In this chapter and the next we have to consider the following question: "Are there any terms which subsist but do not exist?" With regard to certain descriptions of terms we can say that, if anything answers to any of these descriptions, then it certainly exists. McTaggart holds that, if anything answered to the description of a particular, it would certainly exist. Again, any quality which qualified an actual particular would exist, and so would any relation which related two or more actual particulars. Lastly, any quality which qualified an existent quality or relation, and any relation which related existent qualities or relations, would ipso facto exist. It will be convenient to say that qualities and relations of the kind first mentioned "directly characterize" actual particulars, whilst those of the second kind "indirectly characterise" actual particulars. McTaggart's doctrine, as so far stated, might then be summed up in the principle that anything that was a particular, or was a characteristic which directly or indirectly characterised some actual particular, would ipso facto exist.

      Now, prima facie, there appear to be terms which do not answer to any of the above-mentioned descriptions. There appear to be characteristics, such as phoenixhood or perfect virtue, which neither directly nor indirectly characterise any actual particular. There appear to be unlrealised possibilities. And many people hold that there are propositions, as distinct from judgments, sentences, and facts. With regard to each of these descriptions of terms there are two questions to be asked, which McTaggart does not very clearly separate.

1. Are there any terms answering to these descriptions? Are there such entities as characteristics which do not directly or indirectly characterise any actual particular, or as unrealised possibilities, or as propositions?
2. If there were, would they exist?

1. Non-characterising Characteristics.

      1.1. McTaggart's View. McTaggart begins by drawing a distinction between the qualities and relations of actual particulars and qualities and relations in the abstract. He says that the wisdom of Socrates and the moral superiority of Socrates to Nero are examples of the former. And he says that wisdom in general and moral superiority in general are examples of the latter. The former are existent. If there were anything answering to the description of the latter, it would subsist and not exist.

      Now all this seems to me quite untenable. I do not see what "the wisdom of Socrates" can mean except that perfectly determinate degree and kind of wisdom which in fact characterized Socrates. In principle this might have characterised dozens of other men also, though in fact it is most unlikely that it characterized anyone but Socrates. It thus differs from "wisdom in general" only as a determinate differs from the determinable of which it is a specification. If Socrates is characterized by this determinate kind and degree of wisdom, he must ipso facto be characterised by wisdom in general, which is the determinable under which this determinate falls. And so it would seem that, if there is any ground for saying that the wisdom of Socrates exists, there is precisely the same ground for saying that wisdom in general exists. McTaggart seems to have seen that there is a difficulty in his doctrine here. For he remarks in paragraph 2 of p. 6 [paragraph 3 of § 5] that a universal, like wisdom, might be at once existent in respeet of characterising Socrates and non-existent in another respect. This suggestion seems to me to be hopeless. For McTaggart certainly holds that existence is a quality and not a relational property, and I can attach no meaning to the supposition that anything could have a certain quality "in one respect" and lack the same quality "in another respect". Evidently there is a serious confusion of some kind here. What is the explanation of it?

      I think that the truth is somewhat as follows. If there be any qualities which do not directly or indirectly qualify actual particulars, then they are not existent. For example, if there be such a quality as exact straightness, and if nothing be exactly straight, then exact straightness is not existent. Now, whenever a quality is described as "the q-ness of X", where "X" is the proper name of an actual particular, we can infer from the description that, if there is a quality answering to it at all, this does characterise some actual particular. In such cases then we can infer from the deseription of the quality that, if any quality answers to it, the quality is existent. But, when a quality is merely named or is described in some other way, we cannot infer that, if there is such a quality, it is existent. Nevertheless, it may in fact be existent. Wisdom is in fact existent, though we cannot infer this from the description of it as "that quality which Englishmen call wisdom ".

      It should be noted that wisdom in general could have been described by reference to Socrates, and that the wisdom of Socrates could have been described without reference to him. For wisdom in general could have been described, for example, as "that quality in which Socrates excelled all his contemporaries"; and the wisdom of Socrates could have been described, for example, as "that kind and degree of wisdom which scores 93 per cent. on Prof. X's scale of intelligence tests".

      Thus it seems to me that McTaggart has mistaken a purely epistemological distinction for an ontological distinction. The ontological distinction is between qualities which do, and those which do not, directly or indirectly characterise actual particulars. The epistemological distinction is between those descriptions of qualities from which one can infer that they characterise actual particulars and those descriptions from which no such inference can be made. There is no necessary connexion between these two distinctions. And there is no necessary connexion between either of them and the distinction between a quality in general and the determinate form of it which characterises a certain particular. Similar remarks apply, of course, mutatis mutandis, to relations.

      We can now consider McTaggart's argument in Chap. II to prove that there are no non-existent characteristics. This rests on a new principle which is suddenly introduced at the top of p. 29 [end of par. 1] and is asserted to be self-evident. The principle is that the parts of anything that exists must themselves be existent. Before criticizing this dogma we will consider the application which McTaggart makes of it. Suppose it were alleged that there is such a characteristic as phoenixhood, though there are no phoenixes, and that this characteristic is non-existent. McTaggart answers that any actual particular, e.g., the Albert Memorial, has the negative characteristic of being a non-phoenix. Therefore the characteristic non phoenixhood is existent. But this contains phoenixhood as a part, and the parts of any existent are themselves existent. So phoenixhood exists, in spite of there being no phoenixes.

      I will now comment on this argument and on the principle which is used in it.

1. A precisely similar argument would prove that, if there is such a characteristic as round-squareness, it is existent. For the characteristic non-round-squareness exists, since it characterises actual particulars such as the Albert Memorial. Therefore round-squareness, which is part of non-round-squareness, must be existent.
2. Is it at all clear that the phrase "non-P" is the name or a description of a complex attribute of which P is a part? If so, presumably the other part is something of which the syllable "non" is the name. This is certainly not very plausible.
3. McTaggart could have met this objection by slightly modifying his argument. He might have said that, at any rate, there is the negative fact that the Albert Memorial is not a phoenix. Suppose we regard the negation as attaching to the copula and not to the predicate, and do not attempt to introduce the notion of negative characteristics. Still, this negative fact is an existent, since it is a fact about an actual particular. And it contains the characteristic phoenixhood as a part. Therefore this characteristic exists, although there are no phoenixes. I think that this is the most plausible way in which he could have put his argument.

