Manuscript consists of numbered pages 2–17, 19–29, and an unnumbered loose note. Missing are pages 1, 18, and one or more pages after 29.
MS 831 images online at Harvard: http://nrs.harvard.edu/urn-3:FHCL.HOUGH:12486086
831. [Reasoning and Instinct]
A. MS., n.p., n.d., pp. 2–29, incomplete.
The fine gradations between subconscious or instinctive mind and conscious, controlled reason. Logical machines are not strictly reasoning machines because they lack the ability of self-criticism and the ability to correct defects which may crop up. Three kinds of reasoning: inductive, deductive, hypothetical. Quasi-inferences.
Peirce wrote the number of each page in its upper right-hand corner.
[page 2] that no amount of direct scrutiny can enable us to distinguish the quasi-inferential interpolations of sense from those parts of what we seem to see and hear which immediately result from stimulations of the peripheral nerve-terminals.
Nothing that the psychologists have since discovered has been so surprising or so instructive; and I propose to bring out one of the lessons of these phenomena, — a lesson of practical importance, — by ranging along side of these some other facts which will show us how fine are the gradations between subconscious, or instinctive, mind and our more conscious and more controlled reason.
Beginning as far away from consciousness as possible, the reader may probably recollect [page 3] that some fifteen or twenty years ago several “logical machines” were constructed. That wonderful wit, Dean Swift, in his voyage to Laputa, had suggested such a thing only to make fun of it. But Swift’s fun had a way of hitting the object of satire so squarely on the head as to be of more value and force than a labored discussion. After describing a machine that the Laputans were represented as trying to make, he remarks,
“By this contrivance, the most ignorant person, at a reasonable charge, and with little bodily labor, might write books in philosophy, laws, mathematics, and theology, without the least assistance from genius or study.”
He saw that a certain logical idea upon which [page 4] Leibniz and others had bestowed a great deal of thought would, if it were true, render such a machine possible, a result that outrages all experience more than almost anything that can be imagined. Yet in 1870 Prof Jevons actually constructed a machine that would perform all the processes of ratiocination taught in the logic-books of that day, syllogisms, sorites, dilemmas, etc., together with a good many others not down in the books; and at a later date Prof. Allan Marquand of Princeton made a still more effective machine. A few words will suffice to give an essentially correct notion of what the last machine would do, provided accuracy in the details of the description is not expected. Everybody has seen a child’s board with grooves in which slide buttons with letters upon them, enabling him to set up a word [page 5] or sentence. Marquand’s or Jevons’s machine has a face somewhat like that. Only the movement is different, and in place of letters, there are certain conventional signs. The premises are made to appear on the face, whereupon, a crank being turned, the conclusion comes out expressed in the same system of signs. I remember having seen the following premises set up on Mr. Marquand’s machine:
A certain board consists of bondholders and shareholders.
No member of the board is at once a bondholder and a shareholder.
All the bondholders are members of the board.
The crank was turned, and the following appeared:
No shareholder is a bondholder.
Any clear-headed person would see, at once, that this follows. But a machine a little more complicated [page 6] could be made on precisely the same premises (involving too many items for the machines actually made) could be set up:
A scientific society consists of Section A, Section B, and Section C. The following rules are in force:
1. Any member of Section A not belonging to Section B may read a paper if he has paid his subscription, but otherwise not. And the same applies to every member of Section B not belonging to Section C, and to every member of Section C not belonging to Section A.
2. Any member of Section A not belonging to Section C may exhibit an experiment if he has paid his subscription, but otherwise not. And the same applies to every member of Section B or Section C who does not belong to Section A.
[page 7]
3. Every member must either read a paper or exhibit an experiment.
Required the least addition to the rules which shall have the effect of compelling every member to pay his subscription.
The required rule, which the machine would turn out, is, that no member of all three sections can read a paper unless he has paid his subscription, and that no member of Section A or Section C can exhibit an experiment without reading a paper.*
*I borrow this solution of a problem by Mr. W. B. Grove from an article by Mrs. Christina Ladd Franklin in the Johns Hopkins ‘Studies in Logic,’ (Boston: Little, Brown, & Co. 1883, p. 54.)
[page 8]In our day the theory of reasoning, as given in the vast majority of textbooks, has lagged behind the practice worse than ever before. Thus, the books teach that from given premises only one conclusion, or a very small number of conclusions, can be drawn; although the whole science of higher arithmetic, with its hundreds of marvellous theorems, has in fact been deduced from six primary assumptions about number. The logical machines hitherto constructed are inadequate to the performance of mathematical deductions. There is, however, a modern Exact Logic which, although yet in its infancy, is already far enough advanced to render it a mere question of expense to construct a machine that would grind out all the known theorems of arithmetic and advance that science still more rapidly than it is now progressing.
