Jacques Maritain Center : The First Principles of Knowledge

Chapter IV.
Kinds and Degrees of Certitudes


  1. Preliminary remarks about the assent and the motive of judgment.
  2. Species of Certitude. (a) Metaphysical. (b) Physical. (c) Moral.
  3. Degrees of Certitude. Proofs of their existence: (a) From the side of objective truths varying in kind. (b) From the experienced facts of compulsory, of easy, and of laborious assents. (c) From the side of the subjective force of intellect, varying in different men.


BEFORE satisfactory advance can be made towards the next points of discussion, a few further remarks on the nature of judgment are quite indispensable.

It is a controversy amongst the scholastics, {1} which, as Cardinal Zigliara thinks, may, perhaps, be reduced, in the end, to a difference of words,{2} whether the assent in a judgment is completed in the clear perception of the relation between subject and predicate, or whether it is not rather another act, a sort of intellectual nod, following upon the perceived connexion of terms. One side says that the act of judging is itself a compound act, a compounding of predicate with subject; the other side says it is a simple act, a simple affirmation or negation, following upon the comparison of the terms. The former party are careful to insist that there really is affirmation and negation, and they would not be content with any mere linking together or fusion of ideas, or any comparison, short of what is required by the meaning, of the copula "is," or "is not." But, this asserted, they hold that no element of the judgment can be shown to be lacking when, in comparing the terms, the mind perceives, with or without additional light from outside the terms, the connexion between the two. In the following pages no distinct superadded act of assent will be supposed, on the ground that no argument in support of it seems convincing. If a man likes to confirm any of his judgments with a "Yes, that's it," the added act of approval is a new judgment, the result of reflexion on the previous one.

Taking, then, the assent -- at least the legitimate assent -- to be the perceived connexion between subject and predicate, we are able to reject a fallacious procedure which we must briefly describe. Those authors who make the assent a distinct act, following on the perceived connexion of the terms, occasionally manage to play some strange tricks in their account of a judgment, so that they can pronounce those propositions to be possibly doubtful which are generally reckoned indubitable. Thus Descartes, in behalf of his claim to be able to doubt certain mathematical truths, which seem indubitable, asserts, in explanation, his power to look away from the meaning or from the grounds of the proposition. He admits that while he considers the meaning of the terms he cannot doubt; but he contends that he can doubt as soon as be ceases to consider this meaning; and it is on this most flimsy pretext that he declares these truths to form possible objects of doubt: "I have sufficiently explained, on several occasions, how this is to be understood. As long as the mind is attending to some truth of which we have clear conception, it is impossible for us to call it into question."{3}

It must be confessed that this passage, by suggesting the case of wilful, precipitate, and irrationally formed judgments, suggests also a most obvious argument in favour of judgment being a sort of simple nod of the mind, and not being intrinsically constituted by a perceived connexion between terms. The difficulty thus raised must stand over till we come to treat of the nature of error: and meantime it must suffice to say, that a solution is coming, and, further, that all error is sub specie veri; that it is because of some really perceived truth that the mind is able to assent at all; and that if the mind is carried on to add untruth to truth, or falsely to detract from truth, these are not strictly intellectual acts, but effects of obscurity in ideas, of the will, and of the force of association and habit. All which declarations must be expanded afterwards: at present it is enough to plead, that an assent worth the name cannot be wholly a sort of blind nod. In words anything may be said; but an assent not inwardly lit up with some intellectual motives is not strictly an intellectual act, for it is devoid of all insight. In a mixed act, the assent ceases to be intellectual at the point where insight ceases.

Let the word "motive" be clearly understood. The passage from ignorance to knowledge is a movement: therefore a motive power is required, one of the same order as the mind itself, an intelligible motive for an intelligent act. So far as any assent is not thus motived it is not properly an act of intellect. It is quite true that the intellectual faculty itself is a power to move, and the term motive might be used on the subjective side; but it is here regarded on its objective side, as an object soliciting the faculty, not as a faculty answering to the solicitation. In the proposition "A straight line is the shortest way between two points," the motive for the assent is intrinsic to the terms assented to -- it is their own immediate evidence; in the proposition "A pistol-shot killed two recent presidents of the United States," the motive of belief is, with most of us, historic evidence, while with no one is it the intrinsic force of the two terms. In the one case, subject and predicate both terminate and motive the assent: in the other they terminate it, but do not motive. Many assents, the original motives of which are all, or most of them, forgotten, find still an adequate motive in the clear recollection that they have been validly established: at any rate, motive of some sort they must have present, under pain of being irrational.