      At this point we had better consider the general principle. In view of the extreme ambiguity of the word "part" I am not inclined to attach much weight to it. No doubt the extended parts of any extended particular must exist in the same sense in which it exists. Similarly, the successive shorter phases in a longer stretch of history exist in the same sense in which the stretch as a whole exists. But the predicates of facts are not parts of facts in the sense in which the foundations of a house are parts of the house or the performance of an overture is part of the performance of an opera. And it is not in the least clear that the predicate of a negative fact about an existent must exist simply because there is a very recondite sense of "part" in which this predicate can be called a "part" of this negative fact.

      The truth is that McTaggart started with a certain criterion for the existence of characteristics, and then widened it so much that his final conclusion that there are no non-existent characteristics is co:mpletely trivial. His original criterion was that a characteristic is existent if and only if it directly or indirectly characterises some actual particular. When he has this in mind he says quite definitely that "we have every reason to suppose that the characteristic of being a phoenix is not existent" (§ 29, p. 26). His later criterion is, in effect, that a characteristic is existent if ether there is some actual particular which has it or there is some actual particular which lacks it. And the mark of this change of standpoint is that in § 31, pp. 28-9, he concludes that the characteristic of phoenixhood is existent. No doubt, when the criterion of existence is widened to this extent, the Law of Excluded Middle ensures that every characteristic shall have existence. But at this stage the proposition has ceased to be of the slightest interest or importance.

      *1.2. Independent Discussion of the Subject. The really interesting and important question in this connexion is whether there are any characteristics which do not directly or indirectly characterise actual particulars. In its ontological aspect this is the old question of universalia in re and universalia ante rem. In its epistemological aspect it is closely connected with the controversies about a priori concepts and innate ideas. These questions, which McTaggart approached but did not pursue, seem to merit an independent discussion. I propose therefore to say something about them before resuming my exposition and criticism of McTaggart.

      Granted that there are no dragons, is there any reason to believe that there is a characteristic of which "dragonhood" is the name? The first argument which might be proposed in favour of an affirmative answer to this question is the following. We understand the question whether there are or are not dragons, and we answer it in the negative. But the question means: "Is there any particular which has the characteristic of dragonhood?" Unless there were a characteristic of which "dragonhood" is the name we could not think of it, and unless we could think of it we could not understand the question. Since we do understand the question there must be such a characteristic.

      This argument is invalid. Let us take the definition of the word "dragon" to be fire-breathing serpent. The question whether there are dragons is simply the question whether there is any particular in which the two characteristies of being a serpent and of breathing fire both inhere. Now we are acquainted with the characteristic of serpenthood, since we have seen snakes. We are acquainted with the characteristic of breathing fire, since we have seen flames issuing from chimneys and blast-furnaces. And we are acquainted with the relation of co-inherence, since many characteristics co-inhere in every particular that we are acquainted with. Thus the question is perfectly intelligible even though there be no characteristic of which "dragonhood" is the name and fire breathing serpenthood the analysis.

      The following is another argument. Even though there be no dragons and no mermaids, being a dragon is different from being a mermaid. This is a true proposition about the characteristics of dragonhood and mermaidhood. Therefore there must be characteristics of which "dragonhood" and "mermaidhood" are names. This argument is also invalid. The fact is that the two sentences "X is a dragon" and "X is a mermaid" have different, meanings. The first means that X combines the two qualities of being a serpent and breathing flame. The second means that X combines the two qualities of having a woman's body and having a fish's tail. Each of the first pair of qualities is different from each of the second pair. Thus the statement that being a dragon is different from being a mermaid is intelligible and true even though there be no characteristic of which "dragonhood" is the name and no characteristic of which "mermaidhood" is the name.

      We come now to the third, and only serious, argument. There seem to be facts which contain as essential constituents certain simple characteristics which in all probability do not characterise anything. Take, for example, the fact that two straight lines cannot cut each other more than once. This certainly seems to involve as an essential factor a characteristic of which "exact straightness" is the name. Yet we should probably admit that it is very doubtful whether there is any particular whieh is exactly straight. Now to say of anything that it is exactly straight does not seem to mean that two or more characteristics which occur separately in other things, are combined in it. Hence it would seem that straightness cannot be dealt with on the same lines as dragonhood and mermaidhood. It looks then as if we might have to admit that there are simple characteristics about which there is the gravest doubt whether they characterise anything. The most obvious examples of characteristics to which this argument applies are what may be called "Ideal Limits". It seems likely that these were what Plato often had in mind when he talked of "Ideas". I will therefore proceed to discuss the problem of Ideal Limits.

      *1.21. The Problem of Ideal Limits. I will first clear out of the way a complication introduced needlessly by Plato. He seems to have held that geometrical facts imply, not only that there ire such characteristics as exact straightness (Ideas), but also that there are exactly straight particulars. Now, as he held that the particulars which we perceive with the senses do not have these ideal characteristics, he had to postulate a special class of particulars (ta mathematika) with which we become acquainted by some kind of intellectual intuition. (I can make no claim to be a Platonic scholar, and so my statements about Plato's opinions should not be treated too seriously, but we can profitably discuss the theory, whether the experts decide that Plato held it or not.)

      The reason for thinking that geometry requires there to be ideal particulars as well as ideal limits was probably the following. Geometrical propositions are not about straightness or circularity in the abstract; they assume the existence of a plurality of straight particulars and circular particulars, standing in various relations to each other (cf., for example, the proposition that two straight lines cannot cut each other more than once). This reason, however, is quite inconclusive. If it be admitted that there could be straightness and circularity without there being any straight or circular particulars, it is easy to see that the facts of geometry do not force us to assume the latter in addition to the former. The fact that two straight lines do not enclose a space, for example, can quite reasonably be identified with the hypothetical fact, that, if x and y were two exactly straight particulars, then they would either not intersect at all or would do so in only one point. Plainly, if there could be exact straightness without there being any exactly straight particulars, there could be such a fact as this without there being any exactly straight particulars.

