CHAPTER IV.

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.

[Sidenote: Definition of syllogism.]

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.

[Sidenote: In a syllogism there are but three terms.]

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_.

[Sidenote: Major, minor and middle term; also major and minor proposition, what they are.]

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_.

[Sidenote: The middle term in every syllogism to be determined in both propositions to one and the same thing.]

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.

[Sidenote: From two particular propositions nothing can be concluded.]

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_.

[Sidenote: A syllogism is the collection of two propositions into one sum.]

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.

[Sidenote: The figure of a syllogism what it is.]

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.

[Sidenote: What is in the mind answering to a syllogism.]

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.

[Sidenote: The first indirect figure how made.]

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.

[Sidenote: Second indirect figure how made.]

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.

[Sidenote: How the third indirect figure is made.]

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.

[Sidenote: There are many moods in every figure, but most of them useless in philosophy.]

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.

[Sidenote: An hypothetical syllogism when equipollent to a categorical.]

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.

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