have been illustrated in the preliminary survey of language with which this work commenced (Chap. IV. § 60.) Fallacies purely logical may be divided into four sub-classes:

1. Fallacy of Four Terms. This occurs in the syllogism where an attempt is made to use four terms, which can only result in two syllogisms or in a false conclusion.

2. Fallacy of Undistributed Middle. As,--All Frenchmen are Europeans; all Parisians are Europeans; therefore all Parisians are Frenchmen. The conclusion here is true, but the argument fallacious.

3. Fallacy of Illicit Process. As,--Because many nations are capable of self-government, and nations capable of self-government should not receive laws from a despotic government, therefore no nation should receive laws from a despotic government.

4. Fallacy of Negative Premisses. As,-Colonists are not Europeans, and Americans are not Europeans; therefore Colonists are Americans.

5. Fallacies of the Breach of Rule 6 of the Syllogism. As,All Austrians are Europeans; no Australians are Europeans; therefore all Australians are Austrians.

All of the above are violations of the rules of the syllogism, and have been referred to before. The fallacies exhibited in breaches of the other rules of the syllogism are included under the fallacies first named.

§ 44. The following are Material fallacies, or those arising outside of the verbal statement (extra dictionem), and concerned in subject-matter of the argument :

1. Fallacy of Accident and its Converse. This fallacy consists on the one side in arguing erroneously from a general rule to a special case; on the other side, in arguing unwarrantably from a special case to a general one; or, thirdly from a special case to a special case. Of the first case may be cited: Men are forbidden to kill; using capital punishment is killing; therefore men are forbidden to use capital punishment. What you bought yesterday you eat to-day; you bought raw meat yesterday; therefore you eat raw meat to-day. He who thrusts a knife into a person should be punished; a surgeon, in operating, does so; therefore he should be punished. Of the second case may be cited: To give to beggars promotes mendicancy, and the practice should be discouraged; therefore no assistance should be given to anyone who solicits it. This man is white as to his teeth; therefore he is

white. (Fallacia a dicto secundum quid ad dictum simpliciter.) These fallacies arise from changing the premisses in the course of the argument. A proposition is usually taken with some qualification which is omitted or disregarded in the conclusion, or when a qualification, which is necessary and implied in order to make a proposition true, is disregarded in the argument, this fallacy occurs. It is a common fallacy attending the arguments of loose and careless thinkers. Those errors which arise from taking a proposition as true in the abstract,' that is, without limitation, have their place under this head.

2. Fallacy of Irrelevant Conclusion (Ignoratio elenchi). This is a fallacy which introduces a conclusion which the premisses do not prove. This man is accused of crime; but his accuser is a bad man; therefore the accused is innocent. The distrust which is given to anything said by a young man in argument, and a conclusion of the falsity of his arguments because of his youth; the influence of any matter introduced by way of ridicule, and which is extraneous to the subject, afford illustrations of this error. The great mass of mankind act upon this fallacious method of argument. The character of the man who presents and advocates a case or a measure usually determines persons to consider his arguments good or bad. Many people never can be convinced by one whom they dislike. The best and most complete arguments which have ever been advanced have been disposed of, even by intelligent men, upon the consideration that the author was not a man of much profundity or reputation. It is often gravely argued in opposition to considerations for the benefit of some religious body, against which there is a prejudice, that we ought not to displease God, the real question being whether supporting such a sect would be displeasing God, and the statement enunciated in regard to displeasing or pleasing Him not being the matter in question at all. Persons who have weak cases almost invariably introduce into their arguments a series of irrelevant conclusions; the arts of orators are often largely exercised in surreptitiously introducing and skilfully covering results of argument which are of no relevancy whatever.

3. Fallacy of Petitio Principii (Begging the Question). This is the common fallacy of assuming the very point sought to be proven. Every complete syllogism is a petitio principii, the conclusion being included in and asserted by the major premiss. Arguing in a circle illustrates the same difficulty. Those who

attempt to prove the being of God from the Scriptures are in this situation, for the truth of the Scriptures depends upon the prior assumption of God's existence. If we were to argue that we are bound to obey laws by a social compact entered into by our ancestors, we assume that it took place before society was called into existence, whereas there is no such thing as social obligation till society has first been formed. This fallacy, like the preceding, is of great extent. It pervades reasonings upon nearly every subject, and has entered, not only into every science, but into the foundations of all science. It has prevailed in formal reasoning and in informal. Appellations and epithets have conveyed the fallacy as well as extended statements. It is exposed by complete definition, and its evils are thereby more readily corrected than by any other method. If the premisses are clearly and specifically set out in their full import, we are not apt to be misled by this unwarranted assumption.

