Proof is said to be direct when the reasons directly imply the thesis, and indirect when they imply the falsity of all possible alternatives, and hence indirectly imply the truth of the thesis. Thus, if we argue that a given straight line, AB, is equal to another given straight line, Cl), we employ the indirect mode of proof if we show that AB is not greater than CD, and that it is not less. The only possible alternative is that AB is equal to CD.
Argumentation includes also the processes of disproof and of refutation which, however, are fundamentally processes of proof, since dis proof consists in proving that a given thesis is false, and refutation consists in proving that a thesis for which reasons have been given is not proved by them, having regard to the require ments of proof.
Principles may be divided according to their source into two general classes, namely, those derived from Experience and those derived from Authority. Principles derived from Ex perience include the laws of nature, scientific truths and, in short, all general propositions which are suggested or confirmed by experience, as for example, call men are mortal" •, the air has weight" • °unsupported bodies fall to the groune• °division of labor increases its ef ficiency." Principles derived from Authority include civil laws, rules of action and other general propositions, declared, enacted or promulgated, usually for the guidance or government of a class or community, by a legislature, church, judge, lawgiver, teacher, inspired writers or by any man or body of men having or assuming authority, as for example: °every person who, being a witness in a judicial proceeding, makes a statement under oath which he knows to be false is guilty of perjury and is liable to a pen alty"; it is wrong to commit murder"; "all men are created free and equal"; "all who be lieve will be saved." Arguments may be divided into two general classes, according as the principle on which they are based is derived from Authority or from Experience. This division is similar to that adopted by lawyers when they speak of issues of law and issues of fact. The following is an example of an argument where the principle is an enacted law : Thesis: This prisoner is guilty of perjury and is liable to a penalty.
Reason : Because being a witness in a judicial proceeding he made a statement under oath which he knew to be false.
Principle: Because every person who, being a witness in a judicial proceeding, makes a statement under oath which he knows to be false, is guilty of perjury and is liable to penalty.
Arguments based on principles derived from Experience may be conveniently divided into eight general classes, namely: arguments to prove facts of Causation, arguments from Ex ample, from Analogy, from Cause to Effect, from Effect to Cause, from Testimony, from Sign and from Circumstantial Facts of Causation.— That one thing is the cause or the effect of another may be proved by reference to one of the five principles first formulated by John Stuart Mill, which are as follows : (a) Agreement.—When two or more in stances of the phenomenon under investigation have only one circumstance in cir cumstance in which alone all the instancd"agree is the cause (or effect) of the given phenome non.
(b) Difference.—If an instance in which the phenomenon under investigation occurs and an instance in which it does not occur have every circumstance in common save one, that one oc curring only in the former, the circumstance in which alone the two instances differ is the effect or the cause or an indispensable part of the cause of the phenomenon.
(c) Joint Method.— If two or more in stances in which the phenomenon occurs have only one circumstance in common, while two i or more instances in which it does not occur have nothing in common save the absence of that circumstance, the circumstance in which alone the two sets of instances differ is the effect or the cause or an indispensable part of the cause of the phenomenon.
(d) Residues.— Subduct from any phenom enon such part as previous induction has shown to be the effect of certain antecedents and the residue of the phenomenon is the effect of the remaining antecedents.
(e) Concomitant Variations.—Whatever phe nomenon varies in manner whenever an other phenomenon varies in some particular manner is either a cause or an effect of that phenomenon or is connected with it through some fact of causation.