      Having thus disposed of ta mathematika, we can return to our main problem. What is implied by the fact. that we understand sentences which contain words like "exactly straight", "perfectly circular", etc.? It seems to me that we must begin our enquiry by considering what I will eall "judgments of perceptual appearance". These are about perceived physical objects, and they assert of such objects that they "seem" or "look" or "feel" such-and-such. If I am looking at the edge of a saw from the side and at no great distance away, I have a characteristic kind of visual experience which self-evidently justifies me in making the judgment: "That looks jagged". If I were looking at the edge of a penny under similar conditions, or at the edge of the saw from a very long distance away, I should have a characteristically different kind of visual experience which would self-evidently justify me in making the judgment: "That looks smooth". Now there are quite certainly visual experiences which self-evidently justify me in saying of an object which I am seeing that its contour "looks exactly straight". I have such an experience when I look from the side with the naked eye through a homogeneous medium at a tightly stretched thread.

      It seems to me then that each of us understands perfectly well what is meant by "looking exactly straight" or "looking exactly circular". Even if the phrase "looking exactly straight" can no more be defined than the word "red", I can indicate to anyone who is not blind what I mean by it. I have only to show him a tightly stretched thread in a homogeneous medium, and to tell him that anything whose contour looked exactly like the contour of this would look exactly straight, and that nothing else would do so.

      Now, if I know what it means to look straight, I, ipso facto, know what it means to be straight. To say that x is straight means simply that its contour is of that peculiar kind which the contour of a thing looks to be when it looks straight. In short x would be straight if and only if it in fact had that peculiar kind of contour which a tightly stretched thread viewed with the naked eye through a homogeneous medium undoubtedly looks to have. There is then no difficulty in seeing how we can understand suppositions of the form: "Let x be exactly straight", "Let y be perfectly circular", and so on. We shall not be forced to assume that there is a characteristic of which "straightness" is the name and which may not characterise anything, unless we can show

1. that the fact that some things look straight under some circumstances implies that there is a characteristic of which "straightness" is the name, and
2. that probably nothing has this characteristic.

      (a) I shall first try to show that there is no simple positive characteristic of which "straightness" is the name. It seems to me that there is a certain determinable characteristic which belongs to the contours of things. I will call it "linearity". Now there are certain simple positive forms which this may take. A thing whose contour looks linear may look jagged or it may not look jagged. Jaggedness is a positive perceptible characteristic, like redness. It has degrees, and we have seen things which looked very jagged and others which looked hardly jagged at all. Now, if the contour of a thing does not look jagged, it may look curved or it may not look curved. Curvature, like jaggedness, is a positive perceptible characteristic capable of degrees. We have seen things whose contour looked very curved and others whose contour looked hardly curved at all. Now to say that a thing "looks straight" seems to me to mean that its contour looks linear and does not look jagged or curved. If so, to say that a thing is straight means that its contour is linear and is not jagged or curved. Thus it is a statement which is purely affirmative in grammatical form but partly negative in meaning.

      Let us now deal in the same way with circularity. If the contour of a thing looks curved, it may look sinuous or it may not look sinuous. Sinuosity is a positive perceptible characteristic, like curvature and jaggedness. If the contour of a thing looks curved and does not look sinuous it may look to vary in curvature or it may not. To say that a thing "looks circular" means that its contour looks linear and curved and does not look jagged or sinuous or of variable curvature. Once more, a sentence which is linguistically positive has a meaning which is partly negative.

      I believe that, in every case in which an Ideal-Limit-word occurs in a sentence it will be found on reflexion that the meaning of the sentence is partly positive and partly negative, and that there is no reason to think that there is any simple positive characteristic of which the Ideal-Limit-word is the name.

      (b) If the above conclusion be admitted, it ceases to be of much importance to enquire whether it is or is not probable that anything is in fact perfectly straight or exactly circular. For, even if it were certain that no proposition of the form "x is exactly straight" or "y is exactly circular" were true, we could not infer that there were characteristics that characterised nothing. On our view, to say that nothing is exactly straight would merely mean that everything which has a linear contour at all has a contour of some degree of curvature. To say that nothing is exactly circular would merely mean that everything which has a curved linear contour has a contour of variable curvature. And so on. Still, our conclusion may not be accepted, and there are some confusions in connexion with the present question which need to be cleared up. So we will pursue the subject a little further.

      Why is it said to be doubtful whether anything is perfectly straight, exactly circular, and so on? What does it mean, why is it asserted, and is it true? The first point to notice is that the statement that it is doubtful whether anything is exactly straight is ambiguous. It might mean

1. "I cannot be sure that there is anything which is perfectly straight", or
2. "There is nothing with regard to which I can be sure that it is perfectly straight".

1. Under certain conditions both x and y look straight.
2. Under certain other conditions x looks straight and y does not.
3. There are no known conditions under which y looks straight and x does not.

      As I have pointed out, it does not follow frown this that I cannot be sure that there are some physical objects which are exactly straight. It does seem to me most unlikely that there should be no physical object of which any part of the contour, however short, is exactly straight. Certainly none of the facts mentioned in the last paragraph have the faintest tendency to support this sweeping negative proposition.

      But, even if it were certain that no part, however small, of the contour of any physical object were exactly straight, it would not follow that no part of the contour of anything is exactly straight. Whenever I perceive a physical object I am acquainted with a certain particular, which I will call a "sensibile". My judgments of perceptual appearance are not about the sensibilia which I sense, but they are founded upon the latter and their sensible qualities. If I choose to do so, I can attend to the sensibile and inspect it and make a judgment about its sensible qualities. Now, even if no physical object could be known to be exactly straight, it might be that some sensisbilia could be known to have exaetly straight contours. In that case, even if there were a simple positive characteristic of which "straightness" is the name, it would not be a characteristic which characterises nothing. Now many people would lay it down as a general principle that it is impossible that a perceived object should seem to me to have a simple positive characteristic unless I had at some time sensed a sensibile which actually had that characteristic. Some people would go further and would say that I must be sensing a sensibile which actually has the characteristic C whenever I am perceiving something which appears to me to have this characteristic. If even the first and milder of these principles were accepted, it would follow at once that there must have been at various times exactly straight sensibilia.

      What are we to say about these general principles?