1.The way is now clear for treating of the different kinds or species of certitude. In the terminology of Aristotelian logic, the species is what constitutes the essence of a thing: but certitude, in one respect, is not an essence, but only an accident of the mind. Essence, however, is an accommodating word, and allows of being varied in meaning according to the variability of ends in view; the same difference becomes essential or non-essential, specific or non-specific, with the change of purpose. A round biscuit, and a square biscuit, both of the same material, differ specifically for the mathematician, non-specifically for the child who eats them. In general, according to the usage of human speech, that difference in any order is to be regarded as specific, which, in relation to that order, goes to the very essence or nature of the thing. If we want a red object to excite a bull, then the colour, not the material, is the specific character: if we want a woollen garment, then the material, not the colour, is specific.

This being so, we observe that the essential character of certitude, that which radically distinguishes it from other states of mind, such as suspicion or opinion, that which gives it its lower generic place under the higher genus of intellectual assents, is the firmness of the assent. In other cases we either withhold assent, or give it only with reserve; but in certitude we are without any doubt. In the firmness of the assent, therefore, if anywhere, specific differences of certitude are to be found; for special differences here will be difference within the essential constituents. In establishing three such differences we shall be disregarding one pet modern theory about the non-necessary character of all truth; but it will be better to go on our way in disregard of adversaries for the present, and to come back again, in the next chapter, to see what objectors have got to urge.

(a) The highest motive of certitude, giving the highest species of assent, is metaphysical; which implies a necessity so absolute as to be bound up with the immutable nature of God Himself. In this sense we may adopt, or rather adapt, the heathen saying, anagkê d' oude theoi machontai; God cannot fight against the necessities of His own all-perfect Nature, and their inevitable consequences in regard to the possibilities of creation. But we must avoid the pagan error of looking upon this necessity as something extrinsic to God, a fate or destiny having an independent existence. The prime metaphysical necessities are that God should exist as the one absolutely necessary Being; that He should be just what He is, and that from the nature of this First Being should follow the laws regulating the possibilities of all that can be created, and of all finite truths. This is the matter of a whole section in the scholastic treatise on General Metaphysics. Here it must suffice to give a few specimens of truths metaphysically necessary; to which the ordinary mind, unbiased by philosophic theory, will feel no difficulty in allowing a most absolute, irreversible character. "God cannot lie;" "Moral right is sacred;" "Nothing can at once, under the same aspect, be and not be;" "Every new reality or event must have a cause;" "Two straight lines cannot enclose a space." These examples at least give a clue to what is meant by the species of truth called metaphysical.

(b)Strongly contrasted with absolute necessity is physical necessity, which we call contingency. The physical (phusein) is what comes into being, what has an origin and a growth, what is produced or made; and so it differs from the metaphysical, which simply and eternally is. Hence the term physical, as here understood, does not apply to the order of mere possibilities.{4} The physical is the actually created order of real existence, which existence is contingent, and might never have been. As a fact, out of the various worlds which in His Omnipotence God might have created, He has created the existent universe; whereas He might have created another, or might have abstained from creating altogether. Even the present system is not so rigorously settled that He cannot miraculously interfere with the ordinary sequence of effects. Thus the physical necessity, to which we have to bow, is not a priori and immutable, but a posteriori and mutable by Divine power. It is, however, a priori to this extent, that all its possibilities were fixed a priori, and to an intellect able to look into the very constitution of bodies, all their powers would presumably be thence deducible; while from the primitive collocation of world-elements, all subsequent phenomena, apart from what is due to the interference of free will, might be calculated. We, however, who can neither adequately penetrate the inmost nature of matter, nor quite solve even the comparitively simple problem of three attracting bodies, have to proceed on a humbler method: so for us physical truths are a posteriori, and are ultimate facts, which we take on the evidence of experience, without being able to give their final account. All our physical explanations end in mere empirical facts.

