And we have in addition an argument from usage. A necessary judgment, a statement introduced with " It must be so," may assert what not only fails to be actual but is plainly impossible. " If two were three then four must be six " pre sents us with a truth which is compulsory. The result must follow; it is necessary truth; but it does not follow in actual existence, and could not follow there, since both antecedent and consequence, and their actual junction, are impossibilities. It is not true that apodeiktic modality strengthens our asser tions. It serves rather to weaken them.. If S is P, there is an end of doubt. If S must be P, we know indeed that, 2O2 THE PRINCIPLES OF LOGIC BOOK I given something else, we can be sure of S — P, but we are certain of no more. The apodeiktic mode either leaves our doubts, or removes them only by the covert assertion of the condition of S — P. Where the necessary asserts strongly it borrows its strength from a concealed assertorical. I will conclude this section in Sigwart's words. " There is a common idea that the apodeiktic judgment stands for something higher than the assertorical. It is believed that, if we start from the problematic judgment and ascend to the apodeiktic, we steadily increase the certainty of our knowledge, and add to the worth and dignity of our assertions. This idea must be relinquished. All mediate certainty must stand in the end on immediate knowledge: the ultimate premises of every proof can not be proved. The usages of life stand in comic discrepancy with the emphasis we lay upon apodeiktic certainty. The sayings 1 It must be so/ ' It must have so happened,' are judgments apodeiktic: but the confidence they express has most modest limits." (Logik, I. 195.)
§ 12. (c) A necessary truth is a truth which results from assumed conditions.10 If we imply, as we very commonly do, that those conditions are actual, then the result is categorical. But, though the necessary may be real, its necessity is hypo thetical. What have we now to say about possibility? When S — P is possible, does that mean that S — P would exist as fact, if something else were fact? Is possibility in short a form of hypothetical necessity?
It sounds strange when we hear that the possible falls under the head of the necessary. But it is at least as surpris ing to learn that the necessary may be impossible or non existent; and this we already know to "be the case. On such subjects as these our first impressions may be worth very little.
The possible is that which is known or assumed to be the consequence of certain conditions. So far the possible is one with the necessary, where it is implied that the antecedent is real. But it differs in this point; for S — P to be possible all the conditions which make S — P necessary must be sup posed, but only a part of them need be assumed to exist. It is implied that a part of the antecedent exists, but as to the other part we are left in ignorance. Thus the partial existence of the conditions of S — P is the differentia which separates CHAP. VII THE MODALITY OF JUDGMENTS 203 the species " possible " from the genus " necessary." Take a judgment such as this, Given abed then E must follow. Add to it the judgment, or the supposition (§ 15), that ab exists, while cd is not known to exist, and we get the possible. E is now a possibility. We have an assumed fact ab, we also have ideal conditions c and d, assumed to be compatible with ofc/1 but not taken to exist. We have a hypothetical judgment, Given abed, we should have E. And from this, by the as sumption that ab exists, we pass to " We may in fact have E." In other words, ab is the " real possibility " of the possible E. It is known to be real, or at least is treated as if it were so § 13. Everything possible must be really possible. It must stand on a reality assumed to exist, and taken as part of that sum of conditions which would make S — P an actual fact. Possibility apart from or antecedent to the real world is utter nonsense.
But the basis of fact may vary indefinitely. S — P is possible in the highest sense when the detailed conditions which make it necessary are fully known, and a part of these detailed conditions is also taken to exist.12 This highest sense sinks by slow degrees to the lowest of all, where " possible " stands for "not known to be impossible." Here we do not know what special conditions give S — P. Our basis of fact is nothing but the assumption that the nature of the world admits S — P.13 Because reality does not in our knowledge exclude S — P, we take reality as one existing condition of S — P, and we assume not only that the rest may be found, but also that they are compatible with reality. In this lowest and barest sense of possibility it is really wrong to call S — P possible. It is better to say, We do not know that S — P is impossible.* Between these extremes come many degrees. In the hypo thetical judgment about S — P we may not know the special conditions of S — P, but we may know a smaller or greater amount of them, and, where we are ignorant, we may have more or less reason to make an assumption. And in respect to the partial existence of these conditions, our knowledge admits *We rest our assertion on a privative judgment. Cf. Chap. IIL 2O4 THE PRINCIPLES OF LOGIC BOOK I of many stages, and we make assumptions with grounds that may vary almost indefinitely. We should gain nothing here by dwelling on these varieties, and prefer to give some simple illustrations.