4. Fallacy of the Consequent (Non sequitur).--This class includes arguments so inconsequential that they have no cogency. An assertion of a conclusion which does not have any connection with the premisses is of this character. The following is an example: Episcopacy is of Scripture origin; the Church of England is the only episcopal church in England; therefore the Established Church is the church which should be supported.

5. Fallacy of Many Questions.-This division embraces those fallacies which arise when two or three questions are so combined that no true answer can be given to them without analysis. Was Washington the first President of the United States and a man of ill repute? can be answered correctly only by separating the questions. Have you left off practising law? addressed to a man who never had been a lawyer, would be answered fallaciously if replied to by Yes or No. This fallacy scarcely deserves a separate place in the treatment of fallacious arguments, for when embodied in an argument it is really included under some of the other fallacies here referred to and classified.

§ 45. A further division of arguments is sometimes made into Direct (or Ostensive) and Indirect. A direct argument is one in which the proof is directed to the conclusion desired; an indirect, where the proof of the conclusion is reached indirectly-where, for instance, the argument aims to show the truth or falsity of the contradictory of the conclusion really in dispute. If that contradictory is true the conclusion is disproved, and conversely. The

type of indirect arguments is the Reductio ad absurdum, by which everything contradictory to a given proposition is shown to be absurd. This is a common method of proof in geometry and is both legitimate and valuable.

§ 46. It should again be remarked that here, as elsewhere, the divisions made are not separable by sharply drawn demarcations. The constant interference of induction and deduction has been noticed. And as between perfect and imperfect arguments, there is a shading of one class into the other. Arguments are relatively perfect and imperfect. There is no absolutely perfect proof, though some may be esteemed perfect, so far as all practical purposes are concerned. From these conclusions which have the highest certainty to the merest empirical uniformities there is every variety of completeness.

§ 47. To sum up: Arguments are products of inference, being processes of reasoning expressed and preserved in words. They may all be reduced to two forms, which furnish a groundwork for a division into Inductive and Deductive Arguments, which are always found interwoven with each other, though the prevailing character of the argument is either one or the other, the former term characterising an argument which rests in a general conclusion, the latter an argument which rests in the identification of a particular with a general. Arguments are also Perfect, Imperfect and Fallacious. According to still another classification, they are Direct and Indirect. The validity of all arguments is determined finally by the test of universal congruity.

CHAPTER LV.

PRINCIPLES.

§ 1. WE have examined the earliest and most rudimentary of the products of Cognition and found them comprised under the names: Percepts, Re-percepts, Concepts, Abstracts and Judgments. We also found represented by the terms Fictions, Definitions, Divisions and Arguments, certain integrations of knowledge having a distinctive character and a very considerable importance. In the exposition of the last named class we observed that certain propositions acquired an individuality consisting in the fact that

they stand as foundations for arguments, being either the premisses from which a chain of reasoning proceeds or conclusions upon which the mind rests, and which are recognised as a basis for other possible reasonings. In other words, there are many propositions which express uniformities of nature and whose office is to declare those uniformities-to furnish resting places and points of departure for thought. Such propositions are Principles: they are landings on the staircase of thought. Principle and Law are substantially synonymous terms, although sometimes it is claimed that a law is the expression of a principle. If this be accepted, we are then called upon to suppose that a principle is some mental cognition of which the law is the expression in words: this cognition must be a judgment or a single notion. Unless such a cognition be a primitive or ultimate notion, it does not differ in character from any other notion; its distinctive character as a principle comes from its use and its use depends upon its expression. All that which makes it a principle, as distinguished from any other notion, is involved with its expression, so that the law is really the principle. It may be claimed, however, that in so far as a principle is an ultimate notion it is something different from other notions, and that it should hence be distinguished from its expression in words. Without here discussing the questions concerning the points of difference, if there be any, between ultimate and proximate notions, it is sufficient to observe that the term principle is not applied solely to such notions. It has reference as well to maxims of life, to empirical agreements, to high and low generalisation in science and art. To restrict it to the sphere of necessary and universal truth may be (in the view of some) to give it the meanings it ought to have; but no one can with propriety maintain that it is confined within such limits. Accordingly we shall consider principle and law to be convertible terms, preferring, however, the former as having fewer allotropic meanings than the latter, and applying both to propositions and not to single

names.

§ 2. It may be remarked of principles at the outset that they are, as a matter of fact, either Individual or Common. Every person has his own set of principles, however crude or erroneous they may be. A wild man of the woods has his own data from which he reasons as much as has a civilised being, and these data have been formed by the circumstances of the savage's life. But only those principles which are common to a considerable number of 1 Cf. Dugald Stewart, Elements, Vol. II. Chap. I. Sec. 2.