1. It does seem quite incredible that any physieal object should look to me at a certain moment to have a certain highest determinable characteristic, e.g., colour or extension, unless at that moment I were acquainted with a sensibile which actually had that determinable characteristic.
2. It does not seem to me self-evident that the sensibile whieh I am sensing in perceiving a physical object must have precisely the same determinate form of the common determinable characteristic as that which the perceived object looks to have.
3. If such divergence be possible at all, it must lie within very narrow limits. It is inconceivable that an object should look sky blue to me when the sensibile which I sense in perceiving it is pale pink.
4. If "straightness" were the name of a simple positive characteristic, it would be difficult to suppose that any perceived object could look exactly straight to me now unless, either now or at some earlier date, I had sensed a sensibile which was exactly straight.
5. On our analysis of the judgment "This looks exactly straight", there is no need to suppose that I have ever sensed an exactly straight sensibile. It seems most likely that there is a certain low degree of jaggedness, such that, whenever I sense a sensibile whose contour is less jagged than this, the contour of the physical object which I perceive by means of this sensibile does not look jagged at all. It seems likely that the same remarks are true, mutatis mutandis, of curvature. If then "looking exactly straight" means simply "looking linear and not looking jagged or curved", the fact that I have perceived contours which looked exactly straight does not entail that I have sensed sensibilia whose contours were without any degree of jaggedness and without any degree of curvature.
6. Nevertheless, I see no positive reason to doubt that there have been such sensibilia and that I have sometimes sensed them. I have certainly sensed sensibilia in which I could not detect any degree of jaggedness or curvature throughout a finite stretch of their contour, however carefully I inspected. It is, I think, logically possible that all of them had in fact some degree of jaggedness or of curvature. But there is not the least positive reason to think this likely. Relative to the datum that I am perceiving x as exactly straight, it is of course less likely that the sensibile which I sense in perceiving it is exactly straight than that it is not. It is not, of course, any less likely to be straight than to have any one perfectly determinate degree of jaggedness and curvature that falls within the small permissible range; but it is less likely to be straight than to have one or other of these determinate degrees of jaggedness and curvature, since the latter alternative covers a large number of possibilities. But, when the datum is that I have inspected the sensibile as carefully as I can, and have failed to detect any degree of curvature or jaggedness in its contour, the case is quite different. I can see no ground for holding that, relative to this datum, it is more likely that the contour of the sensibile has some degree or other of curvature and of jaggedness than that it has none.

      We can now sum up the results of this long argument. The contention which we set out to examine was that phrases like "exact straightness", "perfect circularity", etc., are names of simple positive characteristics, and that there is good reason to doubt whether there are any particulars which have these characteristics. We have had to deny both parts of this contention. It is almost certain that these phrases, as used by us, are not the names of simple positive characteristics, and that sentences in which they occur can be replaced without loss of meaning by sentences in which neither they nor any synonym of them occurs. And, as regards straightness at any rate, there is no good reason to doubt that there are particulars whose contours are exactly straight throughout a finite stretch of their length. Thus the case of Ideal Limits gives us no ground for thinking that there are characteristics which do not directly or indirectly characterise any particular.

      *1.22. A priori Concepts and Innate Ideas. We ean now turn to an epistemological question which is closely connected with the ontological questions that we have just been discussing. In some sense we "have an idea of" redness, of dragonhood, of exact straightness, of causation, and so on. How did we acquire these ideas? And can ideas be classified according to the different ways in which they are acquired?

      I will begin by pointing out a certain ambiguity in the phrase "to have an idea of so-and-so". If a man says: "I have an-idea of Julius Caesar", he may mean that he is actually thinking of Julius Caesar at the moment. But he may mean merely that he has a permanent capacity to think of Julius Caesar, which may not be in action at the moment, but could be put into action at any time by a suitable stimulus. We may distinguish the two senses by the phrases "occurrent idea" and "dispositional idea" respectively. If an idea of anything has occurred, and particularly if it has occurred often, it tends to produce a corresponding dispositional idea. And, once the dispositional idea has been formed, it may easily be stimulated to give rise to an occurrent idea by very different causes from those which originally produced it. I got my dispositional idea of redness by seeing things that looked red, and performing acts of comparison, contrast, and abstraction. But, now that I have got it, it may be stimulated by my merely reading the word "red", or by my thinking of danger, or by hundreds of other causes. The question of "the Origin of our Ideas " is simply the question of whether we acquired all our dispositional ideas in the course of our present lives, and how precisely we acquired those which we did acquire.

      We must next point out certain other confusions and ambiguities.

      (i) Hume and many others have assumed that to have an idea of x means to have an image which resembles x, if x be a thing, and which has the characteristic x, if x be a charaeteristic. Thus, to have an occurrent idea of a dragon would be to be acquainted with an image which looks as a dragon would look; to have an occurrent idea of redness is to be acquainted with a red image, and so on. This is, of course, ridiculous nonsense. One can have a red image without thinking of redness; one can be thinking of redness without having a red image; one can have an idea of a characteristic, such as charitableness or primeness, which no image could possibly have. Our admiration for the rigour with which Hume drew absurd consequences from his absurd premises should not blind us to the obtuseness which still failed to see the absurdity of the premises even when confronted with that of the consequences.

      (ii) We must distinguish between having an "intuitive idea" of a characteristic, and having a "descriptive idea" of it. To have an occurrent intuitive idea of the characteristic x is to be experiencing an act of acquaintance which has for its object the universal of which "x" is the name. It seems plausible to suppose that at times I stand in this kind of cognitive relation to the universal redness. To have an occurrent descriptive idea of the characteristic x is to believe or to suppose that there is one and only one characteristic answering to a certain description with whose terms I am acquainted at the time. It may be that in fact there is no such characteristic. Suppose, for example, that there is such a quality as perfect virtue. And suppose that Christ in fact was perfectly virtuous. Then there is no characteristic which answers to the description "a higher degree of virtue than that possessed by Christ". But this description is perfectly intelligible. For we know what is meant by "virtue", by "degree of virtue", and by "a degree of virtue being higher than another degree of virtue". Again, one might have both an intuitive idea and a descriptive idea of the same characteristic. As we have said, it seems plausible to suppose that I sometimes have an occurrent intuitive idea of redness. And it is perfectlv certain that I sometimes have an occurrent descriptive idea of redness, for I sometimes think of it as the characteristic which answers to the description of being the colour of the sensibile which I sense when I look at a penny stamp. This distinction enables us to deal quite shortly with Hume's question as to whether I could have an idea of a shade of colour of which I had never seen an instance, provided that it was intermediate between two shades of which I had seen instances. The answer is as follows.