§ 14. Are disembodied spirits possible? Let us agree to take the most unfavourable view for the sake of argument. We have no direct experience of the existence of such spirits, and the question is whether we can call them possible. We know no conditions which would give the result. We have no reason to think such imagined conditions compatible with the real nature of things.14 On the other hand we can not reject the idea as impossible, since we have no right to affirm " It is incompatible with the nature of things." We should content ourselves with saying, " Your proposed assertion is not cer tainly false, but there is no ground for thinking it true. Our ignorance is forced to admit a * bare possibility/ but it gives not the very smallest reason for entertaining that idea as real. And such bare possibilities, we have seen, are none; they are * idle frivolities, that have no place in the minds of reason able men/ " The case we have given is, as we have given it, an ex ample of the lowest sense of " possible." Let us go a step higher. " It is possible that some of the planets are inhabited." We have here the hypothetical judgment that under certain conditions life would result; and to some extent we know these conditions, while we supplement our ignorance by assumptions for which we have reasonable ground. These special condi tions again are in various planets known to exist in part and in different amounts. Our judgment that this or that planet may be tenanted thus varies through different degrees of possibility, according to the amount of this partial existence.
But now take the assertion " That coin may have given head." Here we know, on the one hand, special conditions which must exhibit head, and we know on the other hand that part of these conditions really exists. This is possibility in its highest form.
§ 15. We have noticed that possibility may stand not on fact but on supposition. If a coin had three sides, then it would be possible that neither head nor tail should be upper most. There is here no vital change in the meaning of CHAP. VII THE MODALITY OF JUDGMENTS 2O5 " possible." For the real basis is supposed to exist, and the possible is subject to the supposition. But we should not here say that S — P is possible; we can not strictly go beyond " It would be possible." It is possible, if by a fiction of thought you treat the unreal as if it were real, or the unknown as if it were known. We must distinguish such hypothetical from actual possibility. For, just as we more commonly imply that the necessary exists, so we imply and must ordinarily even be taken to assume that the ground of the possible is actual fact and not merely supposed.15 § 1 6. We have now discussed the meanings of " possible " and " necessary," so far as to see that both are forms of the hypothetical. And with this conclusion we have anticipated the result of our second enquiry, Does logical modality exist in fact?16 (ii) We saw long ago that hypothetical judgments, as such, are not true in rerum natura. Neither the subject, nor the predicate, nor again the connection, need exist in fact. What is true of fact is the quality that forms the base of that con nection. The junction itself may be non-existent and even impossible. We shall verify this result in the possible and the necessary.
§ 17. (a) We have seen that what must be is never neces sary save on the hypothesis of some condition. We have seen that this antecedent, and the consequence which follows, may claim no existence and may have no possibility.17 The neces sity in these cases, if we mean the necessary connection of the elements, does not exist outside our ideas; it is not true of fact.
