The justness of such general observations as have been now given is never so well discerned as when they are elucidated by particular instances; and I will, therefore, briefly cite examples of the three principal sources of erroneous conclusions described, viz., ambiguities of language, insufficient or faulty induction, leading to undue generalisation, and the assumption of mere suppositions for real facts.

The examples which I shall adduce of these three several errors, I have selected with the view of also showing how needful it is to examine, with the utmost vigilance, whether such errors infect the original positions from which any theory sets

out.

Of the first-named error a memorable illustration is to be found in the writings of Mr. Ricardo. A number of erroneous and nugatory conclusions in his principal work on Political Economy, of which some appear glaringly paradoxical, and others, on a cursory inspection, wear such a semblance of profundity, as to have misled distinguished economists, had their source in a confused and ambiguous use of the word value, which may be detected even in the first section of his first chapter, and pervades the whole of his treatise.

The readiest way of explaining and elucidating this ambiguity will be to cite a passage from a work in which it is freely exposed.

"While Mr. Ricardo professedly used the term value in one sense only [that of purchasing power], he insensibly lapsed into a different sense." "The passage in his book where this transition is made, the turning point, if I may so call it, is in the very first section. Having quoted a few sentences from Adam Smith, which explain that, in rude ages, the quantities in which commodities were exchanged would be determined by the quantities of labour necessary to acquire them, he proceeds: If the quantity of labour realised in commodities regulate their exchangeable value, every increase of the quantity of labour must augment the value of that commodity on which it is exercised, as every diminution must lower it.' Now here Mr. Ricardo begins with using value in the sense of exchangeable value, or purchasing power; and, as he uses it in that sense in the premises, he is bound to do it in the conclusion; and the conclusion is true enough, if he means that every increase in the quantity of labour must augment the value of that commodity on which it is exercised in relation to other commodities which continued to require only the same labour as before. This, however, although perfectly consonant with his doctrines, will not be found to have been Mr. Ricardo's peculiar meaning. In this proposition he did not extend his view beyond the one commodity. The word value did not carry him over, as the phrase power of purchasing would have done, to

the consideration of some other. An attentive reader will perceive his meaning to have been, that every increase of labour would augment the value of the commodity on which it was exercised without reference to any other commodity. This proposition is the hook from which all his other propositions inconsistent with his own definition depend. This one false step made, he very logically falls into the obscurities and paradoxes which have excited the admiration of his disciples, and the astonishment of every body else."*

It

The theory of Mr. Malthus on population is a most instructive example of the second error. shows what a long train of unsound inferences may be consequent on the precipitate formation of a general law from an insufficient collection of facts; and this is to be found at the outset of his speculations, where it is assumed, on the slenderest grounds, that in all the various races of men, under all circumstances, habits, climates, and conditions, there is a uniform tendency to double their numbers in twenty-five years or less; a rate of increase which becomes certain provided they are supplied with sufficient food, shelter, and clothing; but such a sufficiency, in the long run, they never can be supplied with, inasmuch as food increases in only an arithmetical ratio. Even if Mr. Malthus's theory

*Letter to a Political Economist on the Subject of Value. See also "A Critical Dissertation on the Nature, Measures, and Causes of Value, 1825," by the Author.

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could be proved to be correct, the way in which he obtained his fundamental principles would ever remain a memorable instance of hasty generalisation, not merely as represented by others, but as recorded by himself.

It fortunately happens that we have an account of the matter in his own words. Nothing can be more explicit than the following statement.

"It has been said," writes Mr. Malthus, "that I have written a quarto volume to prove that population increases in a geometrical ratio, and food in an arithmetical ratio; but this is not quite true. The first of these propositions I considered as proved the moment the American increase was related, and the second proposition as soon as it was enunciated. The chief object of my work was to inquire what effects these laws, which I consider as established in the first six pages, had produced and were likely to produce on society."*

Thus of two important propositions, teeming with consequences, he considered the first (which in truth required to be substantiated by extensive research and cautious discrimination) as proved by one solitary instance; and the second (scarcely to be established by a less severe process) as purely self-evident. This is assuredly not the way in which the foundation of weighty and comprehensive theories ought to be laid.†

* Essay on Population, vol. ii. p. 453., 6th ed.

The reader who may wish to reconsider this important

Of the third error in our list we have a striking instance, almost equally instructive in its logical results although less momentous in its practical consequences, in the great fallacy which forms the basis of Berkeley's celebrated Theory of Vision. A more decided case of the assumption of purely imaginative facts as real and incontrovertible premises can scarcely be adduced from the records of philosophical speculation. The false step in question is committed in the second paragraph of his Essay, in which, with a perfect unconsciousness of what he is doing, he converts distance (an abstract term) into a material line, and represents it as both the patient and the agent of physical operations, which are of course wholly fictitious.

As this passage, however, will form the subject of particular comment in an Appendix to the present treatise, it is needless, after quoting it below, to do more here than point out the general character of

question is recommended to consult Mr. Doubleday's "True Law of Population," and an able tract by Mr. Hickson, first published in the Westminster Review, entitled, "An Essay on the Principle of Population," containing, in my opinion, the justest view of the subject yet given to the world, and remarkable for its abstinence from hasty generalisation, the besetting sin of Mr. Malthus.

* "It is, I think, agreed by all that distance of itself and immediately cannot be seen. For distance being a line directed endwise to the eye, it projects only one point in the fund of the eye. Which point remains invariably the same whether the distance be longer or shorter."