Hume’s Philosophy

In both of his two books on the Human Understanding, Hume had, I think, one main general object. He tells us that it was his object to discover “the extent and force of human understanding,” to give us “an exact analysis of its powers and capacity.” And we may, I think, express what he meant by this in the following way. He plainly held (as we all do) that some men sometimes entertain opinions which they cannot know to be true. And he wished to point out what characteristics are possessed by those of our opinions which we can know to be true, with a view of persuading us that any opinion which does not possess any of these characteristics is of a kind which we cannot know to be so. He thus tries to lay down certain rules to the effect that the only propositions which we can, any of us, know to be true are of certain definite kinds. It is in this sense, I think, that he tries to define the limits of human understanding.

With this object he, first of all, divides all the propositions, which we can even so much as conceive, into two classes. They are all, he says, either propositions about “relations of ideas” or else about “matters of fact.” By propositions about “relations of ideas” he means such propositions as that twice two are four, or that black differs from white; and it is, I think, easy enough to see, though by no means easy to define, what kind of propositions it is that he means to include in this division. They are, he says, the only kind of propositions with regard to which we can have “intuitive” or “demonstrative” certainty. But the vast majority of the propositions in which we believe and which interest us most, belong to the other division: they are propositions about “matters of fact.” And these again he divides into two classes. So far as his words go, this latter division is between “matters of fact, beyond the present testimony of our senses, or the records of our memory,” on the one hand, and matters of fact for which we have the evidence of our memory or senses, on the other. But it is, I think, quite plain that these words do not represent quite accurately the division which he really means to make. He plainly intends to reckon along with facts for which we have the evidence of our senses all facts for which we have the evidence of direct observation—such facts, for instance, as those which I observe when I observe that I am angry or afraid, and which cannot be strictly said to be apprehended by my senses. The division, then, which he really intends to make is (to put it quite strictly) into the two classes—(1) propositions which assert some matter of fact which I am (in the strictest sense) observing at the moment, or which I have so observed in the past and now remember; and (2) propositions which assert any matter of fact which I am not now observing and never have observed, or, if I have, have quite forgotten.

We have, then, the three classes—(1) propositions which assert “relations of ideas”; (2) propositions which assert “matters of fact” for which we have the evidence of direct observation or personal memory; (3) propositions which assert “matters of fact” for which we have not this evidence. And as regards propositions of the first two classes, Hume does not seem to doubt our capacity for knowledge. He does not doubt that we can know some (though, of course, not all) propositions about “relations of ideas” to be true; he never doubts, for instance, that we can know that twice two are four. And he generally assumes also that each of us can know the truth of all propositions which merely assert some matter of fact which we ourselves are, in the strictest sense, directly observing, or which we have so observed and now remember. He does, indeed, in one place, suggest a doubt whether our memory is ever to be implicitly trusted, but he generally assumes that it always can. It is with regard to propositions of the third class that he is chiefly anxious to determine which of them (if any) we can know to be true and which not. In what cases can any man know any matter of fact which he himself has not directly observed? It is Hume’s views on this question which form, I think, the main interest of his philosophy.

He proposes, first of all, by way of answer to it, a rule, which may, I think, be expressed as follows: No man, he says, can ever know any matter of fact, which he has not himself observed, unless he can know that it is connected by “the relation of cause and effect,” with some fact which he has observed. And no man can ever know that any two facts are connected by this relation, except by the help of his own past experience. In other words, if I am to know any fact, A, which I have not myself observed, my past experience must give me some foundation for the belief that A is causally connected with some fact, B, which I have observed. And the only kind of past experience which can give me any foundation for such a belief is, Hume seems to say, as follows: I must, he says, have found facts like A “constantly conjoined ” in the past with facts like B. This is what he says; but we must not, I think, press his words too strictly. I may, for instance, know that A is probably a fact, even where the conjunction of facts like it with facts like B has not been quite constant. Or instead of observing facts like A conjoined with facts like B, I may have observed a whole series of conjunctions—for instance, between A and C, C and D, D and E, and E and B; and such a series, however long, will do quite as well to establish a causal connection between A and B, as if I had directly observed conjunctions between A and B themselves. Such modifications as this, Hume would, I think, certainly allow. But, allowing for them, his principle is, I think, quite clear. I can, he holds, never know any fact whatever, which I have not myself observed, unless I have observed similar facts in the past and have observed that they were “conjoined” (directly or indirectly) with facts similar to some fact which I do now observe or remember. In this sense, he holds, all our knowledge of facts, beyond the reach of our own observation, is founded on experience.