And again, when the antecedent and with it the conse quence have actual existence, and appear in a relation which is clearly the counterpart of logical necessity, the same result holds. We saw that the difference between the cause of knowledge and the cause of existence staggers our assump tions. And even when the two seem to us to coincide, how can we assume that they are ever identical? It is a great thing to say that what is true in thought must hold in fact. But it is something more to maintain that thinking and existence appear as two sides of a single reality, and to insist that every logical process must be found in fact, and that all real con- 2C>6 THE PRINCIPLES OF LOGIC BOOK I nection is, if we could see it, a logical process. We shall recur to these questions in a later Book. For the present we may repeat that, if such a doctrine is tenable in metaphysics, it can not be supported in a logical treatise. The objections it calls forth, if they could be disposed of, could be disposed of only by a complete revolution of our current doctrine as to mind and things.18 For logic the necessary must remain the hypothetical. Facts for logic must be facts that are and that never must be. The real connection which seems the counterpart of our logical sequence, is in itself not necessary. It is necessary for us, when in ideal experiment we retrace the process of actual fact. But, at least in logic, we must not assume that our ideal rela tion is the bond of existence. The ideal compulsion of logical necessity is as strong where the premises are known to be false, and the antecedent can not be believed to exist, as where we start from categorical truths and pass from them to a cate gorical conclusion. If in both these cases there is logical necessity, how can we ever be safe in assuming that such necessity is found in existence?
§ 1 8. (b) And when we pass from the necessary to the possible, our conclusion remains. The possible, as such, exists nowhere at all but in the heads of men.19 The real is not possible unless for a moment you think of it as unreal. When the possible becomes real it ceases at once to be a mere possi bility. For metaphysics I will not deny that the possible might bear another meaning. But for logic, wherever a fact appears, a possibility vanishes. It is not merely that the possible is confined within the limits of human thinking. It can not exist outside the domain of human doubt and human ignorance.
We have seen that to say " S — P is possible," means, " S — P would follow under certain conditions, some at least of which are not known to be present." And at this stage of our enquiry, we may say at once that the sequel of such a hypothetical judgment can not be taken to have actual exist ence. The antecedent is not fact, the connection is not fact, and the consequence is not fact. Or, if they are fact, their " factual " character must be either unknown or put out of our minds, when we treat them as possible. If we knew the reality we should make no supposals; or, if we made them, CHAP. VII THE MODALITY OF JUDGMENTS 2O?
we should know that they were made and, as such, did not exist.
§ 19. Common usage enforces our conclusion. The accused obviously is guilty or is not guilty (Sigwart, 228). But we say " It is possible he may be either." That is grossly false, if you take it as asserting about the fact. A fact is not and can not be an alternative. The possible existence of both guilt and innocence is relative to our knowledge; it exists only in our heads, and outside them has no meaning. A ship has sailed from Liverpool for America, and we say " It may have arrived in New York, or again it may be at the bottom of the sea." If you make this statement of the actual fact, it can not be true. It is not possible that a ship should be in two places at once. It must actually be somewhere; and, being actually there, it is not possibly elsewhere, nor even possibly where it is. The possibility is nothing beyond a supposition founded on our real or hypothetical ignorance. Outside that ignorance and that supposition it is not anything at all.
§ 20.20 We have now shown in the first place that " necessary " and " possible " are both hypothetical. We have seen in the second place that, at least for logic, they do not exist, as such, in the world of fact. It remains to show that, although " subjective," they must rest on a basis of categorical assertion about reality.
(iii) We have only to recall the doctrine we reached in our Second Chapter, to perceive at once the truth of this con clusion. We saw there that all judgment in the end was categorical. The basis of the hypothetical must be fact, and without that basis the judgment would be false.
(a) We need give ourselves no pains to verify this result in the case of necessity. We have seen that " S — P is a necessary truth" means "S — P follows from something else." This something else need not be fact, and, where it is fact, that can not be assumed to make any difference to the ideal connection. We can not say " In fact S — P really is a necessary consequence as such." But, the connection being hypothetical, it on the other hand demands a basis which is categorical. All necessity affirms a real ground explicit or implicit. It thus so far has actual existence, not in itself, but indirectly and simply in its ground (Chap. II.).
