This, that and the other S is all M, _Minor_.

[.'.] All M is P, _Conclusion_.

This, that and the other magnet (_i.e._, magnets individually) attract iron.

This, that and the other magnet (_i.e._, the individuals separately admitted) are all magnets.

[.'.] All magnets attract iron.

This, that and the other S being simply convertible with All M, you have only to make this conversion and you have a syllogism in Barbara where this, that and the other S figures as the Middle Term.

The practical value of this tortuous expression is not obvious.

Mediaeval logicians shortened it into what was known as the Inductive Enthymeme: "This, that and the other, therefore all," an obvious conclusion when this, that and the other constitute all. It is merely an evidence of the great master's intoxication with his grand invention. It is a proof also that Aristotle really looked at Induction from the point of view of Interrogative Dialectic.

His question was, When is a Respondent bound to admit a general conclusion? And his answer was, When he has admitted a certain number of particulars, and cannot deny that those particulars constitute the whole whose predicate is in dispute. He was not concerned primarily with the analysis of the steps of an inquirer generalising from Nature.

[Footnote 1: [Greek: epagoge men oun esti kai ho ex epagoges syllogismos to dia tou eterou thateron akron to meso syllogisasthai; Oion ei ton A G meson to B, dia tou G deixai to A to B hyparchon.] (An. Prior., ii. 23.)]

BOOK II.

INDUCTIVE LOGIC, OR THE LOGIC OF SCIENCE.

INTRODUCTION.

Perhaps the simplest way of disentangling the leading features of the departments of Logic is to take them in relation to historical circumstances. These features are writ large, as it were, in history.

If we recognise that all bodies of doctrine have their origin in practical needs, we may conceive different ages as controlled each by a distinctive spirit, which issues its mandate to the men of the age, assigning to them their distinctive work.

The mandate issued to the age of Plato and Aristotle was _Bring your beliefs into harmony one with another_. The Aristotelian Logic was framed in response to this order: its main aim was to devise instruments for making clear the coherence, the concatenation, the mutual implication of current beliefs.

The mandate of the Mediaeval Spirit was _Bring your beliefs into harmony with dogma_. The mediaeval logic was contracted from Aristotle's under this impulse. Induction as conceived by him was neglected, allowed to dwindle, almost to disappear from Logic. Greater prominence was given to Deduction.

Then as Dogmatic Authority became aggressive, and the Church through its officials claimed to pronounce on matters outside Theology, a new spirit was roused, the mandate of which was, _Bring your beliefs into harmony with facts_. It was under this impulse that a body of methodical doctrine vaguely called Induction gradually originated.

In dealing with the genesis of the Old Logic, we began with Aristotle.

None can dispute his title to be called its founder. But who was the founder of the New Logic? In what circumstances did it originate?

The credit of founding Induction is usually given to Francis Bacon, Lord Verulam. That great man claimed it for himself in calling his treatise on the Interpretation of Nature the _Novum Organum_. The claim is generally conceded. Reid's account of the matter represents the current belief since Bacon's own time.

"After man had laboured in the search of truth near two thousand years by the help of Syllogisms, [Lord] Bacon proposed the method of INDUCTION as a more effectual engine for that purpose. His _Novum Organum_ gave a new turn to the thoughts and labours of the inquisitive, more remarkable and more useful than that which the _Organon_ of Aristotle had given before, and may be considered as a second grand era in the progress of human nature.... Most arts have been reduced to rules after they had been brought to a considerable degree of perfection by the natural sagacity of artists; and the rules have been drawn from the best examples of the art that had been before exhibited; but the art of philosophical induction was delineated by [Lord] Bacon in a very ample manner before the world had seen any tolerable example of it."[1]

There is a radical misconception here, which, for reasons that I hope to make plain, imperatively needs to be cleared up. It obscures the very essence of "philosophical induction".

There are three ways in which movement in any direction may be helped forward, Exhortation, Example, and Precept. Exhortation: a man may exhort to the practice of an art and thereby give a stimulus. Example: he may practise the art himself, and show by example how a thing should be done. Precept: he may formulate a clear method, and so make plain how to do it. Let us see what was Bacon's achievement in each of those three ways.

