The Art of Logical Thinking; Or, The Laws of Reasoning

by William Walker Atkinson

Appeal to Ignorance, in which an appeal is made to the ignorance of the opponent that his conviction may follow from his inability to prove the contrary. It is virtually no argument that: "So-and-so must be true, because you cannot prove that it is not." As Brooks says: "To argue that there is no material world, because we cannot explain how the mind knows it to exist, is the celebrated fallacy of Hume in philosophy. The fact that we cannot find a needle in a haystack is no proof that it is not there."

Introduction of New Matter, also called Non Sequitur, in which matter is introduced into the conclusion that is not in the premises. Hyslop gives the following example of it: "All men are rational; Socrates is a man; therefore, Socrates is noble." De Morgan gives the following more complex example: "Episcopacy is of Scripture origin; The Church of England is the only Episcopal church in England; therefore, the church established is the church that ought to be supported."

Other fallacies, resembling in some respects those above mentioned, are as follows:

Fallacy of Ambiguous Terms, in which different meanings of the same word are used to produce the fallacious argument. As Jevons says: "A word with two distinct meanings is really two words."

Confusion between Collective and General Meanings of a Term, of which Jevons says: "It would be obviously absurd to argue that because all the books in the British Museum Library are sure to give information about King Alfred, therefore any particular book will be sure to give it. By 'all the books in the British Museum Library,' we mean all taken together. There are many other cases where the confusion is not so evident, and where great numbers of people are unable to see the exact difference."

Arguing from the Collective to the General, in which the fallacy consists of arguing that because something is true of the whole of a group of things, therefore it is true of any of those things. Jevons says: "All the soldiers in a regiment may be able to capture a town, but it is absurd to suppose that therefore every soldier in the regiment could capture the town single handed. White sheep eat a great deal more than black sheep; but that is because there are so many more of them."

Uncertain Meaning of a Sentence, from which confusion arises and fallacious argument may spring. Jevons says: "There is a humorous way of proving that a cat must have three tails: Because a cat has one tail more than no cat; and no cat has two tails; therefore, any cat has three tails." Here the fallacy rests upon a punning interpretation of "no."

Proving the Wrong Conclusion, in which the attempt to confuse conclusions is made, with the result that some people will imagine that the case is established. Jevons says: "This was the device of the Irishman, who was charged with theft on the evidence of three witnesses, who had seen him do it; he proposed to call thirty witnesses who had not seen him do it. Equally logical was the defense of the man who was called a materialist, and who replied, 'I am not a materialist; I am a barber.'"

Fallacy of Unsuccessful Argument, in which is attempted the illogical conclusion that because a certain argument has failed the opposite conclusion is proven. This fallacy is quite common, especially in cases of juries. One side fails to prove certain contentions, and the jury leaps to the conclusion that the opposite contention must be correct. This is clearly fallacious, for there is always the possibility of a third explanation. In the case of a claim of alibi juries are apt to fall into this fallacy. The failure of the attempt to establish an alibi is often held to be in the nature of proof of the guilt of the accused. Old trial lawyers assert that a failure to establish a claimed alibi tends to injure the chance of the accused more than direct evidence against him. Yet, as all logical reasoners will see, there is no logical validity in any such inference. As Jevons has well said: "No number of failures in attempting to prove a proposition really disprove it." At the end of each failure the case simply stands in the same position as before the attempt; i.e., "not proven."

All Violations of the Rules of the Syllogism constitute fallacies, as may be seen by forming a syllogism in violation of one or more of the rules.