the conclusions which follow, as seen above, in the cases of total inclusion, follow here. Other conclusions also follow, as will be shortly seen; but every thing that is true, as the result of inclusion, is also true of identity, so that there is no difficulty in applying the diagrams representing total inclusion, in the last paragraph, to propositions that express identity.

196. Ambiguity of Predicate. Take the following irregular quasi-syllogism: —

All equilateral triangles are equiangular triangles;

All isosceles triangles with an angle of 60° are equiangular triangles;

Therefore all equilateral triangles are isosceles triangles with an angle of 60°.

This is correct: why is the following incorrect?

The answer is, that there is an ambiguity in the Predicates of the propositions. In the former argument "all" might have been written before the Middle term "equiangular triangles;" in the latter "all" could not have been written before "animals." This ambiguity would have been avoided if we had written in the first argument "all equiangular triangles," and in the second argument "some animals." In this way we should have defined how much of the predicate is occupied by the subject, whether all or only part. This process has been called "the quantification of the predicate."

1 This error is technically called "the error of the undistributed middle."

197. Conversion of Propositions.

Mistakes are some

times made in converting a proposition; i.e., in changing the subject into the logical predicate, and the logical predicate into the subject. Thus, from "all good men are truthful," it is sometimes inferred that "all truthful men are good;" whereas, since we only know that "all good men are included in the class of truthful men," we can infer no more than that "among truthful men there are some who are also good," or, in other words, "some truthful men are good." A statement or proposition in which the logical predicate is predicated of the whole of the subject, as of "all good men," is called a Universal proposition; where the logical predicate is predicated of a part of the subject, as of "some truthful men," the proposition is called Particular. We therefore see that the conversion of a Universal affirmative proposition1 results in a Particular. If, however, we have a Universal negative, as, "No good men are contemptible," it follows that "in the class of contemptible men there are none who are good,". i.e., "no contemptible men are good;" or generally, a Universal negative may be converted.

198. Denial of the Antecedent. The antecedent is the logical name for a condition; e.g., "if he is guilty." The consequent is the logical name for the consequence of the condition if fulfilled.

If he is guilty, he will blush.

1 Unless it be a "Proposition of Identity" (see 195). Propositions of Identity are of course convertible, e.g.,

Paris is the capital of France.

Right angles are angles of ninety degrees.

They are really definitions.

You can infer nothing from denying an Antecedent. Thus it is futile to argue,

If he is guilty, he will blush;
But he is not guilty;

Therefore he will not blush;

for a man may blush if he is guilty, but he may also blush for other reasons; as, for example, at being accused of guilt. And generally, if I deny an antecedent, I only deny that the consequent will take place as the consequent of that antecedent, but it may take place as the consequent of other antecedents.

Similarly, you can infer nothing from affirming a Consequent. For example, I am not justified in arguing, —

If he is guilty, he will blush;

But he blushes;

Therefore he is guilty;

for, as was said above, blushing may be caused by other feelings beside the consciousness of guilt.

On the other hand, if the Consequent be denied, the Antecedent is denied.

-

199. The Error of the Suppressed Premise. When the Premises are correctly and clearly stated, the conclusion is not often incorrectly deduced. Mistakes more frequently arise from taking for granted a Premise that is not stated, but suppressed. In such cases the Premise, or conclusion, or both, are generally stated informally and loosely, otherwise error would be impossible. Thus:

Falkland was a good man;

Falkland was a man who sided with Charles I. against the Parliament;

Therefore it was a good action to side with Charles I. against the Parliament.

This argument is based upon the suppressed Premise that "every action of a good man is good." All that can be inferred from the Premises is that "a good man sided with Charles I. against the Parliament."

200. The Error of the Variable Middle.

Sometimes, and especially when a syllogism is irregularly stated, the Middle term is used with different meanings in the Major and Minor Premise.

Thus :

The nature of a clock is to indicate the correct time;
To deviate from the correct time is the nature of a clock;
Therefore to deviate from the correct time is to indicate
the correct time.

Here the word "nature" in the first statement means the intention of the maker, but in the second the custom of the thing made. Such errors are exceedingly common with respect to other words in very common use, such as "church,” "happiness," "liberty," "rights," "representative," "necessity," "afford," "must," etc., and mistakes can only be avoided by carefully defining beforehand the sense in which we understand the terms. The neglect of this precaution gives rise to much misunderstanding and waste of time.

It is evident that in passing from one syllogism to another we are even more liable to the error of varying our terms than in passing from one Premise to another.

201. The Error of the Forgotten Condition. - Error sometimes arises when a Premise is stated subject to a certain implied condition which, not being expressed, is afterwards forgotten. Thus:

The doubling of the supply of a useful metal, iron, lead, etc., is a thing to be desired;

The doubling of the supply of gold is the doubling of the supply of a useful metal;

Therefore, the doubling of the supply of gold is a thing to be desired.

Here "useful," as applied to gold in the Minor Premise, implies a utility that is dependent on rarity; and this condition is forgotten in combining the Minor with the Major.

Connected with this error is the forgetfulness of the relative force of an epithet. A rat is an animal, and a chessplayer is a man, but a "huge rat" is not a "huge animal,” nor need "a clever chess-player" be " a clever man."

202. Errors of Confusion. (1) Ignorance of the point in question.1 Error arises from confusing the point in question. This is very common in law courts, and is effectively employed in producing a prejudice. Thus, if a clerk has pleaded guilty to a charge of fraud, but excuses himself on the ground that he was misled by companions, exposed by his employer to overwhelming temptation, or induced by poverty to commit the crime, the counsel for the prosecution. might ignore the point in question, which is, whether the circumstances extenuate the crime, and might insist on what is not denied, that "after all the fellow is a rogue."

1 This error is often called "Ignoratio Elenchi."