Undoubtedly Bacon's powerful eloquence and high political position contributed much to make the study of Nature fashionable. He was high in place and great in intellect, one of the commanding personalities of his time. Taking "all knowledge for his province," though study was really but his recreation, he sketched out a plan of universal conquest with a clearness and confidence that made the mob eager to range themselves under his leadership. He was the magnificent demagogue of science. There had been champions of "Induction" before him, but they had been comparatively obscure and tongue-tied.

While, however, we admit to the full the great services of this mighty advocate in making an "Inductive" method popular, we should not forget that he had pioneers even in hortatory leadership. His happiest watchword, the Interpretation of Nature, as distinguished from the Interpretation of Authoritative Books, was not of his invention. If we read Whewell's _History of the Inductive Sciences_, we shall find that many before him had aspired to "give a new turn to the labors of the inquisitive," and in particular to substitute inquisition for disquisition.

One might compile from Whewell a long catalogue of eminent men before Bacon who held that the study of Nature was the proper work of the inquisitive: Leonardo da Vinci (1452-1519), one of the wonders of mankind for versatility, a miracle of excellence in many things, painter, sculptor, engineer, architect, astronomer, and physicist; Copernicus (1473-1543), the author of the Heliocentric theory; Telesius (1508-1588), a theoretical reformer, whose _De Rerum Natura_ (1565) anticipated not a little of the _Novum Organum_; Cesalpinus (1520-1603), the Botanist; Gilbert (1540-1603), the investigator of Magnetism. By all these men experiment and observation were advocated as the only way of really increasing knowledge. They all derided mere book-learning. The conception of the world of sense as the original MS. of which systems of philosophy are but copies, was a familiar image with them. So also was Bacon's epigrammatic retort to those who wish to rest on the wisdom of the ancients, that antiquity is the youth of the world and that we are the true ancients. "We are older,"

said Giordano Bruno, "and have lived longer than our predecessors."

This last argument, indeed, is much older than the sixteenth century.

It was used by the Doctor Mirabilis of the thirteenth, the Franciscan Friar, Roger Bacon (1214-1292). "The later men are, the more enlightened they are; and wise men now are ignorant of much the world will some day know." The truth is that if you are in search of a Father for Inductive Philosophy, the mediaeval friar has better claims than his more illustrious namesake. His enthusiasm for the advancement of learning was not less nobly ambitious and far-reaching, and he was himself an ardent experimenter and inventor. His _Opus Majus_--an eloquent outline of his projects for a new learning, addressed in 1265 to Pope Clement IV., through whom he offered to give to the Church the empire of the world as Aristotle had given it to Alexander--was almost incredibly bold, comprehensive and sagacious. Fixing upon Authority, Custom, Popular Opinion, and the Pride of Supposed Knowledge, as the four causes of human ignorance, he urged a direct critical study of the Scriptures, and after an acute illustration of the usefulness of Grammar and Mathematics (widely interpreted), concluded with Experimental Science as the great source of human knowledge. I have already quoted (p. 15) the Friar's distinction between the two modes of Knowing, Argument and Experience, wherein he laid down that it is only experience that makes us feel certain. It were better, he cried in his impatience, to burn Aristotle and make a fresh start than to accept his conclusions without inquiry.

Experimental Science, the sole mistress of Speculative Science, has three great Prerogatives among other parts of Knowledge. First, she tests by experiment the noblest conclusions of all other sciences. Next, she discovers respecting the notions which other sciences deal with, magnificent truths to which these sciences can by no means attain. Her third dignity is that she by her own power and without respect to other sciences investigates the secret of Nature.

So far, then, as Exhortation goes, King James's great lawyer and statesman was not in advance of Pope Clement's friar. Their first principle was the same. It is only by facts that theories can be tested. Man must not impose his own preconceptions (_anticipationes mentis_) on nature. Man is only the interpreter of nature. Both were also at one in holding that the secrets of nature could not be discovered by discussion, but only by observation and experiment.

