If we ask, however, how (with the exception of mathematics) we come by the general major propositions, examination shows that it is by way of induction, in that from a larger or smaller number of perceived special cases the general rule is deduced with greater or less probability. This probability is really implicitly contained in the cognition of the major, and among people educated and accustomed to think, can be arrived at numerically by bargaining and higgling about the conditions of a wager proposed for the nearest special case. But of course one has usually only an obscure idea of the coefficient of probability, which consequently is anything but exact, so that, e.g., a tolerably high probability is constantly confused with certainty (vide religious beliefs). Nevertheless, by the proposal of a wager both upper and lower limits may very soon be found, by which the quantity of probability is always to a certain degree determined, and with acute minds these limits may be approximated to one another by continued examination of the conditions of the wager.
The question how one arrives at the belief in the general rule is divisible, then, into the two questions: (1.) how do we come to pass at all from the particular to the universal? and (2.) how do we obtain the coefficient which represents the probability of a real value of the general expression that has been found? The former is only explained by the practical need of general rules, without which man would be quite helpless, since he would not know whether the earth would sustain his next step, or the trunk of a tree the next time support him on the water. It must then be pronounced a happy idea produced by the urgency of necessity, for in the particular cases themselves there is nothing at all to lead to their comprehension into a general rule. The second, however, is explained by inductive logic, so far as one understands by induction the logical deduction of a coefficient of probability. It is true the objective connection is made evident by this, but the subjective process of consciousness does not know these artificial methods: the natural understanding instinctively induces, and finds the result as something pre-formed in consciousness, without being able to give any further account concerning the How. There remains then nothing for it but to admit, that the unconscious logical in man relieves the consciously logical of an office, which is requisite for the existence of mankind, and yet exceeds the power of the unscientific consciousness. For when I have often seen rain or storms occur, along with such and such signs in the sky, I form the general rule, with a degree of probability of real validity dependent on the number of observations, without knowing anything about Mill’s inductive methods of Agreement, Difference, Residues, or Concomitant Variations; and yet my result agrees with the scientific so far as the vagueness of my coefficient of probability can confirm an agreement, and if one takes account at the same time of the possibly influential positive sources of error, as interest, &c.
Hitherto we have always only taken note of tolerably simple processes of thought—its elements, as it were; there still remain, however, the cases where, in the midst of a conscious chain of thought, several logically necessary links are overleapt by consciousness, and yet almost invariably the correct result appears. Here, again, the Unconscious will manifest itself to us very clearly as intuition, intellectual vision, direct knowledge, immanent logic.
If we first regard mathematics in this light, it appears that two methods prevail in it, the deductive or discursive and the intuitive. The former mode of proof consists in gradual inferences, according to the law of contradiction, from admitted premises, thus answering in the main to the consciously logical and its discursive nature: it is usually taken to be the sole and exclusive method of mathematics, because it alone claims to be method and demonstration. The other method must renounce all claim to being a mode of argument, but is nevertheless a form of proof, therefore method, because it appeals to natural feeling, to sound common-sense, and by intellectual intuition teaches at a glance as much as, nay, even more than, the deductive method after a tedious demonstration. It comes before consciousness with its result, with the constraining force of logic, and that, too, without hesitation and reflection, but instantaneously, and has accordingly the character of the unconsciously logical. E.g., nobody who looks at an equilateral triangle, if he has comprehended the question, will for a moment doubt whether the angles are equal. The deductive method can certainly prove it to him from still simpler premises, but the certainty of his intuitive knowledge will assuredly not be increased thereby; on the contrary, if it is proved to him very neatly by calculation, and without perception of the figure, he will obtain less assurance than from simple intuition; he then merely learns that it must be so and cannot be otherwise, but here he sees that it actually is so, and still more, that it is necessarily so: he sees, as it were, as living organism from within, what appears to him by deduction merely as effect of a dead mechanism. He sees, so to speak, the “how” of the matter, not merely the “that;” in short, he feels much more satisfied.
It is Schopenhauer’s merit to have rightly emphasised the value of this intuitive method, although he unduly slights the deductive method on that account. All the axioms of mathematics rest on this mode of proof, although, like more complex propositions, they may just as well be deduced from the law of contradiction; only, by reason of the simple nature of the subject, intuition acts here so strikingly in respect of conviction, that we almost regard the man as a fool who desires to deduce such principles. It accordingly happens that nobody has applied the necessary acuteness to really refer all the axioms of mathematics to the law of contradiction in application to given elements of space and number; hence the fixed idea of many philosophers (e.g., Kant) that this reduction is not possible. But as surely as these axioms are logical, so surely is their deduction possible from the sole fundamental law of logic, the law of contradiction.
