was

tribe which had the prærogativa, or the right of voting first, always indicated the decision of the other tribes: the number of citizens included in a tribe was so great, and the selection w made in such a manner, that the suffrages of that number of citizens were a fair representation of the opinions of the entire free community.(49) On the other hand, the number of cases may be too small, or too uncertain in their selection, to justify the inference that they are a part homogeneous with the whole. The maxim of evidence adverted to in a former chapter, (50) 'mendax in uno præsumitur mendax in alio,' affords another instance of this mode of inductive extension, and of the necessity of analyzing the nature of the instance on which the argument is founded. There may be false statements in the evidence of a witness, of such a nature as not to justify the inference that the rest of his evidence is false. On the other hand, if a deliberate lie, in a material point, is detected in any deposition, the veracity of the witness is successfully impeached, and the credibility of the rest of his evidence is either destroyed or seriously shaken.

In practical politics, a large part of that skill which is derived from special knowledge and experience, consists in judging how many instances may serve as fair specimens of a class; which cases are exceptional and accidental, and therefore of minor importance; which are indicative of a prevailing and general state of things, and therefore require a closer attention. When a

occurrence of the events, that, when thrown into groups, constitute the materials of our averages, the greater should be the number of our facts.

4. That though the possible error to which a given small number of facts is liable is very large, there is always a fair probability in favour of any particular average coinciding with, or approaching very closely to, the true average.

5. That the formula of the mathematician have a very limited application to the results of observation; and that, if incautiously applied, they may lead to very grave errors.

6. That though averages derived from large numbers of facts are worthy of much greater confidence than those founded upon small numbers of facts, the latter class of averages are by no means to be rejected as useless, but should be employed as probabilities of greater or less value, as the number of facts is larger or smaller.

(49) Pro Planc. 20.

(50) Above, ch. vii. § 16.

man, on the one hand, never judges hastily from an insufficient number of cases, and mistakes exceptions for samples; 'when, on the other, he never carries on his inquiries after the true character of the class has been clearly determined, and continues to investigate cases when those already examined have sufficed to ground an inductive extension to the entire class; when he never snatches a rash opinion from a rapid glance, nor goes plodding on with a barren examination of particulars, when the truth is already before his eyes,-his practical judgment may be said to have attained a high pitch of perfection.

All control, supervision, and management, both in public and private life, is conducted upon this principle. No man can watch every act, direct every movement, or verify every item of account, in those who are placed under his authority. The efficient exercise of his functions, whether he be charged with the administration of a public department or establishment, or of a private household, is to carry his examination so far, as to have a reasonable assurance that the facts which he ascertains fairly represent those which he does not ascertain, and that he selects such parts for his personal inquiries as enable him to know the whole.

§ 18 At the same time, too much cannot be said against that popular abuse of the Method of Agreement denounced with so much emphasis by Bacon, which infers causation from the mere juxtaposition or coincidence of two facts in several cases within a man's personal experience; which, by a simple enumeration of circumstances, (51) without subjecting them to any preliminary or ulterior process of analysis, at once blindly concludes that they are related by a law of constant sequence. It is from such inferences as these, that the great majority of

(51) Inductio mala est, quæ per enumerationem simplicem principia concludit scientiarum, non adhibitis exclusionibus et solutionibus sive separationibus naturæ debitis.'-Nov. Org. i. 69. Inductio quæ procedit per enumerationem simplicem, res puerilis est, et precario concludit, et periculo exponitur ab instantiâ contradictoriâ, et plerumque secundum pauciora quam par est, et ex his tantummodo quæ præsto sunt, pronunciat. At inductio, quæ ad inventionem et demonstrationem scientiarum et artium erit utilis, naturam separare debet, per rejectiones et exclusiones debitas ;

popular and prevalent errors upon political questions originate. As Mr. Mill remarks: (52) The tendency of unscientific inquirers is to rely too much upon number, without analyzing the instances; without looking closely enough into their nature, to ascertain what circumstances are or are not eliminated by means of them. Most people hold their conclusions with a degree of assurance proportioned to the mere mass of the experience on which they appear to rest: not considering that by the addition of instances to instances, all of the same kind, that is, differing from one another only in points already recognised as immaterial, nothing whatever is added to the evidence of the conclusion. A single instance eliminating some antecedent which existed in all the other cases, is of more value than the greatest multitude of instances which are reckoned by their number alone.'

It is a capital error to suppose that any multiplication of instances will suffice, if the other necessary safeguards against paralogism are not adopted. In general, however, it happens that the inferences drawn by the unverified Method of Agreement are not founded upon a very wide experience. Very frequently they are cases which have fallen accidentally within the observation of a single man, and neither are derived from an exhaustive enumeration, nor have been selected with scientific judgment; as Bacon says of this arithmetical species

ac deinde post negativas tot quot sufficiunt, super affirmativas concludere.' -Ib. i. 105. See also, i. 46.

