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therefore follow that the test cannot be depended on in other cases ?-does it follow that there are no beliefs uni. versally accepted as necessary, and in respect of which the test of necessity is valid ? Each of these questions may, I think, be rightly answered in the negative.

In alleging that if a belief is said by some to be necessary, but by others to be not necessary, the test of necessity is thereby shown to be no test, Mr. Mill tacitly assumes that all men have powers of introspection enabling them in all cases to say what consciousness testifies ; whereas a great proportion of men are incapable of correctly interpreting consciousness in any but its simplest modes, and even the remainder are liable to mistake for dicta of consciousness what prove on closer examination not to be its dicta. Take the case of an arithmetical blunder. A boy adds up a column of figures, and brings out a wrong total. Again he does it, and again errs.

His master asks him to go through the process aloud, and then hears him say “35 and 9 are 46”—an error which he had repeated on each occasion. Now, without discussing the mental act through which we know that 35 and 9 are 44, and through which we recognize the necessity of this relation, it is clear that the boy's misinterpretation of consciousness, leading him tacitly to deny this necessity by asserting that “35 and 9 are 46," cannot be held to prove that the relation is not necessary. This, and kindred misjudgments daily made by the most disciplined accountants, merely show that there is a liability to overlook what are necessary connections in our thoughts, and to assume as necessary others which are not. In these and hosts of cases, men do not distinctly translate into their equivalent states of consciousness the words they use. This negligence is with many so habitual, that they are unaware that they have not clearly represented to themselves the propositions they assert; and are then apt, quite sincerely though

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erroneously, to assert that they can think things which it is really impossible to think.

But supposing it to be true that whenever a particular belief is alleged to be necessary, the existence of some who profess themselves able to believe otherwise, proves that this belief is not necessary; must it be therefore admitted that the test of necessity is invalid ? I think not. Men may mistake for necessary, certain beliefs which are not necessary; and yet it may remain true that there are necessary beliefs, and that the necessity of such beliefs is our warrant for them. Were conclusions thus tested proved to be wrong in a hundred cases, it would not follow that the test is an invalid one; any more than it would follow from a hundred errors in the use of a logical formula, that the logical formula is invalid. If from the premise that all horned animals ruminate, it were inferred that the rhinoceros, being a horned animal, ruminates; the error would furnish no argument against the worth of syllogisms in general—whatever their worth may be. Daily there are thousands of erroneous deductions which, by those who draw them, are supposed to be warranted by the data from which they draw them; but no multiplication of such erroneous deductions is regarded as proving that there are no deductions truly drawn, and that the drawing of deductions is illegitimate. In these cases, as in the case to which they are here paralleled, the only thing shown is the need for verification of data and criticism of the acts of consciousness.

“ This argument,” says Mr. Mill, referring to the argument of necessity, “applied to any of the disputed questions of philosophy, is doubly illegitimate; ... the very fact that the question is disputed, disproves the alleged impossibility.” Besides the foregoing replies to this, there is another. Granting that there have been appeals illegitimately made to this test-granting that there are many questions too complex to be settled by it, which men have nevertheless proposed to settle by it, and have conse- : quently got into controversy; it may yet be truly asserted that in respect of all, or almost all, questions legitimately brought to judgment by this test, there is no dispute about the answer. From the earliest times on record down to our own, men have not changed their beliefs concerning the trųths of number. The axiom that if equals be added to unequals the sums are unequal, was held by the Greek no less than by ourselves, as a direct verdict of conscious. ness, from which there is no escape and no appeal. Each of the propositions of Euclid appears to us as absolutely beyond doubt as it did to them. Each step in each dem onstration we accept, as they accepted it, because we immediately see that the alleged relation is as alleged, and that it is impossible to conceive it otherwise.

But how are legitimate appeals to the test to be distinguished ? The answer is not difficult to find. Mr. Mill cites the belief in the antipodes as having been rejected by the Greeks because inconceivable, but as being held by ourselves to be both conceivable and true. He has before given this instance, and I have before objected to it (Principles of Psychology, p. 32), for the reason that the states of consciousness involved in the judgment are too complex to admit of any trustworthy verdict being given. An illustration will show the difference between a legitimate appeal to the test and an illegitimate appeal to it. A and B are two lines. How is it decided that they are equal or not equal? No way is open but that of comparing the two impressions they make on consciousness. I know them to be unequal by an immediate act, if the difference is great, or if, though only moderately different, they are close together; and supposing the difference is but slight, I decide the question by putting the lines in apposition when they are movable, or by carrying a movable line

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A

B

D

from one to the other if they are fixed. But in any case, I obtain in consciousness the testimony that the impression produced by the one line differs from that produced by the other. Of this difference I can give no further evidence than that I am conscious of it, and find it impossible, while contemplating the lines, to get rid of the consciousness. The proposition that the lines are unequal is a proposition of which the negation is inconceivable. But now suppose it is asked whether B and c are equal; or whether c and D are equal. No positive answer is possible. Instead of its being inconceivable that b is longer than c, or equal to it, or shorter, it is conceivable that it is any one of the three. Here an appeal to the direct verdict of consciousness is illegitimate, because on transferring the attention from B to c, or c to d, the changes in the other elements of the impressions so entangle the elements to be compared, as to prevent them from being put in apposition. If the question of relative length is to be determined, it must be by rectification of the bent line; and this is done through a series of steps, each one of which involves an immediate judgment akin to that by which A and B are compared. Now as here, so in other cases, it is only simple percepts or concepts respecting the relations of which immediate consciousness can satisfactorily testify; and as here, so in other cases, it is by resolution into such simple percepts and concepts, that true judgments respecting complex per cepts and concepts are reached. That things which are equal to the same thing are equal to one another, is a fact which can be known by direct comparison of actual or ideal relations, and can be known in no other way: the proposition is one of which the negation is inconceivable, and is rightly asserted on that warrant. But that the square of the hypothenuse of a right-angled triangle equals the sum of the squares of the other two sides, cannot be known immediately by comparison of two states of consciousness. Here the truth can be reached only mediately, through a series of simple judgments respecting the likenesses or unlikenesses of certain -relations : each of whicb judgments is essentially of the same kind as that by which the above axiom is known, and has the same warrant. Thus it becomes apparent that the fallacious result of the test of necessity which Mr. Mill instances, is due to a misapplication of the test.

These preliminary explanations have served to make clear the question at issue. Let us now pass to the essence of it.

Metaphysical reasoning is usually vitiated by some covert petitio principii. Either the thing to be proved or the thing to be disproved, is tacitly assumed to be true in the course of the proof or disproof. It is thus with the argument of Idealism. Though the conclusion reached is that Mind and Ideas are the only existences; yet the steps by which this conclusion is reached, take for granted that external objects have just the kind of independent existence which is eventually denied. If that extension which the Idealist contends is merely an affection of consciousness, has nothing out of consciousness answering to it; then, in each of his propositions concerning extension, the word should always mean an affection of conscious

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