is that “in which the extremes are compared with each other,” and the middle term never appears here.
CHAPTER 2
The whole force of the syllogism may be explained from the following axioms.2
Axiom 1. “Those things which agree with a single third thing agree with each other.”
2. “Those of which one agrees and the other does not agree with one and the same third thing, do not agree with each other.”
3. “Those which agree in no third thing, do not agree with each other.”
4. “Those which do not disagree with any third thing, do not disagree with each other.” From these [axioms] the general rules of syllogisms are deduced. The first three are about the quality of propositions.
Rule 1. If one of the premisses is negative, the conclusion will be negative (by axiom 2).
Rule 2. If both the premisses are affirmative, the conclusion will be affirmative (axiom 1).
Rule 3. From two negative [premisses] nothing follows because those which agree with each other and those which disagree with each other may both be different from a third.
Two [rules] on the Quantity of Terms:
Rule 4. The middle must be distributed once, or taken universally; for a common term often contains two or more species which are mutually opposed to each other, and from which predication may be made according to different parts of its own extension; therefore terms do not truly agree with a third term, unless one at least agrees with the whole of the middle.
Rule 5. No term may be taken more universally in the conclusion than it was in the premisses, because an inference from particular to universal is not valid.
On the Quantity of Propositions:
Rule 6. “If one of the premisses is particular, the conclusion will be particular.” For (i) suppose the conclusion is affirmative: therefore (by rule 1) both premisses are affirmative; but no term is distributed in a particular [premiss]; therefore (by rule 4) the middle term has to be distributed in the other one; it is therefore the subject of a universal affirmative; therefore the other extreme is also taken particularly, since it is the predicate of an affirmative, ergo, the conclusion will be particular (by rule 5). (ii): Suppose the conclusion is negative: therefore, its predicate is distributed; hence (by rules 5 and 4) both the major term and the middle term have to be distributed in the premisses, but (rule 3) when one premiss is negative, the other is affirmative. If one [premiss] is particular, only these two terms can be distributed; when one premiss is affirmative, the other should be particular. Therefore the minor extreme, the subject of the conclusion, is not distributed in the premisses; therefore (by rule 5) it is not distributed in the conclusion.
Rule 7. “From two particulars nothing follows,” at least in our normal way of speaking, according to which the predicate of a negative is taken to be distributed. For (i) if the conclusion is affirmative and both premisses are affirmative, no term in the premisses is distributed (contrary to rule 4). (ii) Suppose the conclusion is negative; therefore some predicate is distributed, but the predicate is distributed only in particular premisses; it will therefore be invalid (contrary to rule 4 or 5).
Rules 1 and 7 are thus reduced to one rule. The conclusion follows the weaker side, i.e., the negative or particular. All the rules are contained in these verses:3
You must distribute the middle, and there should be no fourth term.
Both premisses should not be both negative and particular.
The conclusion should follow the weaker side;
And it may not be distributed or negative, except when a premiss is.4
In a curious and unusual manner of speaking, a certain negative conclusion may be reached, with the predicate undistributed, as in this example:
Certain Frenchmen are learned,
Certain Englishmen are not learned,
Therefore,
Certain Englishmen are not certain Frenchmen.
CHAPTER 3
A figure of a syllogism is “the proper arrangement of the middle in the premisses”; there are only four figures.
1. That in which the middle is the subject of the major and the predicate of the minor.
2. That in which the middle is the predicate of both.
3. That in which the middle is the subject of both.
4. That in which the middle is the predicate of the major and the subject of the minor.
In the first [the middle is] sub[ject and] pre[dicate]; in the second [it is] twice a pre[dicate]; in the third [it is] twice a sub[ject]; and in the fourth [it is] pre[dicate and] sub[ject].
The mood of the syllogism is “the correct determination of the propositions according to quantity and quality.”
Sixty-four arrangements are possible of the four letters A, E, I, O; of these, fifty-two are excluded by the general rules. There remain, therefore, twelve concluding modes of which not all lead to a conclusion in every figure because of the nature of the figure; and some are not useful at all.
CHAPTER 4
The special rules of the figures are as follows.
1. i. In figure 1 the minor [premiss] must be affirmative; if it were negative, the conclusion would be negative (by rule 1), and its predicate would be distributed. But the major would be affirmative (by rule 3), and its predicate would not be distributed; hence there would be a fallacy (contrary to rule 5).
ii. The major [premiss] must be universal. For the minor is affirmative (from the former rule), and therefore its predicate is particular, namely the middle term. It must therefore (by rule 4) be distributed in the major of which it is the subject. These things will be more easily made clear by the schema below, where the letters denote distributed terms.5
Here are examples of fallacies.
N.B. Capital letters denote distributed terms; lowercase letters particular terms.
2. Rules of the second figure:
i. One of the premisses must be negative. For since the middle term is predicated of both, it would be distributed in neither if both were affirmative (contrary to rule 4).
ii. The major must be universal. For the conclusion is negative, and its predicate is distributed. It must therefore (by rule 5) be distributed in the major of which it is the subject.
3. Rules of the third figure:
i. The minor must be affirmative, for the same reason as in the previous figure.
ii. The conclusion must be particular. For since the minor is affirmative, its predicate, the