This is Hume’s primary principle. But what consequences does he think will follow from it, as to the kind of facts, beyond our own observation, which we can know? We may, I think, distinguish three entirely different views as to its consequences, which he suggests in different parts of his work.

In the first place, where he is specially engaged in explaining this primary principle, he certainly seems to suppose that all propositions of the kind, which we assume most universally in everyday life, may be founded on experience in the sense required. He supposes that we have this foundation in experience for such beliefs as that “a stone will fall, or fire burn”; that Julius Cæsar was murdered; that the sun will rise to-morrow; that all men are mortal He speaks as if experience did not merely render such beliefs probable, but actually proved them to be true. The “arguments from experience” in their favour are, he says, such as “leave no room for doubt or opposition.” The only kinds of belief, which he definitely mentions as not founded on experience, are “popular superstitions” on the one hand, and certain religious and philosophical beliefs, on the other. He seems to suppose that a few (a very few) religious beliefs may, perhaps, be founded on experience. But as regards most of the specific doctrines of Christianity, for example, he seems to be clear that they are not so founded. The belief in miracles is not founded on experience; nor is the philosophical belief that every event is caused by the direct volition of the Deity. In short, it would seem, that in this doctrine that our knowledge of unobserved facts is confined to such as are “founded on experience,” he means to draw the line very much where it is drawn by the familiar doctrine which is called “Agnosticism.” We can know such facts as are asserted in books on “history, geography or astronomy,” or on “politics, physics and chemistry,” because such assertions may be “founded on experience”; but we cannot know the greater part of the facts asserted in books “of divinity or school metaphysics,” because such assertions have no foundation in experience.

This, I think, was clearly one of Hume’s views. He meant to fix the limits of our knowledge at a point which would exclude most religious propositions and a great many philosophical ones, as incapable of being known; but which would include all the other kinds of propositions, which are most universally accepted by common-sense, as capable of being known. And he thought that, so far as matters of fact beyond the reach of our personal observation are concerned, this point coincided with that at which the possibility of “foundation on experience” ceases.

But, if we turn to another part of his work, we find a very different view suggested. In a quite distinct section of both his books, he investigates the beliefs which we entertain concerning the existence of “external objects.” And he distinguishes two different kinds of belief which may be held on this subject. “Almost all mankind, and philosophers themselves, for the greatest part of their lives,” believe, he says, that “the very things they feel and see” are external objects, in the sense that they continue to exist, even when we cease to feel or see them. Philosophers, on the other hand, have been led to reject this opinion and to suppose (when they reflect) that what we actually perceive by the senses never exists except when we perceive it, but that there are other external objects, which do exist independently of us, and which cause us to perceive what we do perceive. Hume investigates both of these opinions, at great length in the Treatise, and much more briefly in the Enquiry, and comes to the conclusion, in both books, that neither of them can be “founded on experience,” in the sense he has defined. As regards the first of them, the vulgar opinion, he does seem to admit in the Treatise that it is, in a sense, founded on experience; but not, he insists, in the sense defined. And he seems also to think that, apart from this fact, there are conclusive reasons for holding that the opinion cannot be true. And as regards the philosophical opinion, he says that any belief in external objects, which we never perceive but which cause our perceptions, cannot possibly be founded on experience, for the simple reason that if it were, we should need to have directly observed some of these objects and their “conjunction” with what we do perceive, which ex hypothesi, we cannot have done, since we never do directly observe any external object.

