The notion of a Fact is first introduced in §9. In §10 McTaggart tries to define the term "fact". It is said to be "either the possession by anything of a quality or the connection of anything with anything by a relation". Here "anything" is to include both particulars and universals, and, I suppose, facts. whether this description would apply to the fact that there are lions and the fact that there are no dragons seems at best doubtful. The following further remarks about facts must now be noted.

1. He says (§10) that, if my table is square, the squareness of my table is a fact. There is some inconsistency here, for in §5 the wisdom of Socrates was said to be an existent quality, and therefore not a fact.
2. He repeatedly says that beliefs are facts. Cf., for example, p. 11, note 2, where he says: "My belief 'the table is square' is of course itself a fact". Cf.also §18, p. 19, "A belief is a psychical fact in a man's mind". Now all this is extremely odd. For elsewhere he takes states of mind to be particulars, which are parts of the mind whose states they are, and therefore not to be facts. Of course, if I believe at a certain moment that my table is square, there is the fact that I have this belief at that moment. But surely the belief is an event, and the fact is that this belief is happening in my mind at that moment.
3. In §17 he asserts that some facts are in time. Of course he does not believe that anything is really in time, but he does mean that the statement that some facts are in time is true in the same sense and with the same qualifications as the statement that the Albert Memorial is in time, whilst other facts are not in time even in this sense and with these qualifications. Since it is abundantly clear that he sometimes confuses an event which in fact happens at a certain time with the fact that this event happens at that time, it may well be that his statement that some facts are in time depends on this confusion. I think it is evident from these quotations that MeTaggart was either not clear as to what he meant by a "fact" or that he sometimes applied the name "fact" to terms which are not facts on his definition.

1. What are "Propositions", and why are there supposed to be Propositions?

      Let us begin, if we can, with what is admitted by everyone.

1. It is quite certain that situations do from time to time arise which can properly be described by such phrases as: "M is believing at t that S has the characteristic P". In all such cases M is a mind, whilst S may be anything whatever -- a particular, mental or material; a characteristic; a fact; or what not.
2. It is certain that there may exist a number of such situations which differ from this and from each other only by variations in M or t or both. Thus we can have: "M' is believing at t that S is characterized by P", "M is believing at t' that S is characterized by P", and "M' is believing at t' that S is characterized by P". Such facts as these are conveniently expressed by saying that "the proposition that S is characterized by P may be believed by the same mind at different times, and by different minds at the same time".
3. It is certain that there are also situations which can properly be described by such phrases as: "M is disbelieving at t that S is characterized by P", and that it is impossible for there to be two situations which differ only in the respect that "disbelieving" is substituted in the one for "believing" in the other. This fact is conveniently expressed by saying that "the same person cannot at the same moment believe and disbelieve the same proposition".
4. It is, however, quite possible for there to be such situations that statements of the following three forms are all true, viz.,
   1. "M is believing at t that S is characterized by P",
   2. "M' is disbelieving at t that S is characterized by P", and
   3. "M is disbelieving at t' that S is characterised by P".
   Such facts are conveniently expressed by saying that "the proposition that S is characterised by P may be both believed and disbelieved at the same time by different minds, and at different times by the same mind".

      Now there is no doubt about these facts. And the natural and obvious way of analysing them is the following. Such situations consist of a mind related in certain ways to a certain objective constituent. The relation is that of judging, and this has two determinate forms, viz., believing and disbelieving. The objective constituent is something which is believed or disbelieved. We cannot believe or disbelieve without believing or disbelieving something, any more than we can have a sensation without sensing something. And, in the case of judgment, the something in question is a proposition.

      So much might have been inferred from considering each judgment-situation in isolation. But this would have left it possible that the objective constituent of each judgment is private to the mind which makes the judgment. In that case a proposition would be a factor which is inseparable from the judgment-situation of which it is the objective constituent, just as many people would hold that a sensum is inseparable from the sensation of which it is the objective constituent. This possibility is eliminated when we take into account the facts about the relations of one judgment-situation to others. These, it will be said, force us to assume that propositions are neutral and independent of the judgment-situations in which they occur as objective constituents. For otherwise we could not say that the same proposition may be believed at the same time by different minds, that it may be believed on several different occasions by the same mind, that it may at the same time be believed by some minds and disbelieved by others, and that it may at different times be believed and disbelieved by the same mind.

      Thus far, then, two characteristics have been ascribed to propositions, viz.,

1. that they are the kind of entities which occur as objective constituents in judgment-situations, and
2. that they are public and neutral entities, capable of being objective constituents of many different judgment-situations.

      We must now try to carry our analysis a little further. (i) The phrases which express judgment-situations have a grammatical peculiarity which distinguishes them from those which express other kinds of objective situations, such as sensations. The grammatical object of the phrase which expresses a judgment-situation is never a simple noun, such as "flash" or "table", or a simple adjective, such as "red" or "square". It is always a complex phrase which either is, or is equivalent to, a phrase of the form "that S is characterized by P". (I am omitting existential judgments for the present. The argument is not affected thereby, for the grammatical object would still be a "that"-phrase, though it would now take the form "that S exists" or "that there is an S".) You may be said to see a flash or hear a noise, but you cannot be said to believe or disbelieve flash or noise or red or squeaky, though you may be said to believe that the flash is red and to disbelieve that the noise is squeaky. This difference in grammatical form suggests that, although the judgment-situation and the sensation-situation are both objective, yet the former is in some way more complex than the latter.

      Now this extra complexity might, of course, fall on the side of the objective constituent, or it might belong to the relation which relates the subjective and the objective constituents of the judgment-situation. It might be, for example, that the relation of sensing is dyadic, like that of parenthood, whilst the relation of judging is more than dyadic, like that of jealousy. If that were so, there would have to be more than one objective constituent in every judgment-situation; for example, if the judging relation were n-adic, there would have to be n-1 objective constituents in the judgment-situations. If, on the other hand, it is assumed that the judging-relation, like that of sensing, is only dyadic, it will have to be assumed that there is only one objective constituent in the judgment-situation. This must then be assumed to be a single internally complex whole, composed of several terms interrelated in a characteristic way. Suppose we represent the analysis of a typical sensational situation by Sigma (M, O), where Sigma stands for the relation of sensing, M stands for the mind, and O for the sensibile that it senses. Then, if we assume that the judging relation J is dyadic, like the sensing-relation Sigma, we shall have to represent the analysis of the judgment-situation by some such formula as J {M, pi (S, P)}, where pi is a peculiar relation, which might be called the "propositional relation", and pi (S, P) is a peculiar kind of complex whole, which might be called a "proposition".

      If we were prepared to suppose, as Russell at one time suggested, that the judgment-relation J may be triadic, we could represent the analysis of the judgment-situation by some such formula as J (M, S, P). Now it is the first kind of analysis which is tacitly assumed by most people who accept the reality of propositions. They assume without question that the right analysis of a judgment situation is into (M)-believing-or-disbelieving-(that S is characterized by P); and they assume that the proposition is a peculiar kind of complex object, consisting of the terms S and P interrelated in a perfectly unique way. There will be at least two terms in it; and there may be more, for P might itself be a relational property, such as "being jealous of V on account of W".

      Thus one cause which has led people to believe that there must be propositions is that they have assumed without question that the judging-relation must be dyadic, like the sensing-relation. This was, no doubt, partly suggested by language. But it must also be remembered that philosophers have seldom recognised that there are triadic and tetradic relations. (There is still a quaint old-world prejudice against them in the Home of Lost Causes.) And no one, so far as I know, before Russell, had made the important suggestion that the judging-relation might be more than dyadic; whilst he, I suppose, abandoned it, like so many of his philosophic offspring, on the steps of some Foundling Hospital for illegitimate conceptions, when he decided to make an honest woman of Behaviourisrn. We may now add a third characteristic of propositions to the two that we have already mentioned. It is (iii) that the proposition which is the objective constituent of such situations as are expressed by phrases of the form "M believes (or disbelieves) that S is characterized by P" is a peculiar kind of complex unity composed of the terms S and P interrelated in a unique way.

