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middle term (Quarternio Terminorum) consists simply in the substitution of a new term, hav- . ing the same verbal sign as in the original, but a different meaning—as in the examples given.
The case of undistributed middle--as, e. g., “X is Y, Z is Y .. Z is X”- consists in the illicit substitution of species for genus in the predicate of an affirmative proposition (i. e., X for Y in the minor premise).
In the case of illicit process of the minor term,
as, l. g., “ Y is not X, some Z is Y ... Z is not X,"--genus is illicitly substituted for species in the subject of an affirmative proposition (i, e., Z for “Some Z" in the minor premise).
In the case of illicit process of the major,-as, e. g., “ Y is X, Z is not Y... Z is not X,”— genus is illicitly substituted for species in the predicate of a negative proposition (i. e., X for Y in the minor premise).
In the case of negative premise, if the conclusion be affirmative,-as, e. g., “Y is not X, Z is not Y .:Z is X,”-genus is substituted for species in the predicate of a negative proposition (i. e., Not-X for Y in the minor premise). If the conclusion be negative,-as, e.g., “ Y is not X, Z is not Y., Z is not X,”-the fallacy will consist in the illicit substitution of one for another of two unrelated terms (i. e., X for Y); and the same will be true of the other cases, if any there be.
$ 125. THE LAWS OF THOUGHT. — The rules of Logic are founded upon what are called the primary Laws of Thought, viz. : (1) the Law of Identity (or rather the Law of Equivalence); (2) the Law of Contradiction; and (3) the Law of Excluded Middle; the first of which governs the process of Inference, the last two, that of the Judgment. The corresponding fallacies consist in their violation.
These laws may be enunciated in a form to make them of practical utility, as follows:
(1) THE LAW OF IDENTITY.
Significates (i. l., things or quasi-things) remain the same though denoted by different terms.
Hence terms denoting the same significates may, to the extent of their equivalence, be used interchangeably, i. e., the one substituted for the other.
The mathematical axiom that “things equal to the same thing are equal to each other is merely a special application of this principle, its meaning being simply that terms denoting the same class of significates are equivalent to each other.
It is obvious, therefore, that this law is not adequately stated (as is sometimes said) by the equation, A = A, but rather by the equation, A= B; both terms being supposed to denote the same class of significates, and the term B
to be either A, or any other vocable or sign denoting the same significates.
(2) THE LAW OF CONTRADICTION, OR RATHER THE LAW OF NON-CONTRADICTION.
A term, and its negative, or contradictory, cannot be predicated universally of any term.
This law and the next are often misstated. (3) THE LAW OF EXCLUDED MIDDLE.
Of two contradictory propositions, one must be true; or symbolically : “Either A is B,” or "Some A is not B.”?
RULES OF JUDGMENT
$ 126. Rule I. TERMS TO BE SIGNIFICANT.
In every logical proposition—by which is meant every proposition to be used in ratiocination—the terms must be significant, i. l., must have definite signification.
This rule follows from the definition of the term and of the proposition; for unless the word or vocable has such definite signification there is no name, and consequently no term or proposition, or valid ratiocination. The violation of this rule may be called the Fallacy of Non-significance or Nonsense.
Rule II. TERMS TO BE RIGHTLY DEFINED. Terms used in ratiocination must not only have
'V., supra, $ 90.
a definite signification, but the signification must be legitimate, i. e., they must not be falsely defined. This implies (1) that a term shall not be used in an improper sense, i. e., in a sense not permitted by the usage of the language'; and (2) that the term shall be so defined as to signify a real concept ; or, at least, that the contrary shall not affirmatively appear.
The violation of this rule will be called the Fallacy of False Definition.
Rule III. PREMISES NOT TO BE ILLICITLY ASSUMED.
A proposition that is obviously untrue, or that can, on logical principles, be affirmatively shown to be untrue, cannot be legitimately used as a premise.
The violation of this rule is called the fallacy of “ Begging the Question," or Petitio Principii ; and this and the fallacies resulting from the violation of Rules I. and II. may be classed together under the general head of Illicit Premises.
Rule IV. PREMISES TO CORRESPOND TO THE THESIS OR ISSUE.
In all ratiocination—if designed to be fruitful
· The unnecessary use of a term in a sense not justified by usage is commonly indicative either of mental incapacity or fallacious intent; and should therefore be forbidden, as to children we forbid the use of deadly weapons, or to all the possession of counterfeiters' tools.
Shuan -the premises, and, consequently, also the conclusion, must correspond to the Thesis or Issue, whether that be expressed or understood, or merely determined by the conditions of the problem.
By the thesis is meant the proposition to be demonstrated; by the issue, the thesis and the anti-thesis, or contradictory, considered together with a view of determining whether the one or the other is true.
With regard to nearly all subjects presented to us for investigation the material question at issue is more or less definitely determined by the conditions of the problem; and hence it is said, “ A prudent questioning is a kind of half knowledge” (Prudens interrogatio est dimidium sapientiæ). Where the issue is thus determined, it constitutes the real issue, or thesis and antithesis of the problem. In other cases it must be determined by agreement, or by actual intention, either expressed or understood. In many cases it is not formally stated, but we ascertain it, for the first time, from the use made of the conclusion.
The fallacy resulting from a violation of this rule-if we assume there is no fallacy in the inference-will necessarily involve a departure from the thesis or issue, both in the premises and in the conclusion. With regard to the premises, it is called the fallacy of Mistaking