CHAPTER VII.

OF FALLACIES.

§ 1. I.-A General Outline.

A Fallacy, in the proper sense of the term, is a transgression of a rule of inference. A fallacious reasoning is, in fact, an apparent reasoning involving the breach of some rule or other of the various kinds of inference. Thus there are as many different kinds of Fallacies as of Reasoning or Inference.

The breach of the laws of Inductive Reasoning gives rise to the Fallacies of Induction with which we have nothing to do here. The breach of the rules of Deductive Inference gives rise, first, to the Fallacies of Immediate Inference, when the rule transgressed is a rule of Immediate Inference, and, secondly, to the Fallacies of Mediate Inference, when the rule violated is one of Syllogism or of any other kind of Mediate Deductive Reasoning. Thus we have the following classes of Fallacies in the sense we have defined above:

Fallacies of Mediate
Inference.

I. Syllogistic:

Undistributed Middle..

Illicit Process.

Four Terms.

&c. &c.

Permutation.

Contraposition.

Opposition.

Subalternation.

Modal Consequence. II. Non-Syllogistic, e. g.,

Change of Relation.

Mathematical.

In a wider sense a Fallacy is a transgression of any logical rule whatever. In this sense we have in Deductive Logic the Fallacies or Faults of Division and Definition; and in Inductive Logic those of Classification, Hypothesis, &c. The violation of the rules to which every logical division and definition ought to conform gives rise to the faults of division and definition, such as cross division, incomplete division, definition by accidental qualities, &c. To this class belong also the fallacies arising from ambiguity in language, such as those of Ambiguous Middle, of Division, Composition, &c. These are transgressions of the logical rule that our thoughts should be expressed and reasonings conducted in clear and unambiguous language,

In the widest sense, the word fallacy may be taken to mean an error of any kind, whether of Intuition, Perception, Observation, Division, Definition, Inference, &c. In this sense it includes, besides those mentioned above, the fallacies of Irrelevancy or Irrelevant Conclusion, technically called Ignoratio Elenchi, of Petitio Principii (begging the question), of False Premiss, and also those which Mill calls Fallacies of Simple Inspection, or of Erroneous First Principles and Axioms.

It is not necessary that we should describe and explain in detail each of the fallacies mentioned above, for most of them have been already made evident in explaining and illustrating the rules. In the following pages we shall notice and illustrate the more frequent and important kinds only.

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: