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 under what conditions only can this law of consciousness hold? It can hold only so long as there are positive states of consciousness that can exclude and can be excluded. If we are not concerned with positive states of consciousness at all, no mutual exclusion takes place, and the law of the Alternative Necessity does not apply. Here, then, is the flaw

in Sir W. 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 unthinkable, the proposition should be put thus:-Space is either

or is ; neither of which can be conceived, but one of which must be true. In this, as in other cases, Sir W. Hamilton continues to work out the forms of thought when they no longer contain any substance; and, of course, reaches nothing more than semblances of conclusions.

But even were there no such reply as this, Sir W. Hamilton's argument might still be met. He says that inconceivability is no criterion of impossibility. Why? Because, of two propositions, one of which must be true, it proves both impossible-proves that Space cannot have a limit, because a limit is inconceivable, and yet that it must have a limit, because unlimited Space is inconceivableproves, therefore, that Space has a limit and has no limit,

which is absurd. How absurd? Absurd, because "it is impossible for the same thing to be and not to be." But how do we know that it is impossible for the same thing to be and not to be? What is our criterion of this impossibility? Can Sir W. Hamilton assign any other than this same inconceivability? If not, his reasoning is self-contradictory; seeing that he assumes the validity of the test in proving its invalidity.

§ 433. And now let us sum up this argument which has been made so elaborate by the necessity of meeting criticisms. Its leading propositions may be succinctly expressed as follows:

An abortive effort to conceive the negation of a proposition, shows that the cognition expressed is one of which the predicate invariably exists along with its subject; and the discovery that the predicate invariably exists along with its subject, is the discovery that this cognition is one we are compelled to accept. It is a necessary relation in consciousness; and to suppose there can be any higher warrant, is to suppose that there are relations which are more than necessary.

That some propositions have been wrongly accepted as true, because their negations were supposed inconceivable when they were not, does not disprove the validity of the test, for these reasons :-(1) that they were complex propositions, not to be established by a test applicable only to propositions no further decomposable; (2) that this test, in common with any test, is liable to yield untrue results, either from incapacity or from carelessness in those who use it; (3) that if it were needful to abandon the test because an absolute guarantee against the misuse of it cannot be found, still more needful would it be to abandon logical principles, the misapplications of which are immeasurably more numerous; but that (4) as applied only to the undecomposable propositions which embody the ultimate relations of number,

space and time, the test when used with due care has ever yielded, and continues to yield, uniform results.

That experiences of the relations among phenomena in the past, form the only basis for our present knowledge of such relations, is fully admitted. But if it be a fundamental law that connexions of ideas become strong in proportion as they are repeated, then the adjustment between Thought and Things, produced even by the experiences of individual life, must be such that perpetually-repeated absolute relations in things, will generate relations in thought that are also absolute. But the test of the inconceivableness of their negations, used by us to discover which relations among our thoughts are absolute, represents a justification transcendently greater; for the absolute relations in our thoughts are the results not of individual experiences only, but of experiences received by ancestral individuals through all past time.

Reasoning itself can be trusted only on the assumption that absolute uniformities of Thought correspond to absolute uniformities of Things. For logical intuitions there is no warrant assignable other than that assignable for all intuitions accepted as certain; namely, the impossibility of thinking the opposite. Unless it be alleged that the consciousness of logical necessity has a different origin, and a higher origin, it must be admitted that the consciousness of logical necessity is just as much a product of past experiences as is every other consciousness of necessity. Consequently, it must either be said that the experiences which yield the consciousness of logical necessity, are simpler, more distinct, more direct, and more frequently-repeated, than are the experiences which yield any other consciousness of necessity (and this is just the reverse of the fact); or else it must be conceded that the consciousness of logical necessity can have no higher warrant (though it may have a lower) than the consciousnesses of other necessities. It is therefore a corollary from the ExperienceHypothesis itself, in whatever way interpreted, that an

argument which questions the authority of such truths as mathematical axioms, can do so only by claiming for the less-deeply-rooted necessities of thought a validity which it denies to the more-deeply-rooted necessities of thought.

Finally, let me point out that any one declining to recognize the Universal Postulate, can consistently do this only so long as he maintains the attitude of pure and simple negation. The moment he asserts anything-the moment he even gives a reason for his denial, he may be stopped by demanding his warrant. Against every "because" and every "therefore" may be entered a demurrer, until he has said why this proposition he affirms is to be accepted rather than the counter-proposition. So that he cannot even take a step towards justifying his scepticism respecting the Universal Postulate without, in the very act, confessing his acceptance of it.

CHAPTER XII.

THE TEST OF RELATIVE VALIDITY.

§ 434. We are now prepared to formulate a method of deciding between conflicting conclusions. In every way we have been forced to admit that for those ultimate cognitions on which all others depend, the Universal Postulate is our only warrant that for each of them the sole justification is the invariable existence of the predicate along with its subject, tested by an abortive effort to cause non-existence. This is our guarantee for the reality of consciousness, of sensations, of personal existence: no mental effort enables us to suppress, even for a moment, either element of a proposition expressing one of these ultimate truths. This is our guarantee for each axiom: the only reason we can give for accepting it, is that on trying we find no alternative cognition can be framed. And this is our guarantee for every step in a demonstration. To gain the strongest conviction possible respecting any complex fact, we either analytically descend from it by successive steps, each of which we test by the inconceivableness of its negation, until we reach some truth which we have similarly tested; or we synthetically ascend from such truth by such steps.

Still, there rises the question-How are we to choose between opposing conclusions, each of which claims to be legitimately drawn from premisses alleged to be beyond doubt? Arguments of all kinds, including those of metaphysicians, which we have here to value, proceed upon the tacit assumption that each datum, and each successive step, has that in