1. If by "idea of the missing shade" you mean an image which is characterised by the missing shade, the question is purely a question for empirical psychology.
2. If by "idea" you mean "intuitive idea", the answer is in the negative.
3. If by "idea" you mean "descriptive idea", the answer is in the affirmative.

      There is one other point to be mentioned. What is meant by saying that my idea of a certain characteristic is "compound"? It seems to me to have the following meaning. Suppose that the statement: "I am thinking of the characteristic C" can be replaced, without loss or gain of significance, by the statement: "I are thinking of the characteristics C₁, C₂, and C₃ as co-inherent in a common subject". Then it would be in accordance with usage to say that "my idea of C is compound", and it would be in accordance with usage to say that "my idea of C is composed of my ideas of C₁, C₂, and of C₃". To have an idea of dragonhood is, on this definition, to have a compound idea composed of the ideas of serpenthood and of fire-breathing. For it just consists in thinking of these two characteristics, and believing or making the supposition that they co-inhere in some common subject.

      It is now possible to define an "empirical concept." It is quite certain that many, if not all, simple intuitive dispositional ideas are formed in the following way, which may be illustrated by the formation of the idea of redness. I perceive from time to time things which present a characteristic kind of perceptual appearance. They "look red". I compare them with other things that look like them in this respect and look unlike them in other respects. For example, I may see objects which look round, triangular, square, ete., and all look red. Again, I compare them with yet other things which look unlike them in this respect, but look like them in other respects. For example, I compare triangular things which look red with other triangular things which look green, and with other triangular things which look blue, and so on. I perform a similar process of comparison and contrast between circular things that look red, and circular things that look green, and circular things that look blue, and so on. Eventually I am able to perform an act of abstraction, and to contemplate the characteristic of redness in separation from other qualities and in abstraction from any particular substance. Finally a disposition is formed which, whenever it is suitably stimulated, will produce an act of acquaintance with the quality of redness for its object. I have then "acquired the idea of redness". A very important adjunct to the prcess is to link this disposition by association with the traces left by hearing, seeing, and speaking the word red. When this associative link has been formed anything that excites the verbal trace will tend to excite the dispositional idea and will thus tend to evoke an recurrent intuitive idea of redness.

      Any dispositional idea formed in the way just illustrated is an instance of an empirical concept. Any compound idea all of whose components were empirical concepts would also be an empirical concept. And any descriptive idea in which the ideas of all terms in the description were empirical concepts would be an empirical concept. I do not know of any other kind of idea that could be called "empirical". So we may define an "empirical concept" to be either

1. a simple dispositional idea of a characteristic, formed by comparison, contrast, analysis, and abstraction from objects which perceptually appeared to be qualified or related by this charac teristic; or
2. a compound idea whose components are all ideas of the first kind; or
3. a descriptive idea in which the ideas of all the terms in the description are of the first or the second kind.

      Now an "a priori concept" is best defined negatively, in the first instance, as one that is not empirical. It is plain that the question whether there are any a priori concepts turns on the first clause in the above definition of "empirical concepts". Are there any simple dispositional ideas not formed by comparison, contrast, analysis, and abstraction from perceived instances? If there are, then there are a priori concepts; otherwise there are none.

      *1.221. Concepts of Ideal Limits. Some people have held that the concepts of Ideal Limits must be a priori. I think that this was Descartes' opinion. After our discussion of the nature of Ideal Limits it would seem fairly safe to reject this view. It seems to me that our concepts of Ideal Limits are almost certainly empirical concepts of either the second or the third kind.

1. If, as I have suggested, to think of x as perfectly straight is simply to think of it as linear and not jagged and not curved, then "the idea of exact straightness" will be a compound whose components are all empirical concepts of the first kind. It will therefore be an empirical concept of the second kind.
2. If this view be rejected, the most plausible alternative is that "the idea of exact straightness" is a descriptive idea of a rather special kind, which I will now try to explain.

      There are certain phrases, like "hotter than", "straighter than", etc., which express relations of a special sort, which we will call "comparatives". We can often perceive, with regard to two terms with which we are acquainted at the same time, that one stands in a comparative relation, such as "hotter than", to the other. Thus, our ideas of comparatives are often empirical concepts of the first kind. Now, when we reflect on a comparative, we can sometimes see quite clearly that there is no corresponding superlative; in other cases we can see with equal clearness that there is a corresponding superlative. Take, for example, the relation "hotter than". I can see plainly that it is logically impossible for there to be a term which could be hotter than something and such that nothing could be hotter than it. It is of course quite possible that there may be something so hot that nothing ever has been or will be hotter than it. It is possible that the laws of nature may set a limit beyond which it is causally impossible for the temperature of anything to rise. But this is irrelevant for the present purpose. The "could" and "could not" in our statements refer to logical or metaphysical possibility and impossibility. We can now put forward a general definition. To say that the relation R "does not have a superlative" means that R is a comparative relation, and that it is impossible for there to be any term such that it could have R to something whilst nothing could have R to it.

      Now to say that R "does have a superlative" would mean that it is possible for there to be a term such that it could have R to something whilst nothing could have R to it. It is of course quite possible that there may not in fact be such a term. It is even conceivable that the laws of nature might be such as to render the existence of such a term causally impossible. But this, as before, would be irrelevant to the present purpose.

      We must now apply this general doctrine to the special case of concepts of Ideal Limits, like straightness. It seems to me quite clear that there is a comparative relation "straighter than". Some things that we see "look straighter than" others that we see at the same time and under similar conditions. Thus the idea of "straighter than" is an empirical concept of the first kind. Now it seems to me that, when I reflect on this comparative relation, I see quite clearly that it has a superlative. I see that its nature is such that there could be a term than which nothing could be straighter, though it could be straighter than other terms. This seems to me to be a bit of a priori knowledge which I have about the empirically conceived relation "straighter than". The judgment that x is perfectly straight would then be the judgment that x is a term such that, whilst it might be straighter than something, nothing could be straighter than it.