[page 9]Supposing such a machine to be constructed, ought we, or ought we not, to call it a reasoning-machine? If it shall accomplish all that the mind accomplishes in reasoning, to allow ourselves to refuse it that title merely because it is not conscious, or does not come to its end by the same means that the mind employs, would be to fritter away wealth. For such high words as “reasoning,” “probability,” “morals,” and the like, out of doubt conduce more to all the purposes of life than any other instruments of man’s creation; and consequently their utility ought to be the sole consideration in fixing the bounds of their application.
What, then, is the use of designating some formations of opinion as rational, while others (perhaps leading [page 10] to the same results) are stigmatized as blind followings of the rule of thumb or of authority, or as mere guesses? When we reason we set out from an assumed representation of a state of things. This we call our premise; and working upon this, we produce another representation which professes to refer to the same state of things; and this we call our conclusion. But so we do when we go irreflectively by a rule of thumb, as when we apply a rule of arithmetic the reason of which we have never been taught. The irrationality here consists in our following a fixed method, of the correctness of which the method itself affords no assurance; so that if it does not happen to be right in its application to the case in hand, we go hopelessly astray. In genuine reasoning, we are [page 11] not wedded to our method. We deliberately approve it, but we stand ever ready and disposed to reëxamine it and to improve upon it, and to criticise our criticism of it, without cessation. Thus the utility of the word “reasoning” lies in its helping us to discriminate between self-critical and uncritical formations of representations. If a machine works according to a fixed principle involved in the plan of it, it may be a useful aid in reasoning; but unless it is so contrived that, were there any defect in it, it would improve itself in that respect, then, although it could correctly work out every possible conclusion from premises, the machine itself would afford no assurance that its conclusions would be correct. Such assurance could only come from our [page 12] critical examination of it. Consequently, it would not be, strictly speaking, a reasoning machine.
Self-criticism can never be perfectly thorough. For the last act of criticism is always itself open to criticism. But as long as we remain disposed to self-criticism and to further inquiry, we have in this disposition an assurance that if the truth of any question can ever be got at, we shall eventually get at it.
When the minds of the lower animals first began to be studied, it was the unchangeableness of animals’ methods that led observers to draw a sharp line of demarcation between Instinct and Reason. But facts subsequently came to light showing that fixity was only relative, that bees in a clime of perpetual summer, after some generations [page 13] give up storing vast quantities of honey; that beavers, provided with new materials, gradually evolve new styles of architecture; that sheep, carried to valleys where poisonous hellebore grows, learn not to eat it; that birds sometimes take to unaccustomed food, and come to prefer it; that the palm-swifts of Jamaica in 1857 suddenly gave up living in palms, after one of their favorite trees had been blown down, and captured the swallows’ nests in the Assembly-House piazza. Such phenomena evince an element of self-criticism, and therefore of reasoning.
There are three kinds of reasoning, the Inductive, the Deductive, and the Hypothetical. The last consists in the introduction into a confused tangle of given facts [page 14] of an idea not given whose only justification lies in its reducing that tangle to order. This kind of inference is little subject to control, and so not highly rational; and one reason for this is that when once the facts have been apprehended in the light of the hypothesis, they become so swallowed up in it, that a strong exertion of intellect is required to disembarass them from it, and to recall them in their pristine nudity. Where is the man, barring historians, who shall find it easy to specify a poor dozen out of the thousand facts of his immediate experience which have caused him to suppose that the thirteen original states of this union were once British provinces?