      We can now carry our analysis yet a step further. It is admitted by everyone that the adjectives "true" and "false" are specially connected with judgments. Every judgment is either true or false, and no judgment is both. But it is also held that these adjectives apply to propositions. I think that everyone would admit that, if there are both judgments and propositions, there must be a primitive sense of "true" and "false" in which these adjectives apply to one, and a derivative sense in which they apply to the other. Now those who accept the reality of propositions generally hold that the adjectives "true" and "false", in their primitive sense, apply to propositions and not to judgments. The sense in which these adjectives apply to judgments is, on their view, derivative, and definable in terms of the sense in which they apply to propositions. A "true" judgment may be defined as belief in a true proposition or disbelief in a false proposition. A "false" judgment may be defined as belief in a false proposition or disbelief in a true proposition. It is the fact that some beliefs are false and some disbeliefs are true which seems to make it necessary to distinguish propositions from facts. When I believe falsely I am certainly believing something, in exactly the same sense in which I am believing something when I believe truly. And other people may have false beliefs which agree with mine; so that there is just as good a reason here as in the case of true belief to hold that this something is public and neutral. And yet it plainly cannot be identified with any fact. Suppose, for example, that several people believe that Bacon wrote Hamlet, and that I disbelieve it. My disbelief is true, and their beliefs are false. But they believe and I disbelieve the same something, and this something cannot be a fact. If all beliefs had been true and all disbeliefs had been false, there would have been less ground for assuming propositions in addition to facts. A true judgment might then have been just a belief in a fact, and a false judgment might have been just a disbelief in a fact. But this is not so. There are false beliefs and true disbeliefs; and, if truth and falsity are to belong primarily to the objective constituents of such situations, we cannot identify the latter with facts.

      Apart from this there is, I think, another reason for refusing to identify the objective constituents of judgment-situations with the facts which make them true or false. We have so far drawn no distinction between belief and disbelief, on the one hand, and knowledge, on the other. Now it seems certain that true belief can and does exist without knowledge of the corresponding fact. It seems to me plausible to suppose that, when we have knowledge, as distinct from mere true belief, we have true belief founded upon acquaintance with the fact which makes the belief true. Now it seems clear that I can at one time have true belief that S is characterized by P without having knowledge of it, and that at another time I can know that S is characterized by P. For example, I might first believe that the circle cannot be squared, on inductive grounds or on authority, and later on I might come to know it, in the strict sense, by following the proof that pi is a transcendental number. If this be so, it will be necessary, even in the case of true belief, to distinguish between the proposition believed and the fact which makes the belief true.

      We may now sum up the characteristics which together constitute the description of the term "proposition".

1. Every judgment consists of a subjective and an objective constituent united by a dyadic relation of judging. A proposition is the objective constituent of a judgment.
2. Propositions are not merely distinguishable but inseparable factors in judgments. They are neutral and public objects. Any proposition can be judged at various times and by various minds, it can be now believed and now disbelieved; it may sometimes be believed and not known, and at other times or by other minds be known and not merely believed.
3. A proposition is a single internally complex whole, consisting of at least two terms interconnected in a unique way.
4. Truth and falsity, in their primary sense, attach to propositions. Anything else, e.g., a judgment, which is true or false, is so in a sense which is derived from and definable in terms of truth and falsity as applied to propositions.

2. Must we assume that there are Propositions?

      We now know what people have in mind when they talk of "propositions", and we have seen what premises have led some people to the conclusion that there are propositions in the sense described above. Some of these premises are undoubtedly true. It is quite certain that judgments are epistlemologically objective or "intentional", i.e., that in every judgment something is believed or disbelieved. And it is quite certain that there are sets of beliefs and disbeliefs, occurring at various dates and in various minds, which are so related to each other that we speak of then as so many different beliefs or disbeliefs "in the same proposition". Let us call such a set of beliefs and disbeliefs a "Co-referential Set" of judgments.

      On the other hand, two at least of the premises might conceivably be false. It may be false that the relation which unites the subjective and the objective constituents of a judgment is dyadic. And it may be that truth and falsity, in their primary sense, apply, not to propositions, but to judgments . The question then is: "Do the premises necessitate the conclusion that there are propositions; and are the doubtful premises true?"

      2.1. Co-referential Sets of Judgments. It seems clear to me that the facts which are referred to as the "publicity, neutrality, and timelessness of propositions" could all be admitted without assuming that there are any propositions in the sense described above, and without assuming any particular analysis of judgment or any particular theory of what makes judgments true or false.

