lion. By which it is manifest, that in every syllogism, that proposition which has the middle term for its subject, ought to be either universal or singular, but not particular nor indefinite. For example, this syllogism, every man is a living creature, some living creature is four-footed, therefore some man is four-footed, is therefore faulty, because the middle term, living creature, is in the first of the premises determined only to man, for there the name of living creature is given to man only, but in the latter premise it may be understood of some other living creature besides man. But if the latter premise had been universal, as here, every man is a living creature, every living creature is a body, therefore every man is a body, the syllogism had been true; for it would have followed that body had been the name of every living creature, that is of man; that is to say, the conclusion every man is a body had been true. Likewise, when the middle term is a singular name, a syllogism may be made, I say a true syllogism, though useless in philosophy, as this, some man is Socrates, Socrates is a philosopher, therefore, some man is a philosopher; for the premises being granted, the conclusion cannot be denied.

5. And therefore of two premises, in both which the middle term is particular, a syllogism cannot be made; for whether the middle term be the subject in both the premises, or the predicate in both, or the subject in one, and the predicate in the other, it will not be necessarily determined to the same thing. For let the premises be,

Some man is blind, In both which the middle Some man is learned, } term is the subject,

it will not follow that blind is the name of any learned man, or learned the name of any blind man, seeing the name learned does not contain the name blind, nor this that; and therefore it is not necessary that both should be names of the same man. So from these premises,

Every man is a living-creature, } In both which the middle Every horse is a living-creature, } term is the predicate,

nothing will follow. For seeing living creature is in both of them indefinite, which is equivalent to particular, and that man may be one kind of living creature, and horse another kind, it is not necessary that man should be the name of horse, or horse of man. Or if the premises be,

Every man is a In one of which the living-creature, } middle-term Some living creature is four-footed,

} is the subject, and in the

} other the predicate,

the conclusion will not follow, because the name living creature being not determined, it may in one of them be understood of man, in the other of not-man.

6. Now it is manifest from what has been said, that a syllogism is nothing but a collection of the sum of two propositions, joined together by a common term, which is called the middle term. And as proposition is the addition of two names, so syllogism is the adding together of three.

7. Syllogisms are usually distinguished according to their diversity of figures, that is, by the diverse position of the middle term. And again in figure there is a distinction of certain moods, which consist of the differences of propositions in quantity and quality. The first figure is that, in which the terms are placed one after another according to their latitude of signification; in which order the minor term is first, the middle term next, and the major last; as, if the minor term be man, the middle term, living creature, and the major term, body, then, man is a living-creature, is a body, will be a syllogism in the first figure: in which, man is a living creature is the minor proposition; the major, living creature is a body, and the conclusion, or sum of both, man is a body. Now this figure is called direct, because the terms stand in direct order; and it is varied by quantity and quality into four moods: of which the first is that wherein all the terms are positive, and the minor term universal, as every man is a living creature, every living creature is a body: in which all the propositions are affirmative, and universal. But if the major term be a negative name, and the minor an universal name, the figure will be in the second mood, as, every man is a living creature, every living creature is not a tree, in which the major proposition and conclusion are both universal and negative. To these two, are commonly added two more, by making the minor term particular. Also it may happen that both the major and middle terms are negative terms, and then there arises another mood, in which all the propositions are negative, and yet the syllogism will be good; as, if the minor term be man, the middle term not a stone, and the major term not a flint, this syllogism, no man is a stone, whatsoever is not a stone is not a flint, therefore, no man is a flint, is true, though it consist of three negatives. But in philosophy, the profession whereof is to establish universal rules concerning the properties of things, seeing the difference betwixt negatives and affirmatives is only this, that in the former the subject is affirmed by a negative name, and by a positive in the latter, it is superfluous to consider any other mood in direct figure, besides that, in which all the propositions are both universal and affirmative.

8. The thoughts in the mind answering to a direct syllogism, proceed in this manner; first, there is conceived a phantasm of the thing named, with that accident or quality thereof, for which it is in the minor proposition called by that name which is the subject; next, the mind has a phantasm of the same thing with that accident, or quality, for which it hath the name, that in the same proposition is the predicate; thirdly, the thought returns of the same thing as having that accident in it, for which it is called by the name, that is the predicate of the major proposition; and lastly, remembering that all those are the accidents of one and the same thing, it concludes that those three names are also names of one and the same thing; that is to say, the conclusion is true. For example, when this syllogism is made, man is a living creature, a living creature is a body, therefore, man is a body, the mind conceives first an image of a man speaking or discoursing, and remembers that that, which so appears, is called man; then it has the image of the same man moving, and remembers that that, which appears so, is called living creature; thirdly, it conceives an image of the same man, as filling some place or space, and remembers that what appears so is called body; and lastly, when it remembers that that thing, which was extended, and moved and spake, was one and the same thing, it concludes that the three names, man, living creature, and body, are names of the same thing, and that therefore man is a living creature is a true proposition. From whence it is manifest, that living creatures that have not the use of speech, have no conception or thought in the mind, answering to a syllogism made of universal propositions; seeing it is necessary to think not only of the thing, but also by turns to remember the divers names, which for divers considerations thereof are applied to the same.