Hume, therefore, concludes, in this part of his work, that we cannot know of the existence of any “external object” whatever. And though in all that he says upon this subject, he is plainly thinking only of material objects, the principles by which he tries to prove that we cannot know these must, I think, prove equally well that we cannot know any “external object” whatever—not even the existence of any other human mind. His argument is: We cannot directly observe any object whatever, except such as exist only when we observe them; we cannot, therefore, observe any “constant conjunctions” except between objects of this kind: and hence we can have no foundation in experience for any proposition which asserts the existence of any other kind of object, and cannot, therefore, know any such proposition to be true. And this argument must plainly apply to all the feelings, thoughts and perceptions of other men just as much as to material objects. I can never know that any perception of mine, or anything which I do observe, must have been caused by any other man, because I can never directly observe a “constant conjunction” between any other man’s thoughts or feelings or intentions and anything which I directly observe: I cannot, therefore, know that any other man ever had any thoughts or feelings—or, in short, that any man beside myself ever existed. The view, therefore, which Hume suggests in this part of his work, flatly contradicts the view which he at first seemed to hold. He now says we cannot know that a stone will fall, that fire will burn, or the sun will rise to-morrow. All that I can possibly know, according to his present principles, is that I shall see a stone fall, shall feel the fire burn, shall see the sun rise to-morrow. I cannot even know that any other men will see these things; for I cannot know that any other men exist. For the same reason, I cannot know that Julius Cæsar was murdered, or that all men are mortal. For these are propositions asserting “external” facts—facts which don’t exist only at the moment when I observe them; and, according to his present doctrine, I cannot possibly know any such proposition to be true. No man, in short, can know any proposition about “matters of fact” to be true, except such as merely assert something about his own states of mind, past, present or future—about these or about what he himself has directly observed, is observing, or will observe.

Here, therefore, we have a very different view suggested, as to the limits of human knowledge. And even this is not all. There is yet a third view, inconsistent with both of these, which Hume suggests in some parts of his work.

So far as we have yet seen, he has not in any way contradicted his original supposition that we can know some matters of fact, which we have never ourselves observed. In the second theory, which I have just stated, he does not call in question the view that I can know all such matters of fact as I know to be causally connected with facts which I have observed, nor the view that I can know some facts to be thus causally connected. All that he has done is to question whether I can know any external fact to be causally connected with anything which I observe; he would still allow that I may be able to know that future states of my own, or past states, which I have forgotten, are causally connected with those which I now observe or remember; and that I may know therefore, in some cases, what I shall experience in the future, or have experienced in the past but have now forgotten. But in some parts of his work he does seem to question whether any man can know even as much as this: he seems to question whether we can ever know any fact whatever to be causally connected with any other fact. For, after laying it down, as we saw above, that we cannot know any fact, A, to be causally connected with another, B, unless we have experienced in the past a constant conjunction between facts like A and facts like B, he goes on to ask what foundation we have for the conclusion that A and B are causally connected, even when we have in the past experienced a constant conjunction between them. He points out that from the fact that A has been constantly conjoined with B in the past, it does not follow that it ever will be so again. It does not follow, therefore, that the two really are causally connected in the sense that, when the one occurs, the other always will occur also. And he concludes, for this and other reasons, that no argument can assure us that, because they have been constantly conjoined in the past, therefore they really are causally connected. What, then, he asks, is the foundation for such an inference? Custom, he concludes, is the only foundation. It is nothing but custom which induces us to believe that, because two facts have been constantly conjoined on many occasions, therefore they will be so on all occasions. We have, therefore, no better foundation than custom for any conclusion whatever as to facts which we have not observed. And can we be said really to know any fact, for which we have no better foundation than this? Hume himself, it must be observed, never says that we can’t. But he has been constantly interpreted as if the conclusion that we can’t really know any one fact to be causally connected with any other, did follow from this doctrine of his. And there is, I think, certainly much excuse for this interpretation in the tone in which he speaks. He does seem to suggest that a belief which is merely founded on custom, can scarcely be one which we know to be true. And, indeed, he owns himself that, when he considers that this is our only foundation for any such belief, he is sometimes tempted to doubt whether we do know any fact whatever, except those which we directly observe. He does, therefore, at least suggest the view that every man’s knowledge is entirely confined to those facts, which he is directly observing at the moment, or which he has observed in the past, and now remembers.