The axioms of mathematics are altogether useless for clear heads; these might commence the study of mathematics with axioms of a much more complex kind; but our mathematics is intended for schools, where even the stupidest must be taught, and these need to comprehend the axioms as logically necessary. The discursive or deductive method is adapted for everybody, because it proceeds step by step, but intuition is a matter of talent; what the one sees at a glance is apprehended by the other only very circuitously. At a more advanced stage it is possible, by the reforming of geometrical figures, inversion, superposition, and other constructive aids, to assist intuition; but a point is soon reached where even a clear head can go no farther, and recourse must be had to the deductive method; e.g., in the case of the isosceles right-angled triangle, the Pythagorean theorem may be made evident to the eye by folding over the square of the hypothenuse; but in the scalene it is only to be comprehended deductively.—It follows from this, that the intuitive faculty far too soon leaves our most accomplished mathematicians in the lurch for much progress to be made by its means. All depends upon the degree of the capacity; and there is nothing absurd in supposing a higher mind so completely master of the intuitive method that it can altogether dispense with the deductive. The difficulty of intuition is pre-eminently shown very soon in algebra and analysis; only prodigious talents, like Dahse, are here capable of an intuition which is able to conceive and to deal with large numbers as a whole. More frequently one finds among mathematicians the ability, in an orderly chain of inference, to make intuitive leaps and to omit a number of terms, so that from the premises of the first argument immediately the conclusion of the ensuing third and fifth springs into consciousness. All this allows us to conclude that the discursive or deductive method is only the lame walking on stilts of conscious logic, whilst rational intuition is the Pegasus flight of the Unconscious, which carries in a moment from earth to heaven. The whole of mathematics appears from this point of view as the tools and implements of our poor mind, which, obliged laboriously to heap stone on stone, yet can never touch the heavens with its hand, although it build beyond the clouds. A mind standing in closer connection with the Unconscious, then, would instantaneously grasp the solution of every profound pr
oblem intuitively, and yet with logical necessity, as we do in the simplest geometrical problems; and it is accordingly not wonderful that the embodied calculations of the Unconscious, without trouble being given to it, agree with such mathematical precision in the greatest as in the smallest matter; as, e.g., in the cell of the bee, the angle at which the planes are inclined to one another, however exactly it be measured (to half-angular minutes), agrees with the angle which, with the form of the cell, affords the minimum of surface, in this case of wax, for the given space (comp. also p. 190, on the construction of the femur).
In all this we cannot doubt that in intuition the same logical links are present in the Unconscious, only what follows serially in conscious logic is compressed into a point of time. That only the last term comes into consciousness is due to the circumstance that it alone possesses interest for us; but that all the others are present in the Unconscious may be perceived, if the intuition be intentionally repeated in such a way that only the one before the last, then the term before that, &c., emerges into consciousness. The relation between the two kinds is then to be conceived as follows: The intuitive leaps the space to be traversed at a bound; the discursive takes several steps; the space measured is in both cases precisely the same, but the time required for the purpose is different. Each putting of the foot to the ground forms a point of rest, a station, consisting of cerebral vibrations which produce a conscious idea, and for that purpose need time (a quarter–two seconds). The leaping or stepping itself, on the other hand, is in both cases something momentary, timeless, because empirically falling into the Unconscious; the process proper is thus always unconscious, the difference is only whether, between the conscious stations for halting, greater or lesser tracts be traversed. In the case of small steps, even the heavy and clumsy thinker feels sure that he does not trip; with greater leaps, however, the danger of stumbling increases, and only the dexterous and nimble brain attempts them with advantage. The dull brain suffers a twofold loss of time with its greater discursiveness of thought. In the first place, the halt at each single station is greater in its case, because the single idea needs longer time to become conscious with the same clearness; and, in the second place, it must have more pauses. That, however, really the precise process is in every, even the smallest step of thought, intuitive and unconscious, on that point, after what has been said, scarcely any doubt can well remain.
But even outside of mathematics we can follow the interblending of the discursive and intuitive method. The practised chess-player possibly reviews in his mind the result of this and that move three or four moves ahead, but it does not at all occur to him to consider a hundred thousand other possible moves, five or six of which the bad chess-player perhaps considers, without lighting on the two which alone claim the attention of the proficient. How now does it come to pass that the latter does not at all take note of these five or six moves, which would probably only be revealed as less good after two to three other moves had been made? He looks at the chessboard, and without reflection he immediately sees the only two good moves. This is the work of a moment, even if he be a passing spectator of a game played by others. In the same way the general of genius sees the point for the demonstration or the decisive attack, also without reflection (comp. above, p. 23, the reference to Heine). Practice is a word which here does not at all affect the question; practice can facilitate reflection, but never supply the want of it except in mechanical works, where another nerve-centre acts vicariously for the brain. But here, where we are dealing with something quite different, the question is, What instantaneously makes the appropriate choice if it is not conscious reflection? Manifestly the Unconscious.