      Suppose we were to define "the proposition which is the object of the judgment J" as the class of judgments which is composed of J itself and of all judgments that are co-referential with J. There is no doubt that the "proposition", so defined, exists. Again, the proposition, so defined, is something public and neutral, in the sense that it exists provided there is any judgment in this co-referential set. Its existence is not dependent on the judgment of Smith, or on the judgment of Brown, or on the judgment of Robinson, though it would not exist if no one whatever at any time made a judgment that would fall into the set which constitutes the proposition. Again, the proposition, so defined, is timeless, in the sense that it exists if anyone at any time makes a judgment which would fall into the set. With this definition it is possible to define the statement that a "proposition is true or false". A "proposition", in the sense defined, would be "true" if and only if the set of co-referential judgments which is the proposition contained either a true belief or a false disbelief. In that case, of course, all the beliefs within the set would be true, and all the disbeliefs within it would be false. Similarly, a "proposition", in the sense defined, would be "false" if and only if the set of co-referential judgments which is the proposition contained either a false belief or a true disbelief. In that case, of course, all the beliefs within the set would be false, and all the disbeliefs within the set would be true.

      With these definitions "truth" and "falsehood" as applied to "propositions" would have the usual properties. (a) No proposition could be both true and false. For otherwise all the beliefs within the set would be true and all the disbeliefs within it would be false, whilst all the beliefs within the set would be false and all the disbeliefs within it would be true. This would involve that the set contains some judgments that are both true and false. And this is impossible. (b) Again, every proposition must be either true or false. For, if a certain proposition were not true, the set which is the proposition would contain no true belief and no false disbelief. If the same proposition were not false, the same set would contain no false belief and no true disbelief. But, if it contained no true belief and no false belief, it would contain no belief at all. And, if it contained no false disbelief and no true disbelief, it would contain no disbelief at all. Consequently the set defining a proposition which was neither true nor false would contain no judgment at all, and therefore there would be no such proposition.

      I think it is, quite plain, then, that we can define Pickwickian senses of "proposition", and of "truth" and "falsehood" as applied to "propositions", without making any assumption about the right analysis of judgments or about the relations of judgments to facts. And "propositions", so defined, will have all the properties that formal logic requires them to have. So far then there is no reason to assume that there are propositions in the non-Pickwickian sense which we described earlier.

      2.2. The Intentionality of Judgments. We can now pass to the next stage of the discussion. Those who accept propositions in the literal sense might admit that they are not needed for the purposes of formal logic, and might then argue as follows. "You have taken the fact that judgments are objective or intentional occurrences, and the fact that there are co-referential sets of judgments, as ultimate, and have not attempted to analyse these facts further. This is quite legitimate for the formal logician, but it is not enough for the metaphysician and the epistemologist. It is their business to analyse these facts, and then it becomes impossible to dispense with propositions in the literal sense. For judgments are objective or intentional only because they have propositions for their objective constituents; and there are co-referential sets of judgments only because one and the same proposition can be the objective constituent of a number of different beliefs and disbelief This is the contention which we have now to examine. We will take the second point first. |

      2.21. Co-referential Sets do not require Propositions. I think it is quite certain that the fact that there are co-referential sets of judgments does not by itself require that there should be propositions in the literal sense. McTaggart deals with this question in terms of the Correspondence Theory of truth. I shall state the answer in rather different, terms from those which he uses, because I am not altogether satisfied with his form of the Correspondence Theory. I should put it as follows. Two beliefs or two disbeliefs are co-referential if they are such that they both concord or both discord with the same fact. A belief and a disbelief are co-referential if they are such that one accords and the other discords with one and the same fact. Thus, to sum up, two judgments are co-referential if they are such that

1. there is a single fact with which both concord (in which case they are both true), or
2. a single fact with which both discord (in which case they are both false), or
3. a single fact with which one accords and the other discords (in which case one is true and the other is false).

      Now, although this solution of the problem of defining co-referential sets of judgments without assuming propositions in the literal sense is correct so far as it goes, it is not wholly satisfactory for two reasons.

1. It presupposes the Correspondence Theory of truth and falsehood. Now I have no doubt that this theory is true, and I think that McTaggart has given conclusive reasons for it and has made conclusive answers to the objections against it in §§ 9-13 inclusive. But it is not accepted by everyone, and it would therefore be better if we could solve the present problem without assuming it.
2. Even if the Correspondence Theory be true, McTaggart',s analysis of the fact of co-referential sets of judgments cannot be ultimate. It is plain that we know with regard to any pair of judgments by mere inspection whether they are or are not co-referential. On McTaggart's analysis this means that we know by inspection whether they are or are not of such a kind that there is a single fact with which both concord or with which both discord or with which one concords and the other discords. Since we can know this without being acquainted with the fact in question, the ground of our knowledge must be some observable identity of terms and some observable similarity of structure in the judgments themselves. It must be like looking at two keys and seeing from their structure that they will either both fit or both fail to fit the same lock, though we may never have seen the lock in question. Thus the fundamental fact about co-referential judgments will be this observable identity of certain elements in all of them, and this observable similarity in the arrangement of the elements in all of them. This kind of relation must hold, and must be observable, among the judgments of a set, even if the Correspondence Theory be true. And it might hold even if the Correspondence Theory were false. We can therefore drop that theory out of the picture for the present.