We see, then, that Hume suggests, at least, three entirely different views as to the consequences of his original doctrine. His original doctrine was that, as regards matters of fact beyond the| reach of our own actual observation, the knowledge of each of us is strictly limited to those for which we have a basis in our own experience. And his first view as to the consequences of this doctrine was that it does show us to be incapable of knowing a good many religious and philosophical propositions, which many men have claimed that they knew; but that it by no means denies our capacity of knowing the vast majority of facts beyond our own observation, which we all commonly suppose that we know. His second view, on the other hand, is that it cuts off at once all possibility of our knowing the vast majority of these facts; since he implies that we cannot have any basis in experience for asserting any external fact whatever—any fact, that is, except facts relating to our own actual past and future observations. And his third view is more sceptical still, since it suggests that we cannot really know any fact whatever, beyond the reach of our present observation or memory, even where we have a basis in experience for such a fact: it suggests that experience cannot ever let us know that any two things are causally connected, and therefore that it cannot give us knowledge of any fact based on this relation.

What are we to think of these three views, and of the original doctrine from which Hume seems to infer them?

As regards the last two views, it may perhaps be thought that they are too absurd to deserve any serious consideration. It is, in fact, absurd to suggest that I do not know any external facts whatever; that I do not know, for instance, even that there are any men beside myself. And Hume himself, it might seem, does not seriously expect or wish us to accept these views. He points out, with regard to all such excessively sceptical opinions that we cannot continue to believe them for long together—that, at least, we cannot, for long together, avoid believing things flatly inconsistent with them. The philosopher may believe, when he is philosophising, that no man knows of the existence of any other man or of any material object; but at other times he will inevitably believe, as we all do, that he does know of the existence of this man and of that, and even of this and that material object. There can, therefore, be no question of making all our beliefs consistent with such views as this of never believing anything that is inconsistent with them. And it may, therefore, seem useless to discuss them. But in fact, it by no means follows that, because we are not able to adhere consistently to a given view, therefore that view is false; nor does it follow that we may not sincerely believe it, whenever we are philosophising, even though the moment we cease to philosophise, or even before, we may be forced to contradict it. And philosophers do, in fact, sincerely believe such things as this—things which flatly contradict the vast majority of the things which they believe at other times. Even Hume, I think, does sincerely wish to persuade us that we cannot know of the existence of external material objects—that this is a philosophic truth, which we ought, if we can, so long as we are philosophising, to believe. Many people, I think, are certainly tempted, in their philosophic moments, to believe such things ; and, since this is so, it is, I think, worth while to consider seriously what arguments can be brought against such views. It is worth while to consider whether they are views which we ought to hold as philosophical opinions, even if it be quite certain that we shall never be able to make the views which we entertain at other times consistent with them. And it is the more worth while, because the question how we can prove or disprove such extreme views as these, has a bearing on the question how we can, in any case whatever, prove or disprove that we do really know, what we suppose ourselves to know.

What arguments, then, are there for or against the extreme view that no man can know any external fact whatever; and the still more extreme view that no man can know any matter of fact whatever, except those which he is directly observing at the moment, or has observed in the past and now remembers?