(c)The third kind of motive for certitude need not detain us long; for we shall have to give a separate consideration to historic evidence, and then the nature of moral truth, as it is styled, will appear in a fuller light. We have, in this matter, the difficult problem to find a sort of necessity, in spite of free will being mixed up with the elements of our calculation. We shall have to claim, that occasionally we can know how people have used, or will use, their power to choose under given circumstances. Thus moral truth, in the sense at present given to it, is truth about human action, which in many details is free, though it has not a freedom unbounded. The theoretic difficulties against the possibility of ever calculating human conduct on the hypothesis of a real liberty of choice, vanish at once before a concrete case; it is a sheer impossibility that historians should be deceiving us, when they narrate certain substantial events in the lives of Alexander the Great, Julius Caesar, and Charlemagne. Again, there are cases where we may be certain, that a very well tried character will not prove treacherous under moderate temptation and enormous responsibility. These instances convey sufficiently what is to be understood by the third species of certitude, which is here styled moral.

It must be added, however, that the same phrase, "moral certitude," which is here used for strict certitude, is employed also in a looser way to mean high probability, such as would be enough to determine the action of an ordinarily prudent man. It is moral inasmuch as it suffices for a moral agent. Thus a merchant would make a great venture on "a moral certitude," which meant the probability of a thousand to one, yet did not quite leave the level of probability, and mount into that of strict certitude.

While it belongs to philosophy to draw, in general, the distinction between the three species of certitude, it would be preposterous to ask it to settle, in all concrete cases, whether we can have certitude, and if so, of what kind. Not all the departments of science together can discharge this function: but each department is left by philosophy to do what it can in its own sphere, while philosophy itself investigates certitude in its highest generality. Should any one try to illustrate its doctrines by examples confessedly dubious in their own scientific order, it simply begs the person to choose a more suitable illustration; it does not undertake to meddle out of its own province, and it borrows, to exemplify its teaching, only safe instances.

2. Next to difference of kind in certitude may be taken difference of degree. It is maintained by some that from its very nature certitude admits of no degrees, of no less and more; that if a man is sure, he is sure, and that is all about it; so that to talk of assurance being made doubly sure is a mere façon de parler. We are not concerned to maintain that under no acceptation of the word "assent" is it possible to deny the existence of degrees in it; but if we take "assent" in its wider and more ordinary meaning, the certitude of our assent does admit of degrees, in the sense we are about to explain in the following paragraph.

Every certitude must absolutely exclude all solid doubt, which exclusion of doubt is the negative side of certitude and, of its own nature, allows of no degrees; but the positive side, or the positive assent itself, is of a nature to admit degrees. Certitude, then, on its negative side has not, on its positive it has, degrees. The two sides are only distinguishable aspects, not separable elements; by one act, we are sure and do not doubt. Before this doctrine can appear quite satisfactory, it needs a little elaboration. For against it, in its cruder form, must be urged the fact, that the same motives which produce assent also drive out doubt; and that, therefore, doubt is expelled with a force varying with the expelling motives, all of which are alike in that they annihilate doubt, but differ in that some effect the annihilation with greater energy. So of two men who agree in the fact of being no longer in a certain assembly room, one may have been quietly lifted into the adjoining street, and another shot with a catapult into a street some distance away. Thus, it is argued, even the negative side of certitude, the expulsion of all doubt, may differ in degree.

To answer the objection we must limit the meaning of expelled doubt. We must take the absence of doubt purely on its negative side, or on its side of nonentity; then nonentity, as such, is unsusceptible of less and more. Of course mathematicians, with whom, however, positive and negative often mean no more than one direction and its opposite, extend negative quantities as far backward as positive quantities go forward: to the plus series 1, 2, 3, 4, &c., they can oppose a minus series 1, 2, 3, 4. Still it will be only by positive considerations that degrees are estimated in the negative direction. For example, a man who is said mathematically to be minus £1,000, interpreted to have no money, and, worse than that, to be under obligation to give the first available £1,000 he gets to his creditors. Here the negative, as a negative, is the fact of a man having no money: beyond that the degree of his indebtedness must be calculated on positive grounds. The case is not quite parallel with the one in hand; but it sheds upon it some light, by helping to show how a negative, as a nonentity, cannot be greater or less. A negation in the sense of an intellectual denial may be given with greater or less intensity; but a negation in the sense of the mere non-existence of a doubt has no varying intensity. And so the whole statement, that certainty, on its negative side, has no degrees, is reduced to saying, that the non-existence of doubt in every certitude is a simple non-existence, or nothing; and that nothing does not admit of more and less.