      Now it is quite certain that this kind of observable similarity of structure and contents among co-referential judgments could exist without there being propositions in the literal sense. Suppose, for example, that some form of multiple-relation analysis of judgment were, on other grounds, admissible. Suppose that M's belief at t that S is characterized by P were a complex situation of the form B (M, t, S, P), where B is a tetradic relation which relates the terms M, t, S and P in a certain order which is represented by the spatial order in which the letters are written down. Suppose that believing (B) and disbelieving (B') are two determinate forms of the determinable relation of judging (J). Then the set of judgments co-referential with M's belief that S is characterised by P would be all those judgments in which the relating relation is B or B', in which the terms other than M and t are S and P, and which are ordinally similar to B (M, t, S. P). The set would in fact consist of all the judgments whose symbolic expressions could be obtained from the symbol B (M, t, S, P) by varying B to B' or M to M' or t to t', whilst keeping S and P and the order of the symbols within the bracket fixed. We see then that, even without assuming the Correspondence Theory, we could explain the fact that there are co-referential sets of judgments without needing to postulate a proposition in the literal sense to be the common objective constituent of each such set.

      2.22. Does the Intentionality of Judgments require Propositions? We come now to the last defense of the Proposition Theory. It is simply that no satisfactory analysis can be given of the intentionality, which is an essential feature of all judgments, unless we admit that every judgment contains a proposition, in the literal sense, as its objective constituent. This, it is contended, is peculiarly obvious in the case of false judgments. "You admit", it will be said, "that you cannot judge without judging something You admit that this something is not an ordinary term, but is denoted in language by some such phrase as 'that S is A '. And you admit that there are false judgments; so this something cannot in all cases be a fact. What then can it be but a proposition, in the literal sense?"

      Now at this point I propose to do three things.

1. To show that the above challenge, even if unanswerable, would not suffice to prove that there must be propositions in the sense of public and neutral objects.
2. To show that McTaggart's attempt to answer the challenge is a failure. And
3. to try to suggest an answer to it myself.

      The first point can be settled quite easily. Even if the intentionality of judgments cannot be accounted for without assuming that each judgment contains an objective constituent of a unique kind, such constituents might never be common to two different judgments, even though the latter were co-referential. It might be that judgments were like sense-perceptions, propositions like sensa, and facts like physical objects. A number of people can perceive the same physical object, and each one of their perceptions contains an objective constituent of a characteristic kind. But there is good reason to doubt whether any objective constituent is common to several perceptions, and whether any objective constituent is identical with, or is literally a part of, the physical object, if such there be, which all these people are said to be perceiving. It is possible then that "propositions", in the sense in which the present argument would demand them, might be as private as sensa are commonly held to be. When W. E. Johnson was pressed as to what he meant by "propositions" he seemed sometimes to fall back on some such view as this. But he was never clear or consistent about it. He wanted propositions to be public and neutral, in order for there to be something for people to agree about, to differ about, and to alter their minds about. But, when one asked him whether he was really prepared to admit the independent being of objective false propositions he was liable to reply that the proposition is not really separable from the judgment of which it is the objective constituent. His "propositions" in fact seemed to be public and neutral on Mondays, Wednesdays, and Fridays, and to be private and mind-dependent on Tuesdays, Thursdays, and Saturdays. On Sundays they no doubt underwent a higher synthesis, in whieh both these opposed characteristics were absorbed, transmuted, and reconciled.

      2.221. McTaggart's Attempt to dispense with Propositions. We can now pass to the second point, viz., McTaggart's attempt to answer the last challenge of the supporters of the Proposition Theory. This is contained in §20. The essence of it is as follows.

      The opinion that every belief has an objective constituent, which is a proposition, arises from a. confusion about two genuine facts.

1. Every belief professes to correspond to a certain object, but only true beliefs really correspond to such objects.
2. Every belief really has a peculiar relation to a certain fact on which its truth or falsity depends.