It may be pointed out, in the first place, that, if these views are true, then at least no man can possibly know them to be so. What these views assert is that I cannot know any external fact whatever. It follows, therefore, that I cannot know that there are any other men, beside myself, and that they are like me in this respect. Any philosopher who asserts positively that other men, equally with himself, are incapable of knowing any external facts, is, in that very assertion, contradicting himself, since he implies that he does know a great many facts about the knowledge of other men. No one, therefore, can be entitled to assert positively that human knowledge is limited in this way, since, in asserting it positively, he is implying that his own knowledge is not so limited. It cannot be proper, even in our philosophic moments, to take up such an attitude as this.

No one, therefore, can know positively that men in general, are incapable of knowing external facts. But still, although we cannot know it, it remains possible that the view should be a true one. Nay, more, it remains possible that a man should know that he himself is incapable of knowing any external facts, and that, if there are any other men whose faculties are only similar to his own, they also must be incapable of knowing any. The argument just used obviously does not apply against such a position as this. It only applies against the position that men in general positively are incapable of knowing external facts: it does not apply against the position that the philosopher himself is incapable of knowing any, or against the position that there are possibly other men in the same case, and that, if their faculties are similar to the philosopher’s, they certainly would be in it. I do not contradict myself by maintaining positively that I know no external facts, though I do contradict myself if I maintain that I am only one among other men, and that no man knows any external facts. So far, then, as Hume merely maintains that he is incapable of knowing any external facts, and that there may be other men like him in this respect, the argument just used is not valid against his position. Can any conclusive arguments be found against it?

It seems to me that such a position must, in a certain sense, be quite incapable of disproof. So much must be granted to any sceptic who feels inclined to hold it. Any valid argument which can be brought against it must be of the nature of a petitio principii: it must beg the question at issue. How is the sceptic to prove to himself that he does know any external facts? He can only do it by bringing forward some instance of an external fact, which he does know; and, in assuming that he does know this one, he is, of course, begging the question. It is therefore quite impossible for any one \a prove, in one strict sense of the term, that he does know any external facts. I can only prove that I do, by assuming that in some particular instance, I actually do know one. That is to say, the so-called proof must assume the very thing which it pretends to prove. The only proof that we do know external facts lies in the simple fact that we do know them. And the sceptic can, with perfect internal consistency, deny that he does know any. But it can, I think, be shown that he has no reason for denying it. And in particular it may, I think, be easily seen that the arguments which Hume uses in favour of this position have no conclusive force.

To begin with, his arguments, in both cases, depend upon the two original assumptions, (1) that we cannot know any fact, which we have not observed, unless we know it to be causally connected with some fact which we have observed, and (2) that we have no reason for assuming any causal connection, except where we have experienced some instances of conjunction between the two facts connected. And both of these assumptions may, of course, be denied. It is just as easy to deny them, as to deny that I do know any external facts. And, if these two assumptions did really lead to the conclusion that I cannot know any, it would, I think, be proper to deny them: we might fairly regard the fact that they led to this absurd conclusion as disproving them. But, in fact, I think it may be easily seen that they do not lead to it.

Let us consider, first of all, Hume’s most sceptical argument (the argument which he merely suggests). This argument suggests that, since our only reason for supposing two facts to be causally connected is that we have found them constantly conjoined in the past, and since it does not follow from the fact that they have been conjoined ever so many times, that they always will be so, therefore we cannot know that they always will be so, and hence cannot know that they are causally connected. But obviously the conclusion does not follow. We must, I think, grant the premiss that, from the fact that two things have been conjoined, no matter how often, it does not strictly follow that they always are conjoined. But it by no means follows from this that we may not know that, as a matter of fact, when two things are conjoined sufficiently often, they are also always conjoined. We may quite well know many things which do not logically follow from anything else which we know. And so, in this case, we may know that two things are causally connected, although this does not logically follow from our past experience, nor yet from anything else that we know. And, as for the contention that our belief in causal connections is merely based on custom, we may, indeed, admit that custom would not be a sufficient reason for concluding the belief to be true. But the mere fact (if it be a fact) that the belief is only caused by custom, is also no sufficient reason for concluding that we can not know it to be true. Custom may produce beliefs, which we do know to be true, even though it be admitted that it does not necessarily produce them.