2O8 THE PRINCIPLES OF LOGIC BOOK I §21. When we come (b) to the possible, we are tempted to think it has less actuality than belongs to the necessary,21 since a part of its conditions remains unspecified. But, un less we imply that the antecedent of the necessary exists in fact, such a comparison would be illusory. In neither case can we assume that antecedent or consequent exists; and when we pass from what must be to what only may be, the ground of the judgment seems in either case to be equally real.
In the merest hypothetical possibility we have an assertion about actual fact. We affirm the necessity of S — P following from abed, conditions a part of which is supposed. And in this we attribute the base of that connection to ultimate reality. But in an ordinary assertion of possibility we imply the exist ence of a part of abed, and thus make another statement about fact. What we do in a case of so-called bare possibility again is this. We first, on the strength of a privative judgment22 (§ 13), conclude that the conditions are compatible with reality. We then get the existence of a part of these unspeci fied conditions by taking the real (because it is compatible) as a joint condition. Thus reality, taken in some unknown character and passing into the conditions, gives partial exist ence unknown to the antecedent; while the same reality, in another character, then guarantees the hypothetical sequence of S — P. We thus in the end (whatever we may think of them) have two categorical assertions.
In " A disembodied spirit is possible " we start by denying that it is impossible. This judgment rests, first, on the as sumption that the real has an actual unknown quality, which, in the second place, if you take it together with other unspeci fied conditions, makes a hypothetical antecedent from which " disembodied spirit " follows as a consequence. As the ground of this second judgment we have to attribute another unknown quality to the real to serve as the basis of the hypo thetical connection. We have thus two assertions about the nature of things.
§ 22. Let us now take an instance of rational possibility. If we say " It is possible A holds the ace of trumps," we know there are conditions which would give this result. Such or such an arrangement of the pack, such or such adjustments of the muscles in the person who cuts and the person who deals, CHAP. VII THE MODALITY OF JUDGMENTS 2OO, must give the ace to A. The ground of this judgment consists in mechanical and other laws, in accordance with which the result would follow. These laws we regard as qualities of the real, and this is one of our assertions. We next affirm that an event has happened, viz. the dealing of the pack, which presents in fact a certain part of our antecedent; in other words, which gives reality to our supposed conditions to a certain point and within a limit. The antecedent is not actual in that full and especial form which gives the ace to A, but it is there in that outlined and partial character which gives the ace to some one player.
Everywhere, where we say that S — P is possible, we assert a real possibility of S — P. We must assume a fact which actually is, though it is not S — P. And we assume that this fact would under some conditions give us S — P. That is, we categorically assert the ground of an hypothetical judg ment; and again we categorically assert the existence of a fact which forms part of the antecedent. These two positive assertions can everywhere be found in the most guarded state ment about an actual possibility; and the former is required for mere hypothetical possibility.
We have now accomplished the third task we set before us. We have shown that the necessary as well as the possible has a basis in fact and depends upon experience. A modal judg ment has to make an assertion about reality. But the judg ment itself expresses a truth which is not a fact. Modality is but hypothetical, and hypothetical connections exist only in our thoughts.
§ 23. There are various points in connection with the sub ject which claim our attention. We are accustomed to hear of " capacities " and " faculties," and to use such phrases as "potential energy," with but little regard for their actual meaning. The "potential" is regarded as something real, stored up outside existence, which hereafter may emerge in the world of fact. This deplorable piece of effete metaphysics takes a leading place in popular versions of the truths^ of physics. Potential energy of course as such has no real exist ence. It is merely the consequence in a hypothetical judgment where the conditions are not all taken as actual. It would-be better to say, " Though there is no energy, there is something 210 THE PRINCIPLES OF LOGIC BOOK I actual which exists as the real possibility of energy." But even this correction leaves a residue of error.