The way is thus cleared for establishing the possibility of degrees on the positive side of certitude. What a man does is one thing, what in strict logic he ought to do is another; and speaking from the former point of view only, it is not incumbent on us to prove that every man does always regulate the degree of his assent according to the considerations now to be brought forward. Cardinal Newman ably maintains that as a fact man does not so proportion his assents; it is enough for us that the considerations we have been urging are such that, of their own nature and caeteris paribus they produce the effect of varying the force of intellectual adherence. Those who, like Dr. Gutberlet, start from the notion that certitudes are equations{5} and argue that however the terms equated may vary, yet equation itself is constant, plainly leave out of the question elements which claim to be noticed.

St. Thomas, while he allows to the objection derivable from this idea of knowledge as an equation, the truth it contains, still manages to take out of the difficulty all its force as an objection, Not, indeed, that he is designedly combating the adverse view: his words form only the better answer to the difficulty, because they meet it unintentionally and in the mere act of explaining the real position of assent. What he says is this: "According as a thing happens to have more truth in it, it elicits a higher belief. For while truth consists of an equation between intellect and object, if we regard truth merely as an equation, it does not allow of less or more: but if we consider the very Being of the object, and remember that truth has its ground in the Being, and that such as the Being is, such is the truth; then those things which have more of Being have also more of truth."{6} That is, if you regard truth as a mere equation between a mental act and its formal object, equality is equality all the world over, whether the terms equated be greater or less. But intellectual assent is no mere dead uniform sign of equality, like our algebraic symbol: it is a living response to objective evidence, and is apt to vary, caeteris paribus, with the evidence that calls it forth. Hence St. Thomas again affirms: "An assent is nothing but the determination of the intellect to one affirmative: and by so much greater is the certitude by how much stronger is the motive by which it is determined."

Arguing first of all on the line here suggested, we may hope soon to find force of demonstration enough to overpower the hostile statement of Mr. Lewes: "The widest of all axioms, whatever is, is, cannot be more certain, more irresistible, than the most fleeting, particular truth." Against this let us try three arguments.

(a) Whilst certitude always remains up to the level of certitude, and never sinks to the lower grade of strong probability, still its accidental degree may vary: it reasonably so varies when the truth proposed is of a higher order. Thus a man is certain that he lit his fire with one of Bryant and May's matches: he is, or may be, certain in a more intense degree that the fire would not have blazed up without an igniting cause of some sort. He is certain that Victoria in 1887, the Jubilee year, was Queen of England: he is, or may be, certain in a more intense degree that God is sovereign Lord of all. He is certain that he paid a bill for four shillings with two florins: he is, or may be, certain in a more intense degree that two and two make four. Where an adequate cause for intenser degree is assigned, and where we have a faculty susceptible of stronger and weaker excitation, it is fair to infer a possible variation in the effects. To say that the variation is something outside the rational assent, or that it belongs only to concomitant emotion, is to ignore explained facts. It is quite true that some degrees of intensity are emotional; as when an Englishman assents more keenly to the authentic news of a victory for the British arms, than to the equally authentic news of a victory gained by one savage tribe over another. But the possibility of degrees in the region of emotion does not exclude their possibility in another. It was in intellectual motives that a cause for intenser assent was above pointed out; and therefore it is in intellectual assent that the intenser degree may sometimes reside which is all we had to show.

(b) A second argument may be put thus: Always supposing true certitude, sometimes we assent as under compulsion, and perhaps against our wish to believe otherwise: sometimes we assent, with ease indeed, but not with the feeling of strong compulsion; sometimes we assent but not without a certain effort of the will, urging on the mind to put carefully together and admit the just sufficient evidences. Against saying universally that these represent three descending grades of assent stands the fact, that the firmest of all assents, the act of supernatural faith, results from a command of the will; but keeping within the natural order, and speaking of general cases, we may assert of the above, that they are three varying grades, the variation being precisely in the intellectual character of the acts.

(c) Again, if the simple argument, "Certitude is certitude all the world over," were decisive of the whole question, it might be questioned whether Divine and Angelic intelligence were to be regarded as following under the rule. But waiving these points and keeping strictly to human intelligence, just as we drew a proof from the varying force of objective truths, so we may draw a proof from the varying force of human minds; some men, because of their keener faculties, may give an intenser assent to the same argument which draws likewise the assent of their duller brethren. And so once more, a certitude can vary in degree.