And as for Hume’s argument to prove that we can never know any external object to be causally connected with anything which we actually observe, it is, I think, obviously fallacious. In order to prove this, he has, as he recognises, to disprove both of two theories. He has, first of all, to disprove what he calls the vulgar theory—the theory that we can know the very things which we see or feel to be external objects; that is to say, can know that these very things exist at times when we do not observe them. And even here, I think, his arguments are obviously inconclusive. But we need not stay to consider them, because, in order to prove that we cannot know any external objects, he has also to disprove what he calls the philosophic theory—the theory that we can know things which we do observe, to be caused by external objects which we never observe. If, therefore, his attempt to disprove this theory fails, his proof that we cannot know any external objects also fails; and I think it is easy to see that his disproof does fail. It amounts merely to this: That we cannot, ex hypothesi, ever observe these supposed external objects, and therefore cannot observe them to be constantly conjoined with any objects which we do observe. But what follows from this? His own theory about the knowledge of causal connection is not that in order to know A to be the cause of B, we must have observed A itself to be conjoined with B; but only that we must have observed objects like A to be constantly conjoined with objects like B. And what is to prevent an external object from being like some object which we have formerly observed? Suppose I have frequently observed a fact like A to be conjoined with a fact like B: and suppose I now observe B, on an occasion when I do not observe anything like A. There is no reason, on Hume’s principles, why I should not conclude that A does exist on this occasion, even though I do not observe it; and that it is, therefore, an external object. It will, of course, differ from any object which I have ever observed, in respect of the simple fact that it is not observed by me, whereas they were. There is, therefore, this one respect in which it must be unlike anything which I have ever observed. But Hume has never said anything to show that unlikeness in this single respect is sufficient to invalidate the inference. It may quite well be like objects which I have observed in all other respects; and this degree of likeness may, according to his principles, be quite sufficient to justify us in concluding its existence. In short, when Hume argues that we cannot possibly learn by experience of the existence of any external objects, he is, I think, plainly committing the fallacy of supposing that, because we cannot, ex hypothesis have ever observed any object which actually is “external,” therefore we can never have observed any object like an external one. But plainly we may have observed objects like them in all respects except the single one that these have been observed whereas the others have not. And even a less degree of likeness than this would, according to his principles, be quite sufficient to justify an inference of causal connection.

Hume does not, therefore, bring forward any arguments at all sufficient to prove either that he cannot know any one object to be causally connected with any other or that he cannot know any external fact. And, indeed, I think it is plain that no conclusive argument could possibly be advanced in favour of these positions. It would always be at least as easy to deny the argument as to deny that we do know external facts. We may, therefore, each one of us, safely conclude that we do know external facts; and, if we do, then there is no reason why we should not also know that other men do the same. There is no reason why we should not, in this respect, make our philosophical opinions agree with what we necessarily believe at other times. There is no reason why I should not confidently assert that I do really know some external facts, although I cannot prove the assertion except by simply assuming that I do. I am, in fact, as certain of this as of anything; and as reasonably certain of it. But just as I am certain that I do know some external facts, so I am also certain that there are others which I do not know. And the question remains: Does the line between the two fall, where Hume says it falls? Is it true that the only external facts I know are facts for which I have a basis in my own experience? And that I cannot know any facts whatever, beyond the reach of my own observation and memory, except those for which I have such a basis?