In strictness of speech a real possibility of S — P can not exist as such.23 It should mean that reality which, if you place it in an ideal construction, developes S — P as a conse quence. Itself is fact, and the attribute at the base of the hypothetical judgment again is fact: but that judgment with its elements can not be taken as fact. We are met by this dilemma. Apart from the judgment the real is mere fact and has no potentiality; but within the judgment the reality itself has ceased to be real. It has taken its place in a mental con struction. Unless you are prepared to make ideal elements determining forces in the processes of nature, you can not properly believe in real possibilities. And I think, upon any metaphysical theory, it would be better to find some other expression.
§ 24. But I shall hear: " Conditions are surely real.24 Before life began its conditions could be present. And the real possibility being a condition, as such you must allow it to exist." In the above I see nothing but the same mistake. A condition as such can not be said to exist. A condition is an element in a hypothetical judgment and, outside that judgment, it is no condition. If you say, " A exists and is an actual condition of B," you are speaking inaccurately. What real bond corresponds to your phrase? B is not in existence, and if the other conditions do not appear, it will not exist. And yet you say, " A is one of its conditions." If you wish to be accurate you should say, " A is something which, if taken from existence and placed within an ideal construction, mentally gives rise to B." All beyond is unwarranted.
A condition ex vi termini does not as such exist; and to define the cause as " the sum of the conditions " is to commit a serious metaphysical mistake. It is saying, " The reality which gives rise to reality is made up by adding mere ideas together." * But the cause must be fact, and its effect must * Of course the word sum again is open to criticism. It implies a theory of the union of the elements, which certainly can not be taken for granted. But to clear up this point a long digression would be wanted. There are some remarks on causation in Book III. II. Chap. II.
CHAP. VII THE MODALITY OF JUDGMENTS 211 be fact. We should do better to call the cause the meeting of elements which, in the moment of their union, begin a process which issues in the change we call the effect. An actual union of actual elements is the cause. Each element by itself and apart from this union is not even a condition. It becomes a condition when you place it ideally in union with others. But, in order to do that, you must make it an idea. In its character of condition it must so far cease to be fact.
I am far from suggesting that the want of accuracy I have just been noticing is always error. The phrases " potential " and " condition " and " possibility " may be harmless and useful. We ought all to be able to employ them safely. But I fear that too often the case is otherwise. Too often they prove mere engines of illusion, drowsy sops thrown down to make reason slumber. If we believe in something that neither is nor is not, but rules some strange middle-space between existence and nothingness, let us at least have courage to profess our opinion. Do not let us use words in using which we take refuge from doubt in blind ambiguity.
§25. It was blind ambiguity and little beside that lay at the root of a controversy we remember. Amongst those who vexed themselves and others with disputes on the " Perma nent Possibilities of Sensation,"25 how many adopted the obvious course of asking what lay hid in this spell? We know now that a real possibility means something which, in itself and in fact, is no possibility, but must be something actual. It is a veritable fact which actually exists; and to this we must add here the idea of permanence. I suppose this means that our actual fact has, against something else, at least a relative duration and freedom from change. But now what is this real or, I should say, these reals, which do not change, and which an attribute of the reality guarantees to produce the consequence of sensation, so soon, that is, as you have trans formed them into ideas, and placed them within ideal con structions? Are they real things, as distinct from sensations, or, if not, what are they? I do not say that the asking this question is enough to explode the theory of J. S. Mill. I will say that the answer to it, however it is answered, must alter at least the statement of that theory, and change at least some of the points in dispute.