      It seems to me that this is no answer to the challenge, and that it involves confusions of its own. What literal meaning can be attached to the plainly metaphorical statement that every belief "professes" to correspond to a certain object? Beliefs do not literally "profess" to do anything; it is only persons who can make professions. McTaggart's statement therefore seems to mean that anyone who believes that S is characterized by P ipso facto "professes" (i.e., maintains or believes) with regard to something that this something corresponds to a fact. But what can the "something" in question be? Is it his belief? If so, McTaggart's statement amounts to saying that anyone who believes that S is characterised by P ipso facto believes with regard to this belief that it corresponds to a fact. Now this is quite certainly false. In the first place, if taken literally, it would involve a vicious infinite regress. It would be impossible to believe p without ipso facto having a belief about one's belief in p. On exactly the same principle one would ipso facto have a belief about one's belief about one's belief in p; and so on without end. This objection might be removed by making McTaggart's principle hypothetical. It would then take the form that any S one who believed that S is characterized by P would, if the question were raised, believe that his belief corresponds to a fact. But even this is not true. For a man may reject the Correspondence Theory of truth and yet have beliefs. Bradley, for example, rejected the correspondence Theory, and believed that Hegel was a great philosopher. How then can it possibly be said that, in believing Hegel to be a great philosopher, Bradley was ipso facto believing that this belief corresponded to a fact? No doubt, if the belief be true and the Correspondence Theory be true, the belief does correspond to a fact. But this cannot possibly be part of what a person who rejects the Correspondence Theory is believing.

      It seems to me then to be certain that the "something" which a person who believes that S is characterised by P ipso facto believes to correspond to a fact is not his belief that S is characterized by P. And, if the "something" is not this belief, I do not see what other belief it could be. But, if the "something" in question is not a belief at all, what is it? In the first place, beliefs (or disbeliefs) are the only kind of entities which McTaggart has admitted to be capable of corresponding to facts. If we are now to have an entity which is not a belief or a disbelief and yet is capable of corresponding to a fact, what can it be but our old friend the proposition? McTaggart will be reduced to saying that anyone who believes that S is chapracterised by P ipso facto believes that the proposition that S is characterized by P corresponds to a fact. This would be a far more plausible contention than the other alternative which we have discussed and rejected. But it would be a complete abandonment of his position. And it would still be inconsistent with the fact that a man can have beliefs and yet reject the Correspondenee Theory of truth. It seems to me then that McTaggart has made no answer at this point to the challenge of the supporters of the Proposition Theory. He has only got into a hopeless muddle.

      *2.222. Independent Attempt to dispense with Propositions. It remains to be seen whether we can give for ourselves an analysis of judgment which will account for the objective or intentional character of judgments without assuming that there are propositions in the literal sense. I am inclined to think that this can be done on the lines of the theory of judgment put forward by Prof. Stout in his Studies in Philosophy and Psychology in the essay entitled Real Being and Being for Thought.

      Suppose that I am looking at a certain sheet of paper, of which only one side is visible to me from where I am standing. Suppose I make the judgment that the other side of this bit of paper is blue. What is really happening? To simplify matters we will assume that I am acquainted with the side of the paper which is facing me, and am not merely acquainted with a sensibile which is numerically different from this physical surface. In that case it may be said that I know the following facts, and do not merely have beliefs.

1. I know that there is another side to the paper.
2. I know that this other side must have some colour or other, if white and black be counted as colours.
3. I know, with regard to blue, green, yellow, red, white. and black, that they are determinates which fall under the determinable of colour.

      The fact that I believe this must consist in the fact that my thought of the alternative blue stands in a certain special relation to my three states of knowing, which have been mentioned above, whilst my thoughts of the other alternatives do not stand in this relation to these three states of knowing. My thoughts of the other alternatives may indeed stand to these three states of knowing in a certain special relation which is opposed to the special relation in which my thought of the alternative blue stands to these three states of knowing. In the first case I just believe that the opposite side of the paper is blue, without either believing or disbelieving that it is red, etc. In the second case I both believe that the opposite side is blue and positively disbelieve that it is red, etc. Let us call these two opposed relations the relation of "being inserted" and the relation of "being extruded", respectively. It is arguable that each of these relations is capable of various degrees, which might be expressed by the phrases "strongly" or "weakly" inserted or extruded; but I do not want to introduce complications which are needless for our present purpose. Now my belief is true if and only if the thought which stands to my states of knowing in the relation of being inserted is the thought of that determinate colour which in fact characterizes the opposite side of the paper. Here, at any rate, we can see, not only that the Correspondence Theory is true, but also in what the concordance between a true belief and the fact to which it refers consists. My belief is false if and only if the thought which stands to my states of knowing in the relation of being inserted is the thought of one of the other determinate colours. Here, at any rate, we can see in what the discordance between a false belief and the fact to which it refers consists.