This, it seems to me, is the most serious question which Hume raises. And it should be observed that his own attitude towards it is very different from his attitude towards the sceptical views which we have just been considering. These sceptical views he did not expect or wish us to accept, except in philosophic moments. He declares that we cannot, in ordinary life, avoid believing things which are inconsistent with them; and, in so declaring, he, of course, implies incidentally that they are false: since he implies that he himself has a great deal of knowledge as to what we can and cannot believe in ordinary life. But, as regards the view that our knowledge of matters of fact beyond our own observation is entirely confined to such as are founded on experience, he never suggests that it is impossible that all our beliefs should be consistent with this view, and he does seem to think it eminently desirable that they should be. He declares that any assertion with regard to such matters, which is not founded on experience, can be nothing but “sophistry and illusion”; and that all books which are composed of such assertions should be “committed to the flames.” He seems, therefore, to think that here we really have a test by which we may determine what we should or should not believe, on all occasions: any view on such matters, for which we have no foundation in experience, is a view which we cannot know to be even probably true, and which we should never accept, if we can help it. Is there any justification for this strong view?

It is, of course, abstractly possible that we do really know, without the help of experience, some matters of fact, which we never have observed. Just as we know matters of fact, which we have observed, without the need of any further evidence, and just as we know, for instance, that 2 + 2 = 4, without the need of any proof, it is possible that we may know, directly and immediately, without the need of any basis in experience, some facts which we never have observed. This is certainly possible, in the same sense in which it is possible that I do not really know any external facts: no conclusive disproof can be brought against either position. We must make assumptions as to what facts we do know and do not know, before we can proceed to discuss whether or not all of the former are based on experience; and none of these assumptions can, in the last resort, be conclusively proved. We may offer one of them in proof of another; but it will always be possible to dispute the one which we offer in proof. But there are, in fact, certain kinds of things which we universally assume that we do know or do not know, just as we assume that we do know some external facts; and if among all the things which we know as certainly as this, there should turn out to be none for which we have no basis in experience, Hume’s view would I think, be as fully proved as it is capable of being. The question is: Can it be proved in this sense? Among all the facts beyond our own observation, which we know most certainly, are there any which are certainly not based upon experience? For my part, I confess, I cannot feel certain what is the right answer to this question: I cannot tell whether Hume was right or wrong. But if he was wrong—if there are any matters of fact, beyond our own observation, which we know for certain, and which yet we know directly and immediately, without any basis in experience, we are, I think, faced with an eminently interesting problem. For it is, I think, as certain as anything can be that there are some kinds of facts with regard to which Hume was right—that there are some kinds of facts which we cannot know without the evidence of experience. I could not know, for instance, without some such evidence, such a fact as that Julius Cæsar was murdered. For such a fact I must, in the first instance, have the evidence of other persons; and if I am to know that their evidence is trustworthy, I must have some ground in experience for supposing it to be so. There are, therefore, some kinds of facts which we cannot know without the evidence of experience and observation. And if it is to be maintained that there are others, which we can know without any such evidence, it ought to be pointed out exactly what kind of facts these are, and in what respects they differ from those which we cannot know without the help of experience. Hume gives us a very clear division of the kinds of propositions which we can know to be true. There are, first of all, some propositions which assert “relations of ideas ’’; there are, secondly, propositions which assert “matters of fact ” which we ourselves are actually observing, or have observed and now remember; and there are, thirdly, propositions which assert “matters of fact” which we have never actually observed, but for believing in which we have some foundation in our past observations. And it is, I think, certain that some propositions, which we know as certainly as we know anything, do belong to each of these three classes. I know, for instance, that twice two are four; I know by direct observation that I am now seeing these words, that I am writing, and by memory that this afternoon I saw St. Paul’s; and I know also that Julius Cæsar was murdered, and I have some foundation in experience for this belief, though I did not myself witness the murder. Do any of those propositions, which we know as certainly as we know these and their like, not belong to either of these three classes? Must we add a fourth class consisting of propositions which resemble the two last, in respect of the fact that they do assert “ matters of fact,” but which differ from them, in that we know them neither by direct observation nor by memory, nor yet as a result of previous observations? There may, perhaps, be such a fourth class; but, if there is, it is, I think, eminently desirable that it should be pointed out exactly what propositions they are which we do know in this way; and this, so far as I know, has never yet been done, at all clearly, by any philosopher.