The chief use of dignity is to veil ignorance. Thus, it is well known that the most dignified people, as a rule, are schoolmasters, and schoolmasters are usually so occupied with teaching that they have no time to learn anything. And because dignity is used to hide ignorance, it is plain that impudence is not always the opposite of dignity, but that dignity is sometimes impudence. Dignity is said to inspire respect; and this may be in part why respect for others is an error of judgment and self-respect is ridiculous. Self-respect is, of course, self-esteem. William James has remarked that self-esteem depends, not simply upon our success, but upon the ratio of our success to our pretensions, and can therefore be increased by diminishing our pretensions. Thus if a man is successful, but only then, can he be both ambitious and dignified. James also implies that happiness increases with self-esteem. Likeness of thought with one's friends, then, does not make one happy, for otherwise a man who esteemed himself little would be indeed happy. Also if a man is unhappy he could not, from our premisses, by the principles of the syllogism and of contraposition, be dignified--a conclusion which should be fatal to many novelists' heroes. A reflection on pessimism to which this discussion gives rise is the following: It would appear that a man's self-esteem would be increased by a conviction of the unworthiness of his neighbours. A man, therefore, who thinks that the world and all its inhabitants, except himself, are very bad, should be extremely happy. In fact, the effects would hardly be distinguishable from those of optimism. And optimism, as everybody knows, is a state of mind induced by stupidity. CHAPTER XXI THE SYNTHETIC NATURE OF DEDUCTION Doubt has often been expressed as to whether a syllogism can add to our knowledge in any way. John Stuart Mill and Henri Poincaré, in particular, held the opinion that the conclusion of a syllogism is an "analytic" judgment in the sense of Kant, and therefore could be obtained by the mere dissection of the premisses. Any one, then, who maintains that mathematics is founded solely on logical principles would appear to maintain that mathematics, in the last instance, reduces to a huge tautology. Mill, in Chapter III of Book II of his _System of Logic_, said that "it must be granted that in every syllogism, considered as an argument to prove the conclusion, there is a _petitio principii_. When we say All men are mortal, Socrates is a man, therefore Socrates is mortal,