A.-LOGICAL FALLACIES.

1. Inferential.

(1)-Fallacies of Immediate Inference.

In Conversion the most frequent fallacy is the simple conversion of A: 'All A is B, .. All B is A,' 'If A is, B is, .. If B is, A is.' The inference is, of course, fallacious, and violates the rule of conversion, viz., that no term should be distributed in the converse which was not distributed in the convertend; and the valid inference is 'Some B is A,' 'In some cases if B is, A is.' The simple conversion of O is also fallacious for the same reason: 'Some A is not B, .. Some B is not A.' The conversion of O into 'Some not-B is A' is not admissible, because it violates the first rule of conversion, viz., that the subject and the predicate of the convertend should be, respectively, the predicate and the subject in the converse.

In Obversion, Æquepolence, or Permutation the following are fallacious:

(1) All A is B; ... All not-A is not-B.
(2) All metals are elements;

.. All not-metals are not-elements.

(3) Cold is agreeable;

.. Heat is disagreeable.

(4) Virtue will be rewarded;

.. Vice will be punished.

In Contraposition the following are fallacious :

(1) No A is B; ... All not-B is A.

(2) No man is perfect;

.. All imperfect beings are men.

(3) Some A is B; .. Some not-B is A.

(4) Some elements are metals;

.. Some not-metals are elements.

In Opposition the following are fallacious:

(1) All plants are flowerless' is false;
.. 'No plants are flowerless' is true.

(2) 'All philosophers are poets' is false;
.. 'No philosophers are poets' is true.
(3) 'Some plants can move' is true;
... 'Some plants cannot move' is true.
(4) 'Some elements are metals' is true;
.. 'Some elements are not metals' is true.
(5) 'Some men are wise' is true;

.. 'Some men are not wise' is false.

§ 3. (2)-Fallacies of Syllogistic Inference.

These arise from the transgression of the syllogistic rules. Everyone of them is ultimately a breach of some one or other of the fundamental principles of Deductive Logic, and proximately of the general syllogistic rules, or of the special rules for each figure. Regarded as transgressions of the nine general syllogistic rules we have given in Part III. Chap. III. the fallacies are as follows:

:

(1) The Fallacy of Four Terms, arising from the transgression of the 1st rule.

(2) The Fallacy of Four Premisses, arising from the violation of the 2nd rule.

(3) The Fallacy of Undistributed Middle, arising from the breach of the 3rd rule.

(4) The Fallacy of Illicit Process, arising from the transgression of the 4th rule: of the Major Term, when this term is distributed in the conclusion and not in the premiss; and of the Minor Term, when this term is distributed in the conclusion and not in the premiss.

(5) The Fallacy of Negative Premisses, arising from the violation of the 5th rule.

(6) Fallacies also arise from the transgression of the 6th, 7th, 8th, and 9th rules, and belong to one or other of the fallacies mentioned above.

The most important of the fallacies under this head are those of Undistributed Middle and Illicit Process. Of these we shall give the following examples :

A

B

1. The virtuous are happy,

The wealthy are happy;

The wealthy are virtuous.

Undistributed Middle, because the middle term being the predicate in the two affirmative premisses, is not distributed.

B

2. All material bodies are extended,

Shadows are extended;

.. Shadows are material bodies.

3. Whatever thinks exists,
Matter does not think;

.. Matter does not exist. B

Undistributed Middle.

Illicit Process of the Major Term,

which being the predicate in the affirmative major premiss, is undistributed, but which is distributed in the conclusion, being the predicate in a negative proposition.

which is distributed in the conclusion, but not distributed in the minor premiss.

5.

a

1

6. All metals conduct heat and electricity,
All metals are elements;

. All elements conduct heat and electricity.

Illicit Process of the Minor Term.

7. All Hindus are Aryans,

The Persians are not Hindus; .. The Persians are not Aryans.

Illicit Process of the Major Term.

2. Non-Inferential.

§ 4. (1)--Semi-logical Fallacies.

These arise from ambiguous language. If a term is ambiguous, it is really equivalent to two, and there is thus the fallacy of four terms. In a fallacy of this kind, it is the middle term that is generally ambiguous, giving rise to what is called the fallacy of ambiguous middle. In some cases, the middle term is taken distributively in the major premiss, and collectively in the minor; in some it is taken collectively in the major and distributively in the minor premiss. In the former, we have the Fallacy of Composition, and in the latter the Fallacy of Division. We shall now give a few examples of each of these varieties:

1. An organized body is either a plant or an animal; a nation is an organized body: therefore a nation is either a plant or an animal. Here the word body is ambiguous.

2. Light is a mode of motion; feather is light: therefore feather is a mode of motion. Here the double meaning of the word light is obvious.

3. "All cold is to be expelled by heat; this person's disorder is a cold: therefore it is to be expelled by heat." Here the word cold is ambiguous: in the first premiss it means a low degree of heat or the sensation of coldness, and in the second a particular bodily disorder.

4. "Projectors are unfit to be trusted; this man has formed a project: therefore this man is unfit to be trusted." Here projector and formed a project do not mean the same thing.

5. "To be acquainted with the guilty is a presumption of guilt; this man is so acquainted: therefore we may presume that he is guilty." Here the phrases 'presumption of guilt' and 'presume that he is guilty' have different significations.

6. "All the angles of a triangle are equal to two right angles, ABC is an angle of a triangle; .: ABC is equal to two right angles," is a Fallacy of Division; for the middle term is taken collectively in the major and distributively in the minor premiss.

7. "Five is one number; three and two are five: therefore three and two are one number," is also a Fallacy of Division.

8. "Three and two are two numbers; five is three and two: therefore five is two numbers," is a Fallacy of Composition; for the middle term is taken distributively in the major premiss, and collectively in the minor.

9. "All the angles of a triangle are less than two right angles, ABC, ACB, and BAC are all the angles of a triangle; .. they are less than two right angles.”

Here the word all is ambiguous. In the major premiss the term ‘all the angles of a triangle' is taken distributively to mean any angle. In the minor premiss, it is doubtful whether it is taken collectively or distributively. If it is taken collectively, the argument involves the Fallacy of Composition. If it is taken distributively, the argument is valid.

10. "I can afford to buy these books. I can afford to buy these pictures. I can afford to buy these statuettes. The books, the pictures, and the statuettes are all that I, at present, wish to purchase. I can, therefore, buy everything that I want to buy." This is a Fallacy of Composition; these books,' 'these pictures,' and 'these statuettes' are taken distributively or separately in the first premiss, and collectively or jointly in the second..

11. The Fellows of the Royal Society have made the greatest discoveries in Science; A, B, and C are Fellows of the Royal Society; therefore A, B, and C have made the greatest discoveries in Science. This is a Fallacy of Division.

The next fallacy under this head is the Fallacy of Accident, which consists in taking a term simply or without any condition in one premiss, and as modified by certain accidents or as under certain circumstances in the other. For example, "What is bought in the market is eaten, raw meat is bought in the market; therefore raw meat is eaten." In the minor premiss the middle term, bought in the market, is taken simply, while in the major premiss it must be understood as modified by certain accidents or qualities not present in the other. There are, in fact, two middle terms, one 'bought in the market' without anything understood