[page 15] Deductive inference is peculiar in the following respect, namely that its premise may represent a purely imaginary state of things and in any case it is treated as if it were of that character. This imaginary state of things being of our own creation, lies quite open to our observation. We remark some feature of it, and then we easily satisfy ourselves that this feature will remain unchanged, however the imaginary state of things altered, so long as a certain condition is fulfilled. For example, we ![[convex pentagon ABCDE]](peirce-pentagon1.png "[convex pentagon ABCDE]")
imagine a plane pentagon, ABCDE; and we remark that the diagonals AC and AD divide it into three triangles whose internal angles cover, without overlapping, the internal angles of the pentagon. By varying the shape of the [page 16] latter, we convince ourselves that this will always ![[two variations of pentagon ABCDE, one concave at A, the other concave at A and again concave at D]](peirce-pentagon2.png "[two variations of pentagon ABCDE, one concave at A, the other concave at A and again concave at D]")
be true so long as no two sides of the pentagon intersect, in which case it would not properly have any internal angles. Knowing, then, that the sum of the angles of any triangle is two right angles, we conclude that the sum of the internal angles of any plane pentagon (if it has any) is six right angles. In like manner, we may picture to ourselves a number of men each in a coffin to signify that he is mortal, one of the number being labelled Aquinaldo. We easily satisfy ourselves, no matter how, that whether the men be few or many, or whatever their other characters may be, so long as Aquinaldo is a man, and all men are mortal, Aquinaldo is mortal; and this holds good, not only for the actual world, but for every possible world whatsoever. Thus, [page 17] it is a characteristic of deductive reasoning that when it is applied to experience it makes anticipations, and declares that this or that shall be and must be.
Inductive inference finds, reasoning through a fragment of experience, some feature, which it extends to a larger experience embracing that fragment as a part of it. Wherever on the globe geodetic measures have been made, the sea-level has been found approximately to coincide with the surface of a certain ellipsoid; whence, we inductively infer that the same thing will hereafter be found approximately true of that much larger part of the earth’s surface where no geodetic operations have yet been conducted.
We can, in some measure, control even outward events; far more, all that takes place within us. The sheer force of meditation has, ere this, brought out stigmata upon the skin of people’s hands and feet. On the other hand, there is nothing, not even our thoughts, over which our control is complete. Accordingly, we must naturally expect to find among our natural actions, every grade of controlledness from which utter blindness almost to the highest rationality.
A puzzle is an exercise in hypothetic inference. The more we contemplate [page 18 missing]
[page 19] impulses succeed one another at the rate of ten or twenty per second, the effect is about the most disagreeable thing, in the way of a noise, that one can find. To hear a boiler rivetted is a pleasure in comparison. And it is the more disagreeable the faster the sounds come. But let the rate of succession be increased to, say, 40 per second, and there is a complete relief; for what we now hear is a deep musical tone, which is an imported sensation whose analogy to the burst of grief, and through that to the solution of the puzzle, an undoubted case of hypothetic inference, is certainly intimate. True, some of the psychologists tell us that Hooke’s experiment involves no psychical process at all. And why not, I query? Because it is a purely physical effect! But were that a sound observation, it would follow that there is no such thing as [page 20] reasoning, since all that takes place in the brain is acknowledged on all hands to be purely physical, whether the soul has a separable life or not. But, say the objectors, we do not hear the single blows at all. I reply that that only shows how thoroughly the phenomenon partakes of the characteristic feature of hypothetic inference, that the premises are completely swallowed up in the imported idea. I confess that it is somewhat remarkable that the tangle of presentations does not antecede the hypothesis, which, on the contrary, appears from the very first. But then, there are many psychological phenomena whose analogy with hypothesis is generally admitted, and yet where the imported idea starts up along with the tangle of sensations that it puts into order. Such, for example, is the image of space which replaces the intricate tangle of sensation produced by the excitations of the nerve points scattered over the retina of the eye. This is frequently spoken of as a hypothesis and it seems a triumph of intellect beyond all the triumphs of science. Yet every chicken that breaks the shell achieves it within five minutes of its emergence, and probably from the very first.
[page 21]● x
I will now pass to a case [of] a quasi-induction. Does the reader happen to know that he has a blind spot near the middle of each retina? Will he kindly oblige me by shutting his right eye and then looking and trying to see whether his field of vision is an irregularly outlined oval or whether it is ring-shaped. He can detect no hole in it, I venture to say. But now look at the figure which shows a cross four inches to the right of a blot. Shut the right eye, hold the left in front of the cross twelve inches from it and look intently at that cross. The blot will be invisible. Look an inch to the right or left of the cross and the blot will reappear. Your eye has jumped to just the same kind of conclusion that the geodesists come to about the earth’s surface. Your eye has noticed that it saw things [page 22] scattered about within the oval outline of the field of vision and has inductively concluded that it saw all parts of that oval.