      If we adopt this view, are we to say that the concept of perfect straightness is empirical or a priori? What we must say is the following. The only non-formal constituent of this concept is the idea of the comparative relation "straighter than". This is quite certainly an empirical concept. But there is also a formal constituent, viz., the concept of modality, present in the form of ideas of logical possibility and impossibility. I see no objection myself to saying that our ideas of modality are empirical, though non-sensuous. For we have, presumably, derived them by a process of comparison, contrast, analysis, and abstraction, from our acquaintance with facts which were manifestly necessary or manifestly contingent. Still, they are a very peculiar kind of empirical concept. And it must be recognised that, even if they be empirical concepts, our knowledge that a comparative relation does or does not have a superlative is a priori knowledge.

      Now, even if I am right in holding that, when we believe or suppose x to be perfectly straight, we are often merely believing or supposing that x is linear and not jagged and not curved, I do not imagine that this is always what we are doing on such occasions. I have little doubt that often we are believing or supposing x to be such that it is straighter than some things and that nothing could be straighter than it. Thus I am inclined to think that we have two different, though connected, ideas of perfect straightness. Of one of these we can truly say that, although it is not strictly an a priori notion, yet it "has something a priori about it" in a perfectly definite sense which I have explained above. This seems to me to be the modicum of truth which is contained in the Cartesian opinion that our concepts of Ideal Limits are a priori concepts. What I see no reason to believe is that there is a simple positive quality of which "exact straightness" is the name, and that we have an intuitive idea of this, not derived by comparison, analysis, and abstraction from perceived instances of it. If this were so, we should have an a priori concept of exact straightness, in the most literal sense of that phrase.

      *1.222. Concepts of Categories. It has often been held that our ideas of Categories, such as Cause and Substance, are a priori concepts. Let us consider the case of Cause, for example. I see a certain stone moving quickly towards a certain window; then I see the stone and the window in contact; and then I see the window starred and with a hole in it, fragments of glass flying about, and the stone moving along. I make the judgment that this stone broke this window by coming in contact with it when moving rapidly. Some people would say that all that I mean is that, whenever objects like this stone have been observed to come into contact, when in rapid motion, with objects like this window, the latter objects have been observed to become perforated and starred and bits of them have been observed flying about. It seems to me as certain as anything well can be that this is not what I or most people mean by such statements. Others would say that what I mean is that events of the first kind always have been, always are, and always will be followed immediately by events of the second kind, no matter when or where they may happen, and no matter whether they are observed or not. It seems to me that, if this were all that we meant, it is unintelligible that we should ever imagine that we had the slightest ground for making statements of the form "This caused that". Now we do think, rightly or wrongly, that we have good grounds for some of the statements of this kind which we make.

      Now, if either of the analyses which I have rejected as prima facie unsatisfactory were correct and adequate, the idea of Cause would be an empirical concept. But it certainly looks as if there were a factor in Causation which is not manifested in sense-perception. The stone perceptually appears to be moving, to be getting nearer the window, to get in contact with the window, and to pass on. The window perceptually appears to be continuous and at rest before the contact, and to be perforated and flying about after the contact. All this we can quite literally see with our eyes. But we cannot, in the same literal sense, "see" the stone causing the window to break; though we may be perfectly sure, and may even know, that it does so. These facts suggest; that the concept of Causation may be a priori. Even if they be accepted, there is another way in which the concept might yet be empirical. Though objects of sense-perception never perceptually appear to be causally related, it might be that certain objects of introspection perceptually appear to be causally interconnected or to cause certain objects of sense-perception. It has been held, for example, by some people, that, if we introspect a volition, we perceive it as a cause-factor tending to produce the desired state of affairs. I think that this is a highly plausible view, and I wholly agree with Prof. Stout¹ that the facts adduced by Hume against it are quite irrelevant. If it were accepted, we might admit that the idea of Causation is an empirical concept, derived originally from one's own experience of volition, and then transferred, rightly or wrongly, to other things and processes. But many people, whose opinion deserves respect, would reject this account of the origin of the idea. So, without going in elaborate detail into these various alternatives, we may say that the view that the concept of Causation is a priori is plausible enough to deserve serious consideration.

      *1.223. Concepts of Ethical Characteristics. It might reasonably be suggested that, unless a naturalistic theory of ethics can be accepted, we must regard the concepts of Ethical Characteristics, such as goodness, rightness, moral obligation, etc. as a priori. No doubt the concepts of Ideal Limits in ethics, e.g., perfect goodness, could be dealt with in the same way as that which we have indicated for geometrical Ideal Limits. But this presupposes that we have somehow got the idea of good, or at any rate the idea of "better than "; and the question is how, if at all, we acquired such ideas. Now, unless some purely naturalistic analysis be accepted, it seems impossible to suppose that we acquired these ideas by analysis and abstraction from instances which perceptually manifested goodness or rightness. For it does not seem intelligible to suggest that such characteristics could be perceptually manifested either in sense-perception or in introspection. Introspection might tell me that a certain emotion was one of intense indignation, but surely there is no sense in saying that introspection could tell me that this emotion was fitting or unfitting to the object towards which it is felt. Even if this be granted, it does not of course follow that the concepts of ethical characteristics are a priori. For, although it is quite clear that no naturalistic analysis of ethical characteristics with which I am acquainted is satisfactory, it is certainly not clear to me that none could be satisfactory. Still, we may say that the view that our concepts of ethical characteristics are a priori is quite plausible enough to be worth consideration.

      *1.23. Positive Theories of a priori Concepts. We defined an "a priori concept" purely negatively, as one that is not empirical. We then discussed certain alleged instances of a priori concepts in order to see whether they really are a priori or not. The upshot of the discussion has been that none of the concepts examined can be said with complete certainty to be a priori. Concepts of Ideal Limits in geometry are almost certainly not so; the concept of Causation may be derived by reflective analysis from the appearance whieh our volitions present to introspection, or there may be some satisfactory way of analysing it without residue in terms of de facto regularity of sequence; and there may be a satisfactory naturalistic analysis of ethical characteristics, although none has so far come to our notice. On the other hand, it has appeared not improbable that the concepts of Causation and other categories and of ethical characteristics may be a priori. It is therefore worth while to complete the discussion by considering what would be the positive nature of an a priori concept, if there were such concepts. Two theories on this subject seem possible, which I will call the "Theory of Innate Ideas" and the "Theory of Non-Perceptual Intuition". We I will now consider them in turn.