9. The rest of the figures arise either from the inflexion, or inversion of the first or direct figure; which is done by changing the major, or minor, or both the propositions, into converted propositions equipollent to them.

From whence follow three other figures; of which, two are inflected, and the third inverted. The first of these three is made by the conversion of the major proposition. For let the minor, middle, and major terms stand in direct order, thus, man is a living creature, is not a stone, which is the first or direct figure; the inflection will be by converting the major proposition in this manner, man is a living creature, a stone is not a living creature; and this is the second figure, or the first of the indirect figures; in which the conclusion will be, man is not a stone. For (having shown in the last chapter, art. 14, that universal propositions, converted by contradiction of the terms, are equipollent) both those syllogisms conclude alike; so that if the major be read (like Hebrew) backwards, thus, a living creature is not a stone, it will be direct again, as it was before. In like manner this direct syllogism, man is not a tree, is not a pear-tree, will be made indirect by converting the major proposition (by contradiction of the terms) into another equipollent to it, thus, man is not a tree, a pear-tree is a tree; for the same conclusion will follow, man is not a pear-tree.

But for the conversion of the direct figure into the first indirect figure, the major term in the direct figure ought to be negative. For though this direct, man is a living creature, is a body, be made indirect, by converting the major proposition, thus,

Man is a living creature, Not a body is not a living creature, Therefore, Every man is a body;

Yet this conversion appears so obscure, that this mood is of no use at all. By the conversion of the major proposition, it is manifest, that in this figure, the middle term is always the predicate in both the premises.

10. The second indirect figure is made by converting the minor proposition, so as that the middle term is the subject in both. But this never concludes universally, and therefore is of no use in philosophy. Nevertheless I will set down an example of it; by which this direct

Every man is a living creature, Every living creature is a body,

by conversion of the minor proposition, will stand thus,

Some living creature is a man, Every living creature is a body, Therefore, Some man is a body.

For every man is a living creature cannot be converted into this, every living creature is a man: and therefore if this syllogism be restored to its direct form, the minor proposition will be some man is a living creature, and consequently the conclusion will be some man is a body, seeing the minor term man, which is the subject in the conclusion, is a particular name.

11. The third indirect or inverted figure, is made by the conversion of both the premises. For example, this direct syllogism,

Every man is a living creature, Every living creature is not a stone, Therefore, Every man is not a stone,

being inverted, will stand thus,

Every stone is not a living creature, Whatsoever is not a living creature, is not a man, Therefore, Every stone is not a man;

which conclusion is the converse of the direct conclusion, and equipollent to the same.

The figures, therefore, of syllogisms, if they be numbered by the diverse situation of the middle term only, are but three; in the first whereof, the middle term has the middle place; in the second, the last; and in the third, the first place. But if they be numbered according to the situation of the terms simply, they are four; for the first may be distinguished again into two, namely, into direct and inverted. From whence it is evident, that the controversy among logicians concerning the fourth figure, is a mere λογόμαχια, or contention about the name thereof; for, as for the thing itself, it is plain that the situation of the terms (not considering the quantity or quality by which the moods are distinguished) makes four differences of syllogisms, which may be called figures, or have any other name at pleasure.

12. In every one of these figures there are many moods, which are made by varying the premises according to all the differences they are capable of, by quantity and quality; as namely, in the direct figure there are six moods; in the first indirect figure, four; in the second, fourteen; and in the third, eighteen. But because from the direct figure I rejected as superfluous all moods besides that which consists of universal propositions, and whose minor proposition is affirmative, I do, together with it, reject the moods of the rest of the figures which are made by conversion of the premises in the direct figure.

13. As it was showed before, that in necessary propositions a categorical and hypothetical proposition are equipollent; so likewise it is manifest that a categorical and hypothetical syllogism are equivalent. For every categorical syllogism, as this,

Every man is a living creature, Every living creature is a body, Therefore, Every man is a body,

is of equal force with this hypothetical syllogism:

If any thing be a man, the same is also a living creature, If any thing be a living creature, the same is a body, Therefore, If any thing be a man, the same is a body.

In like manner, this categorical syllogism in an indirect figure,

No stone is a living creature, Every man is a living creature, Therefore, No man is a stone, Or, No stone is a man,

is equivalent to this hypothetical syllogism:

If any thing be a man, the same is a living creature, If any thing be a stone, the same is not a living creature, Therefore, If any thing be a stone, the same is not a man, Or, If any thing be a man, the same is not a stone.

And thus much seems sufficient for the nature of syllogisms; (for the doctrine of moods and figures is clearly delivered by others that have written largely and profitably of the same). Nor are precepts so necessary as practice for the attaining of true ratiocination; and they that study the demonstrations of mathematicians, will sooner learn true logic, than they that spend time in reading the rules of syllogizing which logicians have made; no otherwise than little children learn to go, not by precepts, but by exercising their feet. This, therefore, may serve for the first pace in the way to Philosophy.

In the next place I shall speak of the faults and errors into which men that reason unwarily are apt to fall; and of their kinds and causes.

-------