212 THE PRINCIPLES OF LOGIC BOOK I I must be pardoned for seeing in another use of this delu sive phrase an ambiguity which threatens the conclusion. If there are difficulties in the way of making pleasure, in the sense of atomic and momentary feelings, the end of life, can we be said to escape them if we say Happiness is the end, and if Happiness is defined as a permanent possibility of pleasant feeling? We are met by the objection, If the end is pleasure then it surely must lie in actual pleasure. But if it lies in actual pleasure, it can hardly lie in mere possible pleasure. Either the end is pleasure present and actual, such pleasure again as has a quality (itself also pleasure) which guarantees a hypothetical result of ideal pleasure, and this present pleasure is also permanent — either this, I say, or Hedonism is given up, for something not pleasure is made the end. Here again I must venture to make the remark that the answer to the objec tion must modify at least the statement of the doctrine.26 § 26. We may turn from these criticisms to a positive result laid down by Sigwart (182, 227), and which our dis cussion of possibility should have served to make clear. The particular judgment, in the end and really, we found to be nothing but a hypothetical in which the conditions remained imperfect (Chap. II.). In the problematic form of judgment we once again encounter the particular. The one is the other under a disguise which disappears before our scrutiny. The particular judgment " Some S is P " is the same as the judg ment " S may be P." The assertion that S does actually exist is not contained in the particular judgment,27 any more than it is in the problematic. " Some S is P " asserts no more than that, S being given in ideal connection with other conditions, of which conditions some part is assumed or supposed to be actual, then P will follow. And this is precisely the sense of " S may be P." Both are imperfect hypothetical judgments, and both are founded on a basis of fact believed in or sup § 27. Reality in itself is neither necessary, nor possible, nor again impossible. These predicates (we must suppose in logic) are not found as such outside our reflection.28 And to a knowledge and reflection that had command of the facts nothing ever would be possible. The real would seem neces sary, the unreal would seem impossible.
CHAP. VII THE MODALITY OF JUDGMENTS 213 The impossible is that which must be unreal.29 We might call it, if we chose, one kind of the necessary. When we say of S — P that it can not exist, we do not merely mean that in ideal experiment the suggestion of S — P directly vanishes. We suppose for a moment that S — P is real. Then on that hypothesis we see that the conditions from which alone S — P would follow are directly or indirectly incompatible with the real. The real, if changed in ideal construction so as to afford the conditions of S — P, is changed in such a way as to cease to be itself. The alteration removes some attribute that we assign to the real; and this attribute, in our reflection, by means of its exclusion of other possibilities, thus generates the im possible and becomes the necessary.
Impossibility and necessity are correlative ideas. They emerge together. The real does not seem necessary until it has excluded what is incompatible, and reasserted the attribute which is the ground of the exclusion.30 Because of this attri bute nothing else can be, and the attribute must be because nothing else is. The unreal again is not impossible until we have seen, not merely that it fails, but that its supposed success would destroy what is, and what must be because its opposite is excluded.
§ 28. These ideas suggest a number of difficulties. In a later book we must return to one of them, and may content ourselves here with a brief indication. The impossible we see must always imply a positive quality, known or assumed to belong to the real. If X is impossible, this means and must mean that an actual X would remove by its presence some positive attribute we take to be real.
This bears on a point which already has engaged us (§§ 13, 21). The possible may be taken as anything whatever which is not real nor yet impossible.31 We objected to this process, as frivolous in its result and insecure in its method. The method is insecure, since it passes from the absence of known incompatibility to the assumption of compatibility. We take X to be compatible, if the real, as we know it, will pass unabridged into a set of conditions which give X as a consequence. Again, so far as we know, X is not incompatible, when the suggestion of X as an attribute of the real calls forth no answer affirmative or negative. And the doctrine 214 THE PRINCIPLES OF LOGIC BOOK I we object to passes direct from want of incompatibility to compatibility. In the one case X is possible, since it follows from conditions a part of which is supplied by the real. But in the other case we can say nothing about reality, unless we make an enormous assumption.
§ 29. We offer our suggested X to the real, and the real is passive: X is not excluded. This privative judgment, if we wish to understand it, must be reduced to an ordinary negative where a positive quality in the subject rejects. What is the positive quality here? It is the mental presence of the real with such and such attributes. Now even the smallest addition to these present attributes is an alteration of the real, as we have it in our minds, against which it asserts itself in the character it bears at the actual moment. In other words, the base of our assertion that X is not rejected by the real, is the assumption that the real differs in no point from the real as at this moment it is present.