Prior Analytics

Prior Analytics is Aristotle's work on deductive reasoning, or the syllogism. It is part of his Organon, which is the instrument or manual of logical and scientific methods. It is the first part of the Analytics (the second being the Posterior Analytics). The Prior Analytics gives an account of deduction in general, the 'Posterior Analytics deals with demonstrative science.

Book I

The first book of the Prior Analytics consists of forty-six chapters, and is roughly divided into four parts

• the first deals with the conversion of propositions
• the second concerns the structure of syllogisms, in all the different figures and modes;
• the third part is about the 'invention of a middle term'
• the last is about the resolution of syllogisms .

Conversion of propositions

Converting a proposition is when we infer another proposition from it, whose subject is the predicate of the first, and whose predicate is the subject of the first.

Aristotle gives three rules of conversion.

1. The universal negative can be converted into another universal negative. For example, 'No man is a horse, therefore 'No horse is a man' is a valid conversion.
2. The universal affirmative can be converted only into a particular affirmative. For example, 'All men are mortals therefore some mortals are men.'
3. A particular affirmative can be converted into a particular affirmative. Thus 'Some men are white, therefore some white things are men.'

Converting a proposition without changing its quantity is called simple conversion. When the quantity is reduced, as in the universal affirmative, it is called conversion per accidens.

Structure of syllogisms

A syllogism is an argument consisting of three propositions. The last is called the conclusion, which is a necessary consequence of the two preceding, which are called premisses. The conclusion has two terms, a subject and a predicate. The predicate is called the major term, its subject the minor term. To entail the conclusion, each of its terms must be compared in the premises with a third term, the middle term. Thus one premise has the major term and the middle term, and is called the major premise. The other has the minor term and the middle term, and is called the minor premise.

Thus the syllogism consists of three propositions: the major, the minor, and the conclusion. and though each has two terms, a subject and a predicate, there are only three different terms in all. The major term is always the predicate of the conclusion, and so is either the subject or predicate of the major premiss. The minor term is always the subject of the conclusion, and is either the subject or predicate of the minor premise. The middle term is never in the conclusion, but is in both premises, either as subject or predicate.

The figure of the syllogism depends on the the positions which the Middle Term may have in the premises. There are on four possible positions. It may be the subject of the major premise, and the predicate of the minor, and then the syllogism is of the first figure; or it may be the predicate of both premises, and then the syllogism is of the second figure; or it may be the subject of both, which makes a syllogism of the third figure; or it may be the predicate of the major premise, and the subject of the minor, which makes the fourth figure.

Another division of syllogisms is by mode. The mode is determined by the Quality and Quantity of the propositions. Any propositions must be either a universal affirmative, or a universal negative, or a particular affirmative, or a particular negative. These four kinds of propositions, were named by the four vowels A, E, I, O. Thus, AAA is the mode in which the major, minor and conclusion, are all universal affirmatives. EAE is the mode in which the major and conclusion are universal negatives and the minor is an universal affirmative. And so on.

There are sixty-four combinations of the four vowels in each figure, thus in the three figures given by Aristotle there are one hundred and ninety-two (and in all the four figures of Aristotelian logic, two hundred and fifty six).

Not all combinations give a valid syllogism. Aristotle examines all the modes one by one, and judges whether each is valid, and gives rules which to help the memory in distinguishing the vaoid from the invalid. The first figure has only four valid modes. The major premise in this figure must be universal, and the minor affirmative, and yields conclusions of all kinds, affirmative and negative, universal and particular. The second figure also has four valid modes. Its major premise must be universal, and one of the premises must be negative. It yields universal and particular conclusions, of which all are negative. The third figure has six valid modes. Its minor must always be affirmative. It yields affirmative and negative conclusions both, all particular.

There are five rules of validity common to all syllogisms, that may be deduced from what Aristotle says.

1. There must be only three terms in a syllogism. As each term occurs in two of the propositions, it must be precisely the same in both: If it be not, the syllogism is said to have four terms, which makes a vitious syllogism.
2. The middle term must be taken universally in one of the premises.
3. Both premises must not be particular propositions, both must not be negative.
4. The conclusion must be particular, if either of the premises are particular; and negative, if either of the premises are negative.
5. No term can be taken universally in the conclusion, if not taken universally in the premises.

A term is 'taken universally', not only when it is the subject of a universal proposition, but when it is the predicate of a negative proposition. A term is 'taken particularly', when it is either the subject of a particular, or the predicate of an affirmative proposition.

the invention of the middle term

The third part of the book contains rules, general and specific, for the invention of a middle term. The general rule is to consider both terms of the proposition to be proved; their definition, their properties, the things which may be affirmed or denied of them, and those of which they may be affirmed or denied. These thingsare the materials from which the middle term should be taken.

The specific rules are to consider the quantity and quality of the conclusion, in order to determine in what mode and figure of syllogism the proof is to proceed. Then find a middle term which has that relation to the subject and predicate of the proposition to be proved, which the nature of the syllogism requires.

The resolution of syllogisms

The resolution of syllogisms requires no other principles than those given for constructing them. Aristotle mentions hypothetical syllogisms in this part, which he admits cannot be resolved into any of the figures. He says he will deal with these later, although no such word is known in any of his existing works.

Book II

The second book concerns the powers of syllogisms. Aristotle shews, in twenty-seven chapters, how many different powerful arguments can be constructed from syllogisms, and what figures and modes are best adapted to each. He also gives suggestions both to the person prosecuting the argument, and to the one who defends. This suggests that Aristotle introduced in his own school the practice of syllogistical disputation, instead of the rhetorical and dialectical techniques which the Sophists used in earlier periods.