This is unquestionably true; for, if he does not know what things he is speaking about, he cannot possibly bring them to comparison in his mind. A witness who swears that a prisoner did a certain act when, as a matter of fact, he does not know whether the prisoner did it or not, swears falsely, independently of the question whether rebutting evidence can be brought to prove the perjury. It is reported that a man, who wished to be thought an acquaintance of Dr. Johnson, remarked to him in coming out of church, 'A good sermon to-day, Dr. Johnson.' 'That may be, sir,' replied the very much over-estimated doctor, 'but I'm not sure that you can know it.' This hits the point precisely.

It will be shown in a subsequent chapter that a proposition of moderate complexity has an almost unlimited number of contradictory propositions, which are more or less in conflict with the original. The truth of any one or more of these contradictories establishes the falsity of the original, but the falsity of the original does not establish the truth of any one or more of its contradictories, because there always remains the alternative that nothing is known concerning the relations of the terms. It may even happen that no relation at all exists between the terms. In this view of the matter, then, an assertion of the falsity of a proposition means its simple deletion. The contrariety is not between knowledge and knowledge, but between knowledge and ignorance.

It ought also to be remembered, in dealing with the doctrine of falsity, that the falsity of all Xs are Ys' only implies that one or more Xs are not Ys. Now in practice one or a few exceptions are often of no importance; there are in many cases singular exceptions which in a sense agree with, and in a sense falsify, a general proposition. Thus all points of a revolving sphere describe circles, excepting

Other examples of singular

the two points at the poles. exceptions will be found in the Principles of Science, Chapter XXIX. Professor Henrici points out (Elementary Geometry, 1879, p. 37) that a proposition must be considered to be true in general, if it be true in an infinite proportion of cases, and false only in a finite number of exceptions.

This subject of the truth and falsity of propositions as premises and conclusion may be pursued in Karslake's Logic, vol. i. p. 83; Whately, Book II. Chap. iii. § 2; Aristotle, Prior Analytics, Book II. Chaps. i.-iv.; Port Royal Logic, Part II. Chap. vii. Watts' Logic, Part II. Chap. ii. §§ 7 and 8.

Most of the scholastic logicians, such as Thomas Aquinas and Nicephorus Blemmidas, treat this subject elaborately.

9. Trust' (said Lord Mansfield to to Sir A. Campbell) to your own good sense in forming your opinions; but beware of attempting to state the grounds of your judgments. The judgment will probably be right;—the argument will infallibly be wrong.'

Explain this phenomenon, and show its logical significance.

[P.]

If you give reasons for a decision, implying that those reasons are sufficient, and are the reasons upon which you did make the decision, it is possible for critics subsequently to inquire whether such reasons logically support the conclusion derived from them. If they do not, the judge will be detected in a paralogism which there may be no means of explaining away. But, if no reasons be given,

it will seldom be possible for critics to make any such detection. It is impossible, as a general rule, to publish in detail the law as well as the evidence upon which a law case is decided, and, even if it were published, it would generally be impossible to detect bad logic in a man who does not assign the precise points on which he relies, and the way in which he argues about a complex mass of details.

The

Although it may be, from his own point of view, convenient and discreet for a man to avoid giving reasons for any important public decision, if he can avoid it, yet it is an open question how far such means of escaping criticism is likely to increase the carefulness and impartiality of his judgments. There are many cases, including nearly all the verdicts given by juries on points of fact, where it would be highly undesirable to require any statement of reasons. Where the result depends upon oral testimony, the behaviour of witnesses, the estimation of degrees of probability and degrees of guilt, it is quite impossible to define and publish the real premises of the conclusion come to. We must trust to common sense and judicial tact. same remarks may apply to various arbitrations, magisterial decisions, administrative acts, votes of members of deliberative bodies. But where the grounds of decision are precise and brief, so as to be capable of complete statement, it seems absurd to suppose that a judge will judge less well because he needs to disclose his argument. If he displays bad logic, where bad logic can be judged, he is clearly not fit to be a judge. Lord Mansfield's advice may possibly have been prudent and good when given to a man who was forced to act in novel circumstances, and in a distant colony (Jamaica), where his decisions would have more of the nature of administrative acts than law-building

judgments. But the decisions of the High Court of Justice in England not only affect the parties in the cause, but shape the public law of a large part of the civilised world, and it is of course requisite that they should be guided by good logic.

CHAPTER XIII

EXERCISES REGARDING FORMAL AND MATERIAL TRUTH

AND FALSITY

1. COMPARE the following syllogisms, or pseudo-syllogisms, both as regards their formal correctness, and as regards the material truth of their premises and conclusion; then explain how it is that a materially true conclusion is obtained in each case.

(1) All existing things are real things;

No abstract ideas are existing things; .. No abstract ideas are real things.

(2) No real things exist;

All abstract ideas are real things; .. No abstract ideas are real things.

(3) All real things are existing things;

No abstract ideas are existing things; ... No abstract ideas are real things.

2. If there be two syllogisms, of which we know that their major premises are subcontrary propositions, how may we determine the figure and mood of both? May their conclusions be both true in matter?

3. Prove by means of the syllogistic rules, that given the