      We can now generalise this example. To simplify the statement I will confine myself to those judgments which are unmixed beliefs. There will be no difficulty in applying the analysis to judgments which are unmixed disbeliefs or combinations of beliefs and disbelief. Every belief is a complex state of affairs, in which the following factors can be distinguished.

1. Acquaintance with a certain fact whose subject or predicate is a determinable, and lack of acquaintance with the more determinate fact in which this determinable subject or predicate is specifically determined.
2. Acquaintance in the same mind with the fact that certain determinates of which it is thinking are specifications of this determinable.
3. The thought of one of these determinates being marked out from the thoughts of the others by standing to the acts of acquaintance, already mentioned, in the special relation of being inserted in them.

      A mixed state of belief and disbelief might be illustrated by the following diagram:

      Here K stands for the relation of knowing a fact. F (a, X) represents a relatively indeterminate fact involving a particular a and a determinable characteristic X. x₁ and x₂ represent two determinates under X. phi (X, x₁) represents the fact that x₁ is a determinate under X; and phi (X, x₂) represents the fact that x₂ is a determinate under X. I represents the relation of being inserted, and E represents that of being extruded. M represents the mind which makes the judgment. It might, of course, happen that M thinks of one and only one of the alternative specifications of X. If so, there would be a strong tendency for the thought of this alternative to become inserted in the noetic framework, and we should have an instance of "primitive credulity".

      I am of course well aware of the inadequacy of the above statements if regarded as a full theory of the nature of judgment. They deal only with singular characterizing judgments, and make no mention of existential judgments or of more complicated kinds of characterizing judgment, such as universal and particular, alternative and hypothetical, and so on. I cannot attempt to go fully into details, but I will say some thing about existential judgments. Suppose that a certain man believes that there are dragons. What is actually happening when he is engaged in believing this? We will suppose that he understands by a "dragon" a flame-breathing serpent. The noetic framework of his judgment in this case is as follows. He knows that there are serpents. He knows that breathing is an essential factor in the notion of serpenthood, and indeed in that of animality. He knows that breathing must be specified in some determinate way in any particular case, and that it can be specified in several alternative ways. For fishes may be said to breathe water, cats and dogs to breathe air, and chimneys and blast-furnaces to "breathe" flame. Thus the situation in which the man finds himself just before he makes his judgment may be expressed in the sentence: "I know that there are serpents, and that they all breathe something or other. I know that, among the determinate forms of breathing that are possible, there is flame-breathing. Do any serpents have the determinable breathing in the determinate form of flame-breathing?" Suppose now that the man comes to believe that there are dragons. Then presumably his thought of flame-breathing enters into a new relation to his state of knowing. If, on the other hand, he comes to disbelieve that there are dragons, his thought of flame-breathing also enters into a new relation to his state of knowing, but this relation is in opposition to the one previously mentioned. Suppose that, at the end of his reflexions, he believes that there are air-breathing serpents, disbelieves that there are dragons, and is doubtful whether there are water-breathing serpents. Then his thought of air-breathing has come to stand in the first mentioned relation to the noetic framework, his thought of flame-breathing has come to stand in the second and opposed relation to this framework, and his thought of water-breathing has not changed its relation to the framework.

      There is one other point which must be mentioned if my general account of judgment is to avoid the accusation of absurdly over-simplifying the facts. Suppose I have a certain visual experience and make the judgment which would be expressed by the sentence: "That is a solid object". I might be mistaken in any of the following ways.

1. It might not be solid but hollow, though it really is voluminous.
2. It might not be voluminous but a cunningly painted and shaded flat expanse, though it really is a physical object.
3. The visual sensum with which I am acquainted might be hallucinatory, and not the appearance of an external physical object at all.

