science" not intending by the epithet to qualify the substantive to which it is prefixed, or to apply it in the same sense as when we say that the emotions of hope and joy and fear and grief are natural, but to mark the character of the objects of which the science treats. It is a convenient form of compendious expression, and does not entail much risk of our inferring that the knowledge, in virtue of its being natural, will, like hope and joy, spring up spontaneously in the mind, and needs not to be sought after by assiduous study.

Yet it is really an inference of a similar kind which Kant has fallen into. Having transferred the term necessary from the facts to the cognition of the facts, he has drawn his conclusions without adverting to the elliptical character of the epithet in its new position and the different offices it is meant to serve in the two cases. He has overlooked the consideration that our knowledge of a necessary fact is itself neither more nor less necessary than our knowledge of any other kind of fact.

If on a sheet of paper, at which we are looking, two right lines drawn with black ink not yet dry (I purposely introduce these trivial circumstances) intersect each other, we cannot help seeing the lines and their intersection and also that they are black and wet; nor can we help (at least when it is pointed out to us) observing that they make four angles, or discerning, if we happen to be mathematicians, that

the four angles are together equal to four right angles.

In this case, if our knowledge of the facts, some of which are called contingent and some necessary, may be said to be itself necessary, it is in the sense of unavoidable: the exhibition of the sheet of paper to our sight obliges us, if we look at all, to see what it contains; but this unavoidableness is quite independent of the differences in character of the several facts discerned. We cannot avoid seeing the contingent facts that the lines are black and wet any more than the necessary facts that their intersection makes four angles and that these four angles are together equal to four right angles. In both cases we perceive the facts as they exist because they so exist.

Should our vocabulary be so scanty or our dislike of circumlocution so great, that we are obliged or choose to resort to the expedient of designating our knowledge as necessary because the facts known are so, the least we can do is not to draw our conclusions as if the epithet in both cases equally and similarly qualified the substantive to which it is attached.

LETTER IX.

GENERAL PROPOSITIONS (IN CONTINUATION).

CON

TINGENT PROPOSITIONS AND LAWS OF NATURE. THE À PRIORI COGNITIONS OF KANT FURTHER CONSIDERED.

PERHAPS you will think, and not without reason, that I have bestowed sufficient attention on cognitions à priori, but there is another class of them which must not be entirely passed over.

The so-called cognitions considered in my last letter are what are usually termed necessary truths -propositions, namely, the contraries of which involve a contradiction and which are said to be necessary because the facts affirmed by them are so.

But the propositions which I have now in view have not this character, inasmuch as the contraries of them may be imagined without any contradiction being implied. Such are propositions relating to the events around us, to the operation of various substances on each other, to the succession of natural phenomena, to the causes of effects, and to the effects of causes.

Amongst these there are some of extreme generality which have been considered by certain philo

sophers as necessary or as expressing necessary truths in the same way as mathematical axioms.

Of this kind are the following: "every change has a cause;" "similar causes have similar effects;" "similar effects have similar causes."

Applying to these his test of universality and necessity, Kant pronounces them (with a modification regarding the first) to be cognitions à priori independent of experience. They are, he says, necessary, and they admit of no exceptions.

There is, nevertheless, a wide and fundamental distinction between the facts expressed by this class of propositions and the facts expressed by mathematical propositions. While, as I have just had occasion to remark, the facts affirmed by the latter are discerned to be necessary, those affirmed by the former are not discerned to be so. While there would be self-contradiction in asserting that some parallel lines meet, there would be no self-contradiction in the assertion that some changes occur spontaneously without causes; or that similar causes do not always produce similar effects, although there might be and indeed would be an utter inconsistency between such assertions and others which we are habitually and unavoidably making.

Self-contradiction in a proposition is one thing, and the inconsistency of a proposition held by any one with other propositions maintained by the same person, is another.

By those who admit that mathematical proposi

tions are not independent of perception or experience, this other class cannot obviously be considered as being so. Much of the reasoning, indeed, in my last letter, will, mutatis mutandis, apply to both classes, and hence the necessity of any long explanation is superseded: but still, as there is a real and important difference between them, let us briefly consider the first of these maxims: " every change has a cause."

It is obvious that no one could know what a change is and what a cause is, except by perceiving some particular cause and some particular change following it, such as the application of fire to wood and the consequent charring of the material. Having witnessed a number of similarly consecutive circumstances a variety of particular events followed by other events-we designate the first events in the sequence by the common name "cause," and the second by that of "effect," or, as here, "change:" and from these observations, following our natural propensity to generalise, we draw the universal conclusion "every change has a cause." We manifestly could not have drawn it had we seen changes happening without causes.

There is no difference between the origin of these comprehensive propositions and that of such minor generalisations as "metals are expanded by heat;"

* Kant acknowledges this in the case of "change; " it is curious how he failed to discern that " cause is exactly in the same predicament.