principles are perceived to be necessary only by a few minds of highly cultivated insight, such principles as the axioms of Geometry and Arithmetic may be perceived to be necessary by all minds which have any habit of abstract thought at all and I conceive also, that though these axioms are brought into distinct view by a certain degree of intellectual cultivation, they may still be much better described as conditions of experience, than as results of experience :-as laws of the mind and of its activity, rather than as facts impressed upon a mind merely passive.

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XII. Absurdities in Mr. Mill's Logic.-72. will not pursue the subject further: only, as the question has arisen respecting the absurdities to which each of the opposite doctrines leads, I will point out opinions connected with this subject, which Mr. Mill has stated in various parts of his book.

He holds (i. 317) that it is merely from habit that we are unable to conceive the last point of space or the last instant of time. He holds (ii. 360) that it is strange that any one should rely upon the à priori evidence that space or extension is infinite, or that nothing can be made of nothing. He holds (i. 304) that the first law of motion is rigorously true, but that the axioms respecting the lever are only approximately true. He holds (ii. 110) that there may be sidereal firmaments in which events succeed each other at random, without obeying any laws of causation; although one might suppose that even if space and cause are both to have their limits, still they might terminate together: and then, even on this bold supposition, we should no where have a world in which events were casual. He holds (ii. 111) that the axiom, that every event must have a cause, is established by means of an induction by simple enumeration:" and in like manner, that the principles of number and of geometry are proved by this method of simple enumeration alone. ascribes the proof (i. 162) of the axiom, "things which are equal to the same are equal to each other," to the fact that this proposition has been perpetually found true and never false. He holds (i. 338) that "In all

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propositions concerning numbers, a condition is implied, without which none of them would be true; and that condition is an assumption which may be false. The condition is that 1=1."

73. Mr. Mill further holds (i. 309), that it is a characteristic property of geometrical forms, that they are capable of being painted in the imagination with a distinctness equal to reality :-that our ideas of forms exactly resemble our sensations: which, it is implied, is not the case with regard to any other class of our ideas; that we thus may have mental pictures of all possible combinations of lines and angles, which are as fit subjects of geometrical experimentation as the realities themselves. He says, that "we know that the imaginary lines exactly resemble real ones;" and that we obtain this knowledge respecting the characteristic property of the idea of space by experience; though it does not appear how we can compare our ideas with the realities, since we know the realities only by our ideas; or why this property of their resemblance should be confined to one class of ideas alone.

74. I have now made such remarks as appear to me to be necessary, on the most important parts of Mr. Mill's criticism of my Philosophy. I hope I have avoided urging any thing in a contentious manner; as I have certainly written with no desire of controversy, but only with a view to offer to those who may be willing to receive it, some explanation of portions of my previous writings. I have already said, that if this had not have been my especial object, I could with pleasure have noted the passages of Mr. Mill's Logic which I admire, rather than the points in which we differ. I will in a very few words refer to some of these points, as the most agreeable way of taking leave of the dispute.

I say then that Mr. Mill appears to me especially instructive in his discussion of the nature of the proof which is conveyed by the syllogism; and that his doctrine, that the force of the syllogism consists in an inductive assertion, with an interpretation added to it, solves very happily the difficulties which baffle the

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other theories of this subject. I think that this doctrine of his is made still more instructive, by his excepting from it the cases of Scriptural Theology and of Positive Law (i. 260), as cases in which general propositions, not particular facts, are our original data. I consider also that the recognition of Kinds (i. 166) as classes in which we have, not a finite but an inexhaustible body of resemblances among individuals, and as groups made by nature, not by mere definition, is very valuable, as stopping the inroad to an endless train of false philosophy. I conceive that he takes the right ground in his answer to Hume's argument against miracles (ii. 183) and I admire the acuteness with which he has criticized Laplace's tenets on the Doctrine of Chances, and the candour with which he has, in the second edition, acknowledged oversights on this subject made in the first. I think that much, I may almost say all, which he says on the subject of Language, is very philosophical; for instance, what he says (ii. 238) of the way in which words acquire their meaning in common use. I especially admire the acuteness and force with which he has shown (ii. 255) how moral principles expressed in words degenerate into formulas, and yet how the formula cannot be rejected without a moral loss. This "perpetual oscillation in spiritual truths," as he happily terms it, has never, I think, been noted in the same broad manner, and is a subject of most instructive contemplation. And though I have myself refrained from associating moral and political with physical science in my study of the subject, I see a great deal which is full of promise for the future progress of moral and political knowledge in Mr. Mill's sixth Book, "On the Logic of the Moral and Political Sciences." Even his arrangement of the various methods which have been or may be followed in "the Social Science," "the Chemical or Experimental Method," "the Geometrical or Abstract Method," "the Physical or Concrete Deductive Method," "the Inverse Deductive or Historical Method," though in some degree fanciful and forced, abounds with valuable suggestions; and his estimate of "the

interesting philosophy of the Bentham school," the main example of "the geometrical method," is interesting and philosophical. On some future occasion, I may, perhaps, venture into the region of which Mr. Mill has thus essayed to map the highways: for it is from no despair either of the great progress to be made in such truth as that here referred to, or of the effect of philosophical method in arriving at such truth, that I have, in what I have now written, confined myself to the less captivating but more definite part of the subject.

CHAPTER XXIII.

POLITICAL ECONOMY AS AN INDUCTIVE SCIENCE

(Moral Sciences.)-1. BOTH M. Comte and Mr. Mill, in speaking of the methods of advancing science, aim, as I have said, at the extension of their methods to moral subjects, and aspire to suggest means for the augmentation of our knowledge of ethical, political, and social truths. I have not here ventured upon a like extension of my conclusions, because I wished to confine my views of the philosophy of discovery to the cases in which all allow that solid and permanent discoveries have been made. Moreover in the case of moral speculations, we have to consider not only observed external facts and the ideas by which they are colligated, but also internal facts, in which the instrument of observation is consciousness, and in which observations and ideas are mingled together, and act and react in a peculiar manner. It may therefore be doubted whether the methods which have been effectual in the discovery of physical theories will not require to be greatly modified, or replaced by processes altogether different, when we would make advances in ethical, political, or social knowledge. In ethics, at least, it seems plain that we must take our starting-point not without but within us. Our mental powers, our affections, our reason, and any other faculties which we have, must be the basis of our convictions. And in this field of knowledge, the very form of our highest propositions is different from what it is in the physical sciences. In Physics we examine what is, in a form more or less general: in Ethics we seek to determine what OUGHT to be, as the highest rule, which is supreme over all