      *1.231. Theory of Innate Ideas. In stating this theory the distinction between occurrent and dispositional ideas is very important. There is not the least reason to believe that there are innate occurrent ideas. The people who have held that the idea of God, or of cause, or of exact straightness, is innate cannot possibly have meant that babies are born thinking of these objects, and that everyone goes on thinking of them continually night and day from the cradle to the grave. Nor do I suppose that such people have meant that these ideas were present, even in a dispositional form, at birth. This would imply that, if one gave a suitable stimulus to a newly born baby, it would at once begin to think of God, or causation, or straightness, as the case might be. Now it seems almost certain that no stimulus which could possibly be applied to a newly born baby would have such effects. What then did upholders of Innate Ideas mean?

      We must begin by distinguishing between dispositions of various orders. A disposition to think of a certain object may be called a disposition "of the first order". A disposition to form a disposition of the first order may be called a disposition "of the second order ". And so on. No baby is born with the power to talk. But practically all babies are born with the power to acquire the power to talking. If suitable stimuli be applied, they gradually acquire the power of talking. If such stimuli be not applied, they never aquire this power. And, if one applied the same, or any other, stimuli to an oyster, or a cat, or an idiotic baby, it would never acquire this power. If any sense is to be made of the theory of Innate Ideas, it must be interpreted by analogy with such facts as these.

      The theory of Innate Ideas may now be stated as follows. All sane human beings are born with certain very general intellectual powers, e.g., that of retentiveness, that of making comparisons and contrasts between perceived objects, that of abstracting universals from perceived instances of thern, and so on. These general intellectual powers, together with the objects that we perceive in the course of our lives, suffice to account for the formation of the vast majority of our dispositional ideas. There is plainly no need to assume, for example, a special second-order disposition to account for our acquirement of the power to think of redness. The fact that we see things that look red, together with the general powers of comparison, abstraction, etc., suffice to account for the acquirement of the dispositional idea of redness. But there are some of our dispositional ideas which cannot be accounted for in this way, and yet all sane human beings do in fact acquire them, provided that they are supplied with suitable experiences. For example, we all form the idea of cause, of straightness, and so on, provided that we meet with cases of regular sequence, of approximate straightness, and so on. And, it is alleged, these ideas cannot be formed in the way in which we form our idea of redness. It is therefore necessary to postulate, in addition to these general innate intellectual powers, more specific intellectual powers. For example, we must postulate a disposition to form the idea of Cause when presented with instances of regular sequence; a disposition to form the idea of Substance when presented with instances of recurrent bundles of qualities; a disposition to form the idea of Rightness or Wrongness when we contemplate certain kinds of situation with certain kinds of emotion; and so on. Probably the order of events would be somewhat as follows.

1. We begin by acting in certain situations as it would be reasonable to act if we had judged that we were in presence of substances with definite properties, interacting in accordance with general laws. No judgment may actually have been made. This stage is presumably reached by the higher animals as well as by men.
2. All sane human beings go on in many cases to make explicit judgments which involve the categories of Cause and of Substance, e.g., "The stone broke the window".
3. Finally, some men reflect on such behaviour and on such judgments, and, by a process of analysis and abstraction, form the concepts of Cause and of Substance in the abstract.

      When the theory of Innate Ideas is stated in the way which I have been explaining it is certainly not open to any of the objections that are commonly brought against it. These objections may be summed up as follows.

1. It is absurd to suppose that babies are born thinking of Cause or Substance, or that anyone is thinking of such objects at every moment of his life. This objection is answered by the distinction between having an idea as an occurrent experience and having an idea as a cognitive disposition.
2. No conceivable stimulus applied to a newly born baby would make him have the idea of Cause or of Substance. This objection is answered by distinguishing between a dispositional idea and a second-order disposition to acquire this dispositional idea. All that we can assume to be present in the newly born baby is the latter.
3. Idiots and savages probably never form these ideas at all. As regards idiots, the answer is that they may be so defective as to lack an innate disposition which is common to all normal men. Sufficiently idiotic babies never learn to talk or too walk, yet the power to acquire the power of walking and the power of talking is certainly innate in all normal human beings. As regards savages, the answer is twofold.
   1. They may never have been supplied with suitable stimuli to set their innate intellectual powers in full operation. If a perfectly normal baby were never put on the ground and never spoken to, it would probably never acquire the power to walk or to talk properly.
   2. Even if savages never get to the stage of forming the concepts of Cause and Substance in the abstract, they certainly make judgments which involve determinate forms of these categories, and they still more certainly often act as if they had made such judgments.
4. If "idea" be used to mean "disposition" or "power", it is trivial to ascribe innate ideas to anyone. Naturally we have the power to think of anything of which we do actually think. This objection is irrelevant. The real question is: "How did we acquire the power to think of certain objects?" In some cases no explanation is needed except that we have certain very general innate intellectual capacities, and that subsequent experience provides us with suitable material for them to work upon. But in other cases, it is contended, this explanation is not adequate. We have to postulate much more specific innate intellectual capacities in order to explain the fact that all normal human beings, when appropriately stimulated, acquire certain ideas, such as those of Cause and Substance.

      It seems to me then that the theory of Innate Ideas, when properly stated, is immune to all the ordinary objections that have been made against it, and that it may very possibly be true. It is, of course, most undesirable to postulate innate intellectual powers rashly, and no doubt many supporters of the theory of Innate Ideas did this and made it a cloak for intellectual laziness and lack of analysis. But it is certainly not obvious that no powers except the general powers of retentiveness, comparison, and abstraction are needed to explain the formation of all our dispositional ideas.