These two phenomena are instances of quasi-inferences thoroughly irrational, in the sense of being utterly beyond control. At least, I never heard of an ear being educated to hear the single vibrations of a musical note, however low. But there are many quasi-inferential illusions of sense which disappear after more or less training; and some of them may subsequently return if the training is not kept up. Thus, it is a fact which the eye duly reports, that all out-of-door shadows are very markedly bluish, while the sunshine is yellow. Yet the majority of people cannot see this. The reason is that they subconsciously make allowance [page 23] for it. That is to say, they are so prepossessed with the idea that an object partly in the sun and partly in the shade is really all of one color, that this theory (which happens to be a correct one) quite overclouds the direct testimony of the eye to the contrary. I have remarked, however, that painters generally see the naked truth in this particular. A person in whom I take a certain interest, — he happens to be seated at my table, at this instant, using my ink, my paper, and my only pen, — when he was formerly engaged in experiments on the color-sense used to think that it was the most astonishing thing in the world that so many people could open their eyes and not see a phenomenon so glaringly obtrusive as this blueness of the shadows. But now that he has long given up those experiments, though shadows still look blue, they do not look so very blue that he is surprised that people do not remark their blueness. [page 24] The illusion of the marble that feels like two when rolled between crossed fingers disappeared after a little practice. So does the error about the height of a silk hat on the floor, as well as does the vertical elongation of a square. Even effects of color contrast, which deceive one at first so absolutely, become much weakened, in time. In this cases, we have a very slow yielding to criticism, much like what we observe in the instincts of animals. In order to get these contrast-effects in their full intensity, it is necessary to have a special machine. Yet for our present purpose, the following easy experiment will answer still better. You procure a sheet of high-colored paper, say bright red, and a piece of tracing-muslin* large enough to cover it. You also get a piece of perfectly neutral gray paper of a middling shade. You cut out two squares of the gray paper of an inch on
*Tracing paper will not answer so well; but it will do.
[page 25] the side. One of these you place on the red paper beneath the tracing muslin. The other you cover with a separate piece of tracing-muslin of precisely its size, and put it with its cover on the large piece of tracing muslin near the other square. Now you call in a friend and point out the two squares of gray paper, and ask him whether they are of the same color, or not. “Of course not,” he wll say. “This one, beneath the large piece of tracing-muslin is green. This other, with a small piece of tracing-muslin is gray.” Yet, in fact, they were both cast from adjacent parts of the same sheet, and are both covered with the same thickness of the same tracing-muslin. The only difference is that the discontinuity of the tracing muslin, due to the outline of the small piece, prevents the mind from comparing its [page 26] color with that of the red paper and so ascribing to it the contrast-color. This is a plain case of an inferential fallacy looking for all the world exactly like a presentation of sense. Or if it is not properly to be called inference, it is only because it does not readily yield to criticism. You yourself, who are in the secret, will experience the illusion, though not so strongly as your friend. After much practice the effect will almost disappear, or perhaps entirely.
Another remarkable experiment which requires some apparatus and many precautions which cannot here be set down, is to produce with two magic lanterns two adjacent square spots of light, one deep red and the other appearing quite white when seen by itself, the two being brought to the same degree of apparent luminosity. The observer looks [page 27] through a tube with a diaphragm at its further end, so that the round space he sees is bisected by the boundary between the two spots. The result is that the white appears of a high blue-green. The spots are now slowly moved, so that the red is not seen at all. Nevertheless, the white continues to appear blue-green. The lantern making the red spot is extinguished; but that naturally makes no difference. Now the observer removes his eye from the tube and looks directly at the white spot on the wall. Instantly, the illusion disappears, and the spot shows as white.
That these are quasi-inferences of sense, is manifest. To what logical class of inferences, then, shall they be likened? An ex- [page 28] aggeration takes place. An imaginary degree of blueness is attributed to the white, because its color seems to contrast strongly with the red and turquoise is the opposite to red. It is not exactly hypothetic inference, because no tangle of impressions is reduced to order by the exaggeration. It is rather as if the eye reasoned, thus:
The color of this spot is violently opposed to red;
But that which is violently opposed to red is turquoise;
Hence, the color of this spot is turquoise.
Now this is deductive inference. It is not, I grant, a characteristically marked deduction. It is rather on the border between deduction and hypothesis. But it is as good a case of deductive inference as the [page 29] the ordinary normal operation of the senses can furnish. Instances have occurred in which an observer intently watching for the emergence of a star from behind the dark side of the moon, — an event as easy to observe as a flash of lightening — has tapped the chronograph-key too early. A spasmodic movement might result from the intense strain of expectation, — a movement belonging basically to the class of quasi-deductions. It then, before the observer had time to realize what he had done, for which needs 0.3 or 0.4 of a second, the star should actually have appeared, he might easily suppose that he had seen it before he tapped. In that way, what was in reality a muscular an- [next page or pages missing]
[loose note]
Our Senses as Reasoning Machines?
