In a certain sense all knowledge is inductive. We can only learn the laws and relations of things in nature by observing those things. But the knowledge gained from the senses is knowledge only of particular facts, and we require some process of reasoning by which we may collect out of the facts the laws obeyed by them. Experience gives us the materials of knowledge: induction digests those materials, and yields us general knowledge. When we possess such knowledge, in the form of general propositions and natural laws, we can usefully apply the reverse process of deduction to ascertain the exact information required at any moment. In its ultimate foundation, then, all knowledge is inductive—in the sense that it is derived by a certain inductive reasoning from the facts of experience.

The alternatives before us are simple. Our empire and race already comprise one-fifth of the world's population, and by our plantation of new states, by our guardianship of the seas, by our penetrating commerce, by the example of our just laws and firm constitution, and above all by the dissemination of our new arts, we stimulate the progress of mankind in a degree not to be measured. If we lavishly and boldly push forward in the creation and distribution of our riches, it is hard to over-estimate the pitch of beneficial influence to which we may attain in the present. But the maintenance of such a position is physically impossible. We have to make the momentous choice between brief greatness and longer continued mediocrity.

You will perceive that economy, scientifically speaking, is a very contracted science; it is in fact a sort of vague mathematics which calculates the causes and effects of man's industry, and shows how it may be best applied. There are a multitude of allied branches of knowledge connected with mans condition; the relation of these to political economy is analogous to the connexion of mechanics, astronomy, optics, sound, heat, and every other branch more or less of physical science, with pure mathematics.

Neither in deductive nor inductive reasoning can we add a tittle to our implicit knowledge, which is like that contained in an unread book or a sealed letter. ...Reasoning explicates or brings to conscious possession what was before unconscious. It does not create, nor does it destroy, but it transmutes and throws the same matter into a new form.

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There is no such thing as absolute cost of labour; it is all a matter of comparison. Every one gets the most which he can for his exertions; some can get little or nothing, because they have not sufficient strength, knowledge or ingenuity; others get much, because they have, comparatively speaking, a monopoly of certain powers.

I need hardly stay to demonstrate that facts are valueless unless connected and explained by a correct theory; that analogies are very dangerous grounds of inference, unless carefully founded on similar conditions; and that experience misleads if it be misinterpreted.

Aristotle's dictim... may then be formulated somewhat as follows:—Whatever is known of a term may be stated of its equal or equivalent. Or, in other words, Whatever is true of a thing is true of its like. ...the value of the formula must be judged by its results; ...it not only brings into harmony all the branches of logical doctrine, but... unites them in close analogy to the corresponding parts of mathematical method. All acts of mathematical reasoning may... be considered but as applications of a corresponding axiom of quantity...