Arguments from example, from analogy and to prove facts of causation are usually classed as inductive arguments and all others as deductive. For the distinction between in ductive and deductive see the article on Disproof, like proof, may be direct or indi rect. It is direct when the reasons directly imply the falsity of the thesis, and it is indirect when the reasons imply the truth of any one alternative, or of any fact inconsistent with the truth of the thesis. Thus, the thesis in a crim inal trial that the prisoner at such a time and place committed a certain offense may be dis proved indirectly by the proof that the prisoner at that time was elsewhere, usually called prov ing an alibi. A general proposition may be dis proved indirectly in two ways, first, by proving exceptions called exceptive disproof ; secondly, by showing that a proposition manifestly absurd is logically deducible from it, called a reductio ad absurdum.
Refutation consists in showing the fallacy of an argument having regard to the require ments of proof. This may be done in two ways, first, by showing that the reason or the principle relied on, whether express or implied, is untrue. Thus, an argument from Testimony may be refuted by showing that the witness is untrustworthy, as for example, that he lacked the means or opportunity for accurately observ ing the facts testified to, that he was biased by interest or hostility, that his testimony is incon sistent with itself or with other facts better known or better established, that his memory is defective, that he is known to be untruthful, etc. An argument from 'Example may be re futed by showing exceptions to the general law sought to be proved, or by showing that the search for negative examples has not been ex haustive. An argument from Analogy may be refuted by showing points of essential dif ference between the things compared; an argu ment from Cause to Effect, by showing the operation of other causes to prevent the effect; and an argument from Effect to Cause, by show ing the operation of other causes to produce the same effect. The common fallacy com mitted in arguments to prove facts of causation is to argue that one thing is the effect of an other merely because it follows that post hoc ergo propter antecedents of the effect besides the alleged cause being overlooked. In an argument from circum stantial evidence there is an implied assump tion that the facts given as a reason cannot be explained or accounted for in any reasonable way except on the supposition that the thesis is true. The argument may be refuted by showing that the facts may be otherwise ex plained. The so-called "theory of the defense' in a criminal trial is usually a thesis by which the facts may be accounted for consistently with the prisoner's innocence.
Secondly, an argument may be refuted by showing that the principle and the reason even if true, do not imply the thesis. Fallacies of
this kind all involve some form of irrelevancy. Thus, in the fallacy of "evading the issue,' the reasons imply an irrelevant conclusion, or in other words, the conclusion proved is not the question in dispute, but is either (1) a thesis that is like it and is intended to be mistaken for it; or (2) a thesis that is entirely different from the question at issue, the argument being often employed to distract attention from the real issue, or as it is sometimes expressed, Ito draw a herring across the trail?' The argu ment ad hominem which is addressed, not to the merits of the case, but to the character, principles or conduct of an opponent; the argu ment ad populum or ad captandum, which con sists in making an improper appeal to the feel ings of those addressed; the argument ad vere cundiam (reverence) which invokes the au thority of a great name as concluding the ques tion; the to quoque argument—are all forms of the fallacy of evading the issue, as opposed to the argument ad rem, which is addressed to the matter in dispute. This fallacy is often committed in refutation when our opponent by way of answer elaborately disproves a proposi tion which we never maintained, a process which is sometimes called °setting a straw man up only to knock him down' In like manner the reason or the principle or both may be ir relevant through ambiguity of language or otherwise.
The fallacy of °begging the con sists in attempting to prove a thesis by itself which in the course of the argument is either tacitly assumed to be true or, if expressed as a reason, is disguised in an equivalent form of words.
The fallacy of non sequitur (it does not fol low) really includes all the foregoing fallacies of the second class, but the name is usually restricted to loosely constructed arguments, for which no appropriate name has been found. Professor DeMorgan gives the following ex ample: °Episcopacy is of Scripture origin; the Church of England is the only Episcopal Church in England; therefore, the Church established is the Church that should be supported.) Bibliography.— Bain, (Logic Deductive and Inductive' ; Baynes,
of Logical Forme ; Boole,