has no value except for the particular facts which it sums up.

"The mortality of John, Thomas, and company is, after all, the whole evidence we have for the mortality of the Duke of Wellington. Not one iota is added to the proof by interpolating a general proposition. Since the individual cases are all the evidence we can possess, evidence which no logical form into which we choose to throw it can make greater than it is; and since that evidence is either sufficient in itself, or, if insufficient for the one purpose, cannot be sufficient for the other; I am unable to see why we should be forbidden to take the shortest cut from these sufficient premisses to the conclusion, and constrained to travel the high priori road' by the arbitrary fiat of logicians." 1

"The true reason which makes us believe that Prince Albert will die is, that his ancestors, and our ancestors, and all the other persons who were their contemporaries, are dead. These facts are the true premisses of our

reasoning." It is from them that we have drawn the general proposition; they have taught us its scope and truth; it confines itself to mentioning them in a shorter form; it receives its whole substance from them; they act by it and through it, to lead us to the conclusion to which it seems to give rise. It is only their representative, and on occasion they do without it. Children, ignorant people, animals know that the sun will rise, that water will drown them, that fire will burn them, without employing this general proposition. They reason, and we reason, too, not from the general to the particular, but from particular to particular :

"All inference is from particulars to particulars; General propositions are merely registers of such inferences already made,

1 Mill's Logic, i. 211.

and short formulæ for making more: The major premiss of a syllogism, consequently, is a formula of this description: and the conclusion is not an inference drawn from the formula, but an inference drawn according to the formula: the real logical antecedent, or premisses, being the particular facts from which the general proposition was collected by induction. Those facts, and the individual instances which supplied them, may have been forgotten; but a record remains, not indeed descriptive of the facts themselves, but showing how those cases may be distinguished respecting which the facts, when known, were considered to warrant a given inference. According to the indications of this record we draw our conclusion; which is to all intents and purposes, a conclusion from the forgotten facts. For this it is essential that we should read the record correctly: and the rules of the syllogism are a set of precautions to ensure our doing so."

"1

"If we had sufficiently capacious memories, and a sufficient power of maintaining order among a huge mass of details, the reasoning could go on without any general propositions; they are mere formulæ for inferring particulars from particulars.” 2

Here, as before, logicians are mistaken: they gave the highest place to verbal operations, and left the really fruitful operations in the background. They gave the preference to words over facts. They perpetuated the nominalism of the Middle Ages. They mistook the explanation of names for the nature of things, and the transformation of ideas for the progress of the mind. It is for us to overturn this order in logic, as we have overturned it in science, to exalt particular and instructive facts, and to give them in our theories that superiority and importance which our practice has conferred upon them for three centuries past.

1 Mill's Logic, i. 218.

• Ibid. i. 240.

VI.

There remains a kind of philosophical fortress in which the Idealists have taken refuge. At the origin of all proof are Axioms, from which all proofs are derived. Two straight lines cannot enclose a space; two things, equal to a third, are equal to one another; if equals be added to equals, the wholes are equal. These are instructive propositions, for they express, not the meanings of words, but the relations of things. And, moreover, they are fertile propositions; for arithmetic, algebra, and geometry are all the result of their truth. On the other hand, they are not the work of experience, for we need not actually see with our eyes two straight lines in order to know that they cannot enclose a space; it is enough for us to refer to the inner mental conception which we have of them the evidence of our senses is not needed for this purpose; our belief arises wholly, with its full force, from the simple comparison of our ideas. Moreover, experience follows these two lines only to a limited distance, ten, a hundred, a thousand feet; and the axiom is true for a thousand, a hundred thousand, a million miles, and for an unlimited distance. Thus, beyond the point at which experience ceases, it is no longer experience which establishes the axiom. Finally, the axiom is a necessary truth; that is to say, the contrary is inconceivable. We cannot imagine a space enclosed by two straight lines: as soon as we imagine the space enclosed, the two lines cease to be straight; and as soon as we imagine the two lines to be straight, the space ceases to be enclosed In the assertion of axioms, the constituent ideas are irresistibly drawn together. In

the negation of axioms, the constituent ideas inevitably repel each other. Now this does not happen with truths of experience: they state an accidental relation, not a necessary connection; they lay down that two facts are connected, and not that they must be connected; they show us that bodies are heavy, not that they must be heavy. Thus, axioms are not, and cannot be the results of experience. They are not so, because we can form them mentally without the aid of experience; they cannot be so, because the nature and scope of their truths lie beyond the limits of experience. They have another and a deeper source. They have a wider scope, and they come from elsewhere.

Not so, answers Mill. Here again you reason like a schoolman; you forget the facts concealed behind your conceptions; for examine your first argument. Doubtless you can discover, without making use of your eyes, and by purely mental contemplation, that two straight lines cannot enclose a space; but this contemplation is but a displaced experiment. Imaginary lines here replace real lines: you construct the figure in your mind instead of on paper: your imagination fulfils the office of a diagram on paper: you trust to it as you trust to the diagram, and it is as good as the other; for in regard to figures and lines the imagination exactly reproduces the sensation. What you have seen with your eyes open, you will see again exactly the same a minute afterwards with your eyes closed; and you can study geometrical properties transferred to the field of mental vision, as accurately as if they existed in the field of actual sight. There are, therefore, experiments of the brain as there are

ocular ones; and it is after just such an experiment that you deny to two straight lines, indefinitely prolonged, the property of enclosing a space. You need not for this purpose pursue them to infinity, you need only transfer yourself in imagination to the point where they converge, and there you have the impression of a bent line, that is of one which ceases to be straight.1 Your presence there in imagination takes the place of an actual presence; you can affirm by it what you affirmed by your actual presence, and as positively. The first is only the second in a more commodious form, with greater flexibility and scope. It is like using a telescope instead of the naked eye; the revelations of the telescope are propositions of experience; so are those of the imagination. As to the argument which distinguishes axioms from propositions of experience under the pretext that the contraries of the latter are conceivable, while the contraries of axioms are inconceivable, it is nugatory, for this distinction does not exist. Nothing prevents the contraries of certain propositions of experience from being conceivable, and

1 "For though, in order actually to see that two given lines never meet, it would be necessary to follow them to infinity; yet without doing so we may know that if they ever do meet, or if, after diverging from one another, they begin again to approach, this must take place not at an infinite, but at a finite distance. Supposing, therefore, such to be the case, we can transport ourselves thither in imagination, and can frame a mental image of the appearance which one or both of the lines must present at that point, which we may rely on as being precisely similar to the reality. Now, whether we fix our contemplation upon this imaginary picture, or call to mind the generalisations we have had occasion to make from former ocular observation, we learn by the evidence of experience, that a line which, after diverging from another straight line, begins to approach to it, produces the impression on our senses which we describe by the expression a bent line,' not by the expression 'a straight line.""-MILI's Logic, i. 364.