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to stand. When remembering a certain thing as in a certain place, the place and the thing are mentally represented together; while to think of the non-existence of the thing in that place, implies a consciousness in which the place is represented but not the thing. Similarly, if, instead of thinking of an object as colorless, we think of it as having color, the change consists in the addition to the concept of an element that was before absent from it-the object cannot be thought of first as red and then as not red, without one component of the thought being totally expelled from the mind by another. The doctrine of the Excluded Middle, then, is simply a generalization of the universal experience that some mental states are directly destructive of other states. It formulates a certain absolutely-constant law, that no positive mode of consciousness can occur without excluding a correlative negative mode; and that the negative mode cannot occur without excluding the correlative positive mode: the antithesis of positive and negative, being, indeed, merely an expression of this experience. Hence it follows that if consciousness is not in one of the two modes, it must be in the other. But now, under what conditions only can this law of conscious. ness hold? It can hold only so long as there are positive states of consciousness that can exclude the negative states, and which the negative states can in their turn exclude. If we are not concerned with positive states of conscious ́ness at all, no such mutual exclusion takes place, and the law of the Alternative Necessity does not apply. Here, then, is the flaw in Sir William Hamilton's proposition. That Space must be infinite or finite, are alternatives of which we are not obliged to regard one as necessary, seeing that we have no state of consciousness answering to either of these words as applied to the totality of Space, and therefore no exclusion of two antagonist states of consciousness by one another. Both alternatives being un

or is

thinkable, the proposition should be put thus: Space is either ; neither of which can be conceived, but. one of which must be true. In this, as in other cases, Sir William Hamilton continues to work out the forms of thought when they no longer contain any substance; and, of course, reaches nothing more than verbal conclusions.

Ending here these comments on doctrines of Sir William Hamilton, which Mr. Mill rejects on grounds that will be generally recognized as valid, let me now pass to a doctrine, partly held by Sir William Hamilton, and held by others in ways variously qualified and variously extended—a doctrine which, I think, may be successfully defended against Mr. Mill's attack.

In the fourth and fifth editions of his Logic, Mr. Mill treats, at considerable length, the question, Is inconceivability an evidence of untruth ?—replying to criticisms previously made on his reasons for asserting that it is not. The chief answers which he there makes to these criticisms, turn upon the interpretation of the word inconceivable. This word he considers is used as the equivalent of the word unbelievable; and, translating it thus, readily disposes of sundry arguments brought against him. Whether any others who have used these words in philosophical discussion, have made them synonymous, I do not know; but that they are so used in those reasonings of my own which Mr. Mill combats, I was not conscious, and was surprised to find alleged. It is now manifest that I had not adequately guarded myself against the misconstruction which is liable to arise from the double meaning of the word belief-a word which, we have seen, is used for the most coherent and the least coherent connections in consciousness, because they have the common character that no reason is assignable for them. Through

out the argument to which Mr. Mill replies, the word is used only in the first of these senses. The "invariably existent beliefs," the "indestructible beliefs," are the indissoluble connections in consciousness-never the dissoluble ones. But unbelievable implies the dissoluble ones. By association with the other and more general meaning of the word belief, the word unbelievable suggests cases where the proposition admits of being represented in thought, though it may be with difficulty; and where, consequently, the counter-proposition admits of being decomposed. To be quite sure of our ground, let us define and illustrate the meanings of inconceivable and unbelievable. An inconceivable proposition is one of which the terms cannot, by any effort, be brought before consciousness in that relation which the proposition asserts between them-a proposition of which the subject and the predicate offer an insurmountable resistance to union in thought. An unbelievable proposition is one which admits of being framed in thought, but is so much at variance with experience, in which its terms have habitually been otherwise united, that its terms cannot be put in the alleged relation without effort. Thus, it is unbelievable that a cannon-ball fired from England should reach America; but it is not inconceivable. Conversely, it is inconceivable that one side of a triangle is equal to the sum of the other two sides-not simply unbelievable. The two sides cannot be represented in consciousness as becoming equal in their joint length to the third side, without the representation of a triangle being destroyed; and the concept of a triangle cannot be framed without a simultaneous destruction of a concept in which these magnitudes are represented as equal. That is to say, the subject and predicate cannot be united in the same intuition-the proposition is unthinkable. It is in this sense only that I have used the word inconceivable; and only when rigorously restricted to this

sense do I regard the test of inconceivableness as having any value.

I had concuded that when this explanation was made, Mr. Mill's reasons for dissent would be removed. Passages in his recently-published volume, however, show that, even restricting the use of the word inconceivable to the meaning here specified, he still denies that a proposition is proved to be true by the inconceivableness of its negation. To meet, within any moderate compass, all the issues which have grown out of the controversy, is difficult. Before passing to the essential question, however, I will endeavor to clear the ground of certain minor questions.

Describing Sir William Hamilton's doctrine respecting the ultimate facts of consciousness, or those which are above proof, Mr. Mill writes:

"The only condition he requires is that we be not able to 'reduce it (a fact of this class) to a generalization from experience.' This condition is realized by its possessing the 'character of necessity.' 'It must be impossible not to think it. In fact, by its necessity alone can we recognize it as an original datum of intelligence, and distinguish it from any mere result of generalization and custom. In this Sir William Hamilton is at one with the whole of his own section of the philosophical world; with Reid, with Stewart, with Cousin, with Whewell, we may add, with Kant, and even with Mr. Herbert Spencer. The test by which they all decide a belief to be a part of our primitive consciousness-an original intuition of the mind-is the necessity of thinking it. Their proof that we must always, from the beginning, have had the belief, is the impossibility of getting rid of it now. This argument, applied to any of the disputed questions of philosophy, is doubly illegitimate: neither the major nor the minor premise is admissible. For in the first place, the very fact that the question is disputed, disproves the alleged impossibil

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ity. Those against whom it is needful to defend the belief which is affirmed to be necessary, are unmistakable examples that it is not necessary. These philosophers, therefore, and among them Sir William Hamilton, mistake altogether the true conditions of psychological investigation, when, instead of proving a belief to be an original fact of consciousness by showing that it could not have been acquired, they conclude that it was not acquired, for the reason, often false, and never sufficiently substantiated, that our consciousness cannot get rid of it now."

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This representation, in so far as it concerns my own views, has somewhat puzzled me. Considering that I have avowed a general agreement with Mr. Mill in the doctrine that all knowledge is from experience, and have defended the test of inconceivableness on the very ground that it. expresses the net result of our experience up to the present time" (Principles of Psychology, pp. 22, 23)—considering that, so far from asserting the distinction quoted from Sir William Hamilton, I have aimed to abolish such distinction-considering that I have endeavored to show how all our conceptions, even down to those of Space and Time, are "acquired "—considering that I have sought to interpret forms of thought (and by implication all intuitions) as products of organized and inherited experiences (Principles of Psychology, p. 579)-I am taken aback at finding myself classed as in the above paragraph. Leaving the personal question, however, let me pass to the assertion that the difference of opinion respecting the test of necessity itself disproves the validity of the test. Two issues are here involved. First, if a particular proposition is by some accepted as a necessary belief, but by one or more denied to be a necessary belief, is the validity of the test of necessity thereby disproved in respect of that particular proposition? Second, if the validity of the test is disproved in respect of that particular proposition, does it