(1) In distinguishing three kinds of certitude it is worth while to notice their interdependence. Though some physical conditions of brain must be fulfilled in order that the mind may understand a metaphysical truth, yet man may claim, in regard to metaphysical truths, that he can obtain them without the admixture of truths of a different order. The principle of contradiction is reached in its purely metaphysical character. But all physical truth must be inseparably bound up with some metaphysical principles; for example with the just-mentioned principle of contradiction. For where would be the use of discovering that a planet exists, if there were no guarantee that its existence was incompatible with its non-existence. Obviously the metaphysical principle is not applied after the physically ascertained fact, but enters indissolubly into union with such ascertainment, which else would be impossible. In the third place moral truth must have joined with it, not only metaphysical, but also physical truths: for we judge human conduct through physical manifestations; and human speech or writing is equally a physical phenomenon.

(2) It has been asserted that the intenser degree is never in the certitude as such, but in some concomitant emotion. Thus a writer in Mind, who betrays the fact that he has not cleared up his own thoughts on the subject, ventures on the declaration, that "there are no degrees of intensity in cognition: the intensity is a matter of feeling concomitant with the cognition."

The relation between what are called feeling and cognition forms a matter of much vague discussion.{a} Some place the foundation of feeling in cognition, on a wide extension of the principle, "There is neither desire nor fear of the unknown;" others reverse the position, and make blind feeling primitive -- pure subjective feeling without an object. Feeling again is made to include all consciousness; so that a stronger intellectual assent, making itself felt in consciousness, could be put down to feeling.

In face of such ill-defined terms in the objection, it is enough to reply, that if, from an examination of any case, it appears that one assent has no intellectual motive or cause stronger than another, then it is no illustration of our thesis; but if a distinctly intellectual ground of superiority can be shown, then it is an illustration. If exactly the same vouchers tell a man of the equally credible events that a friend and a stranger have both perished in a shipwreck, then the intenser act in regard to the friend's death may be put down to emotion. There may also be something intenser in the intellectual energy, but this element would be difficult to detect and estimate.

And generally we may say, that people are too apt to think that they can mark off, with nicety, assent from assent, affective movement from affective movement, and the former of the two elements from the latter. Whereas clearly to isolate an act in reflexion, is often most difficult or impossible. It may very well be that, not acting on the possible principles explained in the argument which we used to prove the greater force of a metaphysical over a physical truth, a schoolboy will concentrate even a greater intellectual energy on the very contingent fact that he, a poor player usually, has had the luck once to score fifty at a cricket match, than on the eternally abiding, necessary truth that two straight lines cannot enclose a space. But in a concrete case of this kind, who is to disengage the intellectual from the emotional elements? Again, the mere size, or amplitude of the object assented to may easily get confused with a notion that the assent itself is intenser; and who then is neatly to discriminate extension from intensity? Take once more the rule sometimes laid down, that in any given case feeling and intelligence are in inverse ratio; the heavier drain in one direction exhausting the supply in the other. There is some truth expressed in such a rule; but on the other hand, the force of an emotion is sometimes to increase the intellectual power, not to diminish it, as in those who speak best under a fairly strong excitement. Let us not, then, be deceived by a fancied simplicity, but rather apply to acts of the human soul what a French writer, quoted by Sir H. Maine, says of human society: "I have hitherto discovered but one principle which is so simple as to appear childish, and which I scarce dare to express; it is no other than the observation, that a human society, a modern society especially, is an immense and complicated object."{b}

A human intelligence too works by a very complicated process.

{1} Suarez, De Anima, Lib. III. sec vi.

{2} Logica, Lib. II. cap. i. art. i. § iii.

{3} J'ai assez expliqué, en divers endroits, en quel sens cela se doit entendre. C'est à savoir que tandis que nous sommes attentifs à quelque vérité que nous concevons clairement, nous ne pouvons alors au même façon douter." (Méditations, p. 467 -- Jules Simon's edition).

{4} This use would exclude God from the order of the "physical," though as far as He has real existence He is often included under it; the fact being, that "physical" is a term of varied meaning, as when we distinguish physical science from the science of things spiritual, physics from chemistry, physics from physic, and so forth.

{5} Logik, Die Erkenntnisstheorie, I. 4.

{6} St. Thos., Quaest. Disp. De Caritat., art. ix. ad 1.

{a} See Mr. Bain's The Senses of the Intellect, Introduction, c. i.; Mr. Spencer's Psychology, Part IV, c. viii.; Lotze's Microcosmus, Book II, c. ii.

{b} "Jusqu' à présent je n'ai guère trouvé qu'un principe si simple qu'il semblera puéril, et que j'ose à peine l'annoncer. Il consists tout entier dans cette remarque, qu'une société humaine, surtout une société moderne, est une chose vaste et compliquée."

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