      *1.232. Theory of Non-Perceptual Intuition. As regards empirical concepts of the first kind, such as the idea of redness, their origin guarantees their having instances. We derived our idea of redness from perceiving things that looked red. Even if no physical object were really red, it seems incredible that such an object should look red to a person unless in perceiving it he was sensing a sensibile which is red. Empirical concepts of the second and third kinds may be wholly fictitious. There is no reason to believe, and strong reason to doubt, that the characteristics of serpenthood and flame-breathing ever have been or ever will be co-inherent in any particular. Now, if the theory of Innate Ideas be true, we have no guarantee that our innate ideas may not be as fictitious as our idea of dragonhood or phoenixhood. On this theory the notions of Cause, Substance, etc., are read into perceived objects by human minds. When our perceptual experiences take a certain form we inevitably believe ourselves to be in presence of substances, when they take a certain other form we inevitably believe ourselves to be witnessing or initiating or suffering a causal interaction; and so on. Now the fact that a certain concept is innate, and is applied by all sane and developed human minds on all occasions of a certain kind, is no guarantee of its validity. There might be innate racial delusions, and the concepts of Cause and Substance and Rightness and Duty might be instances of such racial delusions. Unless there be some kind of pre-established harmony between the human mind and the rest of nature, it would seem just as likely that our innate ideas should be delusive as that they should be veridical. This fact is a motive for a quite different type of theory which I will now briefly outline.

      May there not be certain characteristics of the real, which cannot be manifested either in sense-perception or in introspection? And may not the human mind be able to recognise the presence of these characteristics, in favourable conditions, by the exercise of a kind of Non-Perceptual Intuition? Let us take a concrete case to illustrate the theory. When a stone approaches a window, hits it, breaks it, and passes through, there are certain relations which I can perceive with my senses. But there is another relation, viz., that of causation, between the coming in contact of stone with window and the subsequent starring and flying in pieces of the latter. This is certainly not manifested in sense-perception; if it were, it, or something analogous to it, would have to relate the visual sensibilia which I am sensing in perceiving the process. But why should sense-perception be the only way in which I can become aware of a relation which in fact holds between objects that I am perceiving with my senses? May there not actually be a causal relation between the earlier and the later phases of the total perceived process, just as there is a spatio-temporal relations And may I not have an intuitive awareness of this relation, though not by any of my senses?

      On such a view as this we have only to postulate in the human mind a general power of non-perceptual intuition. Categories, ethical relations, etc., will be relations or types of structure actually present in reality, but incapable of manifesting themselves sensuously or introspectively, as colours, shapes, and spatio-temporal relations can do, and as psychological qualities and relations can do. When our perceptual experience takes certain specific forms this power of non perceptual intuition is stimulated, and we intuit these objective types of relation or structure in the perceived objects.

      Such a theory as this is logically possible, and it plainly has certain advantages over the theory of Innate Ideas. It might be objected that it has the opposite defect to the latter theory. On the theory of Innate Ideas we have no reason to believe that such judgments as: "This caused that" or "That emotion was unfitting" are ever true; whilst, on the present theory, it might be said, it is difficult to see how they could ever be false or even doubtful. If I perceive X and perceive Y I cannot intuit the relation R between them unless they do in fact stand in that relation to each other. And, if they do stand in the relation R, and I do intuit it, then I must know that they do so. Now it is certain that we can make mistaken judgments of the form: "X caused Y"; and many people would say that no such judgment ever expresses knowledge, as distinct from probale opinion.

      I do not think that the occurrence of false judgments, involving the categories or ethical characteristics, is a serious objection to the view that our concepts of categories or ethical characteristics are derived from non-perceptual intuition. Suppose I have acquired a dispositional idea of causation or of rightness by intuiting a causal relation or a relation of ethical appropriateness in actual instances of it. I might quite well misapply this idea in certain cases in future. I might be misled through association to think that I was perceiving an instance of causation when I was perceiving a mere instance of regular sequence. And I might be misled through association to think that a certain emotion was unfitting to a certain object when the fact merely is that I have a feeling of quasi-moral disapproval when I contemplate other people having this kind of emotion in this kind of situation. The second objection is a more serious one. If it be really true that I never know any fact of the form: "X caused Y", it seems incredible that I ever intuit the causal relation as holding between two terms which I perceive. But to this it might be answered, in my opinion with very great plausibility, that, in the case of my own volitions at any rate, I do know, in the strictest sense, that a certain volition is a cause-factor which, if the remaining cause-factors are as I believe them to be, is necessary and sufficient to produce the desired result.

2. Possibilities.

      We can now return to the task of expounding and criticising McTaggart. The next question is whether there are Possibilities, and whether, if so, they are existents.

      McTaggart points out that the statement that so-and-so is possible may have an epistemic or an ontological meaning. It may mean: "I know of no reason why so-and-so should not be, or have been, the case". On that interpretation it is simply a fact about myself and my state of knowledge, and these are existents. It may, however, mean that a certain set of data, which I explicitly mention or tacitly assume, do not either entail or exclude that so-and-so should be the case. When I say that it is possible for a triangle to be equilateral I generally mean that the characteristic of being bounded by three straight lines neither entails nor excludes the characteristic of being equilateral. Now we are supposed to have shown that all characteristics are existent. But all facts about existents exist, and possibilities turn out to be negative facts about the entailment or exclusion of one characteristic by another. Therefore there are no non-existent possibilities.

      McTaggart's account of possibilities seems to be unduly negative. When we say that a triangle may be equilateral an important part of our meaning surely is that the presence of triangularity involves that of a certain disjunction of determinate relations of length, one of which is equilateralness. This is at least as important as the fact that it neither entails nor excludes equilateralness. This modification does not, however, affect the principle of McTaggart's argument that every possibility is existent. His doctrine must not, of course, be confused with the doctrine that everything that is possible is actual, i.e., that there are no unrealised possibilities.

      In § 40 McTaggart proceeds to infer from the existence-of all possibilities that "it is not the case, as is sometimes supposed, that what is actually existent is surrounded by a sort of framework of possibilities of existence, which limit what does exist, and do not depend on it". This conclusion sounds interesting and important. It seems, for example, to contradict such a theory of the universe as Leibniz held. Leibniz's doctrine is often misunderstood, and it may be well to state it clearly in order to see what bearing McTaggart's conclusion really has on it. I think that the following is an accurate account of Leibniz's doctrine.

1. There is one Existent whose existence is a necessary consequence of its nature.
2. The being of all possibilities, whether actualized or not, depends on the nature and existence of the Necessarily Existent.
3. Not all possibilities are realized.
4. The actualisation of those possibilities which are actualized depends on the volition of the Necessarily Existent.