Look at the antics of a young ape. Cuvier tells of a young Bhunder (Macacus Rhesus) (see Brehm’s Illustr. Thierleben, i. 64): “After about the lapse of a fortnight it began to separate from its mother, and at once exhibited in its first steps an adroitness, a strength, which could not but excite universal astonishment, practice and experience both having been wanting. The young Bhunder from the very first clung to the perpendicular iron bars of its cage, and clambered up and down according to its fancy; perhaps made also a few steps on the straw; sprang of its own accord from the summit of its cage on to its four hands, and then again against the bars, to which it clung, with a velocity and accuracy which would have done honour to the most experienced monkey.” How does this ape, just released from the skin of its mother, upon whose breast it has hitherto hung, come to measure aright the force and direction of its leaps? How does the lion, springing at the distance of twelve feet upon its prey, calculate the curve with the proper angle and velocity? How the dog the curve of the morsel which it catches so cleverly at any distance and at any angle? Practice only facilitates the action of the Unconscious on the nerve-centres, and where these are already sufficiently prepared for their office without practice we see even this practice dispensed with, as in the above-mentioned ape; but that which is substituted for the lacking mathematical calculation can, as in the cell-structure of the bee, only be mathematical intuition combined with the instinct to execute the movement.
As concerns the overleaping of conclusions in ordinary thought, this is a very well-known experience. Without this acceleration thought would be of such a snail’s-pace that, as now frequently happens in the case of human beings with sluggish brains, in many practical reflections one would arrive too late with one’s result, and would hate the whole labour of thought on account of its cum-brousness, as it is now hated and avoided merely by specially lazy thinkers. The simplest case of skipping is when the conclusion is immediately drawn from the minor premiss without our being conscious of the major premiss; but also one or several actual conclusions are sometimes omitted, as we have already seen in mathematics. This commonly happens only in one’s own thinking; in communication we have regard to the understanding of others, and recover the principal intermediate links that have previously remained unknown. Women and the uneducated frequently neglect this, and then there arise those leaps in their trains of thought which may be convincing to the speaker, although the hearer is wholly unable to see how he is to get from point to point. Any one accustomed to introspection will be able to catch himself making considerable leaps in oarrying on a train of thought and in drawing inferences, if he make this review directly after prosecuting a new and very interesting study with zeal and success
An observation of Jessen, the well-known student of mental disease, on an allied topic, is interesting (“Psychology,” pp. 235, 236), which I will take the liberty of quoting:—“When we reflect on anything with the whole force of our mind, we may fall into a state of entire unconsciousness, in which we not only forget the outer world, but also know nothing at all of ourselves and the thoughts passing within us. After a shorter or longer time, we then suddenly awake as from a dream, and usually at the same moment the result of our meditation appears clearly and distinctly in consciousness, without our knowing how we have reached it. Also, in a less severe meditation, there occur moments in which a perfect vacancy of thought is combined with the consciousness of our own mental effort, to which in the next moment a more vivid stream of thought succeeds. Certainly some practice is required to combine serious reflection with simultaneous self -observation, as the endeavour to observe thoughts in their origin and their succession may easily produce disturbances of thinking and arrest the evolution of our thoughts. Repeated attempts, however, put us in a position clearly to perceive that in fact in every arduous reflection a constant inner pulsation, or a changing ebb and flow of thoughts, as it were, takes place—a moment in which all thoughts disappear from consciousness, and only the consciousness of an inner mental strain remains, and a moment in which the thoughts stream in in greater fulness and distinctly emerge into consciousness. The lower the ebb, the stronger the succeeding flood is wont to be; the stronger the previous inner tension, the stronger and livelier the contents of the emerging thoughts.” The purely empirical observations of this fine mental obser
ver are a confirmation of our way of regarding the matter, the more above suspicion as he is not at all acquainted with our conception of unconscious thinking, and nevertheless is constrained to the verbal acknowledgment of our assertions (in the passages in italics) by the pure force of facts; although his subsequent attempts at explanation, which are in essentials (brainless thinking) quite correct, do not hit the nail on the head, just because they do not grasp the notion of the Unconscious as principle of thought apart from a brain. The consciousness of mental effort observed in these processes is only the feeling of the tension of the brain and the scalp (by reflex action). The moments of vacancy of consciousness that are described, on which the result follows without our being aware how it has been arrived at, are those very moments when, in the productive thinking out of a zealously pursued object of study, the skipping of a longer train of inferences takes place.
Philosophy of the Unconscious Page 35
