[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.
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.
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.
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.
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.