      At the back of "taking something for granted" there is always a knowing of some fact, though exactly how far back this knowing is, and exactly what is the fact known in any particular case, is a matter of controversy. Suppose, for example, that we accepted Prof. Stout's doctrine that, whenever I sense a sensum, I ipso facto know that it is a manifestation of something somewhere in the physical world. Then my knowing this fact would be at the back of my taking for granted that I am in the presence of an external voluminous physical object. I ignore the possibility that the sensum might be a manifestation of a centrally excited process in my own body. I ignore the possibility that it might be a manifestation of a flat diagram drawn in perspective and suitably shaded. The first stage at which I begin to consider alternative possibilities is in recognizing the fact that what is voluminous may be either solid or hollow, and in recognizing that I do not know whieh of these alternatives is fulfilled in this particular case.

      Now, supposing that something like the analysis of judgment which I have been describing were true, the last challenge of supporters of the Proposition Theory could be met. In judgment, whether true or false, there really is a unique kind of complex object before the mind. But it is a fact, and not a proposition; it is known, and not believed; and, in judging, there are always other terms before my mind. A judgment is made at a given moment if and only if my thinking of a certain term then becomes related to my knowing certain facts by the kind of relation which I have tried to describe.

      2.23. The Correspondence Theory. It only remains to make a few comments on McTaggart's statements about the Correspondence Theory. (i) McTaggart assumes that those who accept propositions do so because they want something for judgments to correspond to, and because they think that nothing but propositions would answer this purpose. His reply is that, on any form of the Correspondence Theory, there must be correspondence with facts; and that, given judgments and facts, all the requirements of the Correspondence Theory can be met without assuming that there are propositions.

      This whole argument seems to me to rest on a complete misunderstanding of the nature and motives of the Proposition Theory. Propositions were not supposed to be needed in order to correspond to judgments, in the sense in which the Correspondence Theory talks of "correspondence". They were supposed to be needed as the objective constituents of judgments, and as the common objective constituents of sets of co-referential judgments. A supporter of the Proposition Theory who also accepted the Correspondenee Theory would say that a proposition is the objective constituent of a belief, that the belief is true or false according as the proposition believed is true or false, and that the proposition is true or false according as it corresponds or fails to correspond to the fact to which it refers. Thus the argument in §8 and §14 is beside the mark.

      (ii) I am not altogether satisfied with McTaggart's account of correspondence. His doctrine is that, when a belief is true, there is one and only one fact which corresponds to it, and, when a belief is false, there is no fact which corresponds to it. This is eked out by the doctrine, which we have seen to be barely intelligible and certainly false, that every belief "professes" to correspond to a fact.

      This seems to me to be unsatisfactory in two respects.

1. Judgments include disbeliefs as well as beliefs, and so a complete account of correspondence ought to deal with both.
2. Whilst it is no doubt true that a false belief corresponds to no fact, this is not the essential point. The essential point is surely its positive discordance with a certain one fact; its lack of correspondence to all other facts is trivial. The falsity of the belief that Charles I died in his bed does not depend in any way on its lack of correspondence to the fact that Mr Gladstone reduced the income-tax, but on its positive discordance with the determinate fact that Charles I died on the scaffold.

      I would prefer to deal with the matter as follows. Every judgment refers to a certain fact, and it is true if it concords with this fact and false if it discords with it. Suppose I believe that the other side of a certain bit of paper is blue. The fact to which this judgment refers is the (to me unknown) determinate fact about the colour of the other side of this bit of paper. Suppose that it is in fact blue. Then my belief concords with the fact to which it refers and is therefore true. Suppose that it is in fact red. Then my belief discords with the fact to which it refers, and is therefore false. Now consider disbeliefs. Suppose I disbelieve that the other side of this bit of paper is blue. The fact referred to is still the same. If the other side of the paper is in fact blue, my disbelief discords with the fact to which it refers, and is therefore false. If the other side of the paper is in fact red, my disbelief concords with the fact to which it refers, and is therefore true.

      If we generalise this example the result is as follows. The fact to which a judgment refers is the unknown determinate specification of that relatively indeterminate fact which the maker of the judgment already knows and is trying to specify further. When the judgment is a belief, it will concord with the fact to which it refers if and only if the thought which is inserted into the noetic framework of the judgment is the thought of that determinate which occurs in the fact referred to. When the judgment is a disbelief, it will concord with the fact to which it refers if and only if the thought which is extruded from the noetic framework of the judgment is the thought of a different determinate from that which occurs in the fact referred to. A judgment neither concords nor discords with any fact except the fact to which it refers; but it must either concord or discord with that fact, and it cannot do both. This seems to me, on the whole, the most satisfactory way of stating the Correspondence Theory.