Compare the Distributio Operis, vol. ix. p. 167; and the Partis Instaurationis Secunda Delineatio, vol. xi. p. 164, where this passage is in part repeated. See also Mr. Mill's comment upon it, Logic, b. v. c. 5, § 4.

In lib. ii. aph. 15 and 16, Bacon further insists upon the necessity of a negative process in induction. In the latter aphorism he says: "Est itaque inductionis veræ opus primum (quatenus ad inveniendas formas) rejectio sive exclusiva naturarum singularum, quæ non inveniuntur in aliquâ instantiâ, ubi natura data adest; aut inveniuntur in aliquâ instantiâ, ubi natura data abest; aut inveniuntur in aliquâ instantiâ crescere, cum natura data decrescat; aut decrescere, cum natura data crescat. Tum vero post rejectionem et exclusivam debitis modis factam, secundo loco (tanquam in fundo) manebit (abeuntibus in fumum opinionibus volatilibus) forma affirmativa, solida, et vera, et bene terminata. Atque hoc breve dictu est, sed per muitas ambages ad hoc pervenitur.'

As to the inventio formarum (which Bacon makes the end of all human knowledge), and the meaning of forma, see lib. ii. aph. 1-4.

(52) Vol. i. p. 510.

of induction, Plerumque secundum pauciora quam par est, et ex his tantummodo quæ præsto sunt, pronunciat.' (5) Hence we may observe the proneness of people to generalize cases which have occurred to themselves, to one of their own family or friends, or to an inhabitant of their own neighbourhood. Without attempting any analysis of the circumstances, they pronounce confidently from some complex but undissected case, and infer from it a general law of causation. Thus, they not unfrequently reason as to the treatment of a disease from the apparent efficacy of a cure in a single case, or in a few cases, forgetting the obscurity of the antecedents in such an instance, and the necessity of observing the same mode of treatment upon a large scale, before any confident judgment is formed. Thus, too, in judging of political matters, they sometimes assume that a complex law or institution is incapable of separation, because their experience has only exhibited its elements to them in a combined form; and hence they attribute to the whole, an effect which is in fact due exclusively to one of its parts. Accordingly, a person might suppose that the oral examination of witnesses is a result of the system of trial by jury, or that the spectacle of an execution is the necessary effect of capital punishments: not having been accustomed to see them divided, it might not occur to him to consider that witnesses may be examined orally in open court, where the judge decides without a jury; and that capital punishment may be inflicted without the ceremony of a public

execution.

It might be thought that the proneness to generalize rapidly from a few instances is a sign of a philosophic and reflecting mind. On the contrary, it is the characteristic of the vulgar. There is a prevailing tendency to the incautious use of the in

(53) Compare also his remarks in the Parasceue ad Historiam Naturalem :- In historiâ quam requirimus et animo destinamus, ante omnia videndum est, ut late pateat, et facta sit ad mensuram universi. Neque enim arctandus est mundus ad angustias intellectûs (quod adhuc factum est), sed expandendus intellectus, et laxandus, ad mundi imaginem recipiendam, qualis invenitur. Istud enim respicere pauca, et pronunciare secundum pauca, omnia perdidit.'-vol. xi, p. 415.

ductive argument from one or a few cases to the entire class, without the necessary safeguards. This is noticed by Aristotle, who uses it to account for the pleasure taken by ordinary and uneducated hearers in the sweeping affirmations of an orator, who lays down as a general apophthegm what they have observed partially. If a man has bad neighbours or children, he derives much pleasure from hearing it announced that no evil is greater than a bad neighbour or a bad child.(5)

Many of the generalizations of speculative politicians with respect to the tendencies of certain political forms-in other words, their fitness to produce certain effects-have been formed in this manner. Certain phenomena have been observed in connexion with a certain form of government, or a certain political system, in a given country, and from that single instance it has been inferred, that the form of government or political system with which they co-exist is their cause, and that they are its effect. This mode of reasoning (which will be illustrated at length in a future chapter), (5) is in fact nothing more than a feeble application of the Method of Agreement, supported, perhaps, by a few subsidiary arguments, and sometimes by an ineffective use of the Method of Difference, as in the example of comparisons of different countries, stated above.

§ 19 As, in cases of this description, the error of reasoning arises from the neglect or misapplication of the negative process of rejection or exclusion, so forcibly inculcated by Bacon, it will be proper to inquire further into the manner of employing this process. Bacon specifies the following three modes of its application :

1. Certain circumstances are absent in an instance where the phenomenon is present.

2. The phenomenon is absent in an instance where the circumstances are present.

3. The circumstances increase where the phenomenon decreases; or the converse. . (56)

(54) Rhet. ii. 22, § 15.

(55) Below, ch. xv. § 5.

(56) See Nov. Org. ii. aph. 16, cited above, n. 51.