Francis Bacon, however, went beyond all his predecessors in furnishing an elaborate Method for the interpretation of Nature. When he protested against the intellect's being left to itself (_intellectus sibi permissus_), he meant more than speculation left unchecked by study of the facts. He meant also that the interpreter must have a method. As man, he says, cannot move rocks by the mere strength of his hands without instruments, so he cannot penetrate to the secrets of Nature by mere strength of his intellect without instruments. These instruments he undertakes to provide in his Inductive Method or _Novum Organum_. And it is important to understand precisely what his methods were, because it is on the ground of them that he is called the founder of Inductive Philosophy, and because this has created a misapprehension of the methods actually followed by men of science.

Ingenious, penetrating, wide-ranging, happy in nomenclature, the _Novum Organum_ is a wonderful monument of the author's subtle wit and restless energy; but, beyond giving a general impulse to testing speculative fancies by close comparison with facts, it did nothing for science. His method--with its Tables of Preliminary Muster for the Intellect (_tabulae comparentiae primae instantiarum ad intellectum_, facts collected and methodically arranged for the intellect to work upon); its Elimination upon first inspection of obviously accidental concomitants (_Rejectio sive Exclusiva naturarum_); its Provisional Hypothesis (_Vindemiatio Prima sive Interpretatio Inchoata_); its advance to a true Induction or final Interpretation by examination of special instances (he enumerates twenty-seven, 3 3 3, _Prerogativas Instantiarum_, trying to show the special value of each for the inquirer)[2]--was beautifully regular and imposing, but it was only a vain show of a method. It was rendered so chiefly by the end or aim that Bacon proposed for the inquirer. In this he was not in advance of his age; on the contrary, he was probably behind Roger Bacon, and certainly far behind such patient and concentrated thinkers as Copernicus, Gilbert, and Galileo--no discredit to the grandeur of his intellect when we remember that science was only his recreation, the indulgence of his leisure from Law and State.

In effect, his method came to this. Collect as many instances as you can of the effect to be investigated, and the absence of it where you would expect it, arrange them methodically, then put aside guesses at the cause which are obviously unsuitable, then draw up a probably explanation, then proceed to make this exact by further comparison with instances. It is when we consider what he directed the inquirer to search for that we see why so orderly a method was little likely to be fruitful.

He starts from the principle that the ultimate object of all knowledge is use, practice (_scimus ut operemur_). We want to know how Nature produces things that we may produce them for ourselves, if we can.

The inquirer's first aim, therefore, should be to find out how the qualities of bodies are produced, to discover the _formae_ or formal causes of each quality. An example shows what he meant by this. Gold is a crowd or conjugation of various qualities or "natures"; it is yellow, it has a certain weight, it is malleable or ductile to a certain degree, it is not volatile (loses nothing under fire), it can be melted, it is soluble. If we knew the _forma_ or formal cause of each of those qualities, we could make gold, provided the causes were within our control. The first object, then, of the investigator of Nature is to discover such _formae_, in order to be able to effect the transformation of bodies. It may be desirable also to know the _latens processus_, any steps not apparent to the senses by which a body grows from its first germs or rudiments, and the _schematismus_ or ultimate inner constitution of the body. But the discovery of the _formae_ of the constituent qualities (_naturae singulae_), heat, colour, density or rarity, sweetness, saltness, and so forth, is the grand object of the Interpreter of Nature; and it is for this that Bacon prescribed his method.

The _Sylva Sylvarum_, or Natural History, a miscellaneous collection of facts and fictions, observations and traditions, with guesses at the explanation of them, affords us a measure of Bacon's own advancement as an interpreter of Nature. It was a posthumous work, and the editor, his secretary, tells us that he often said that if he had considered his reputation he would have withheld it from the world, because it was not digested according to his own method: yet he persuaded himself that the causes therein assigned were far more certain than those rendered by others, "not for any excellence of his own wit, but in respect of his continual conversation with Nature and Experience," and mankind might stay upon them till true Axioms were more fully discovered. When, however, we examine the causes assigned, we find that in practice Bacon could not carry out his own precepts: that he did not attempt to creep up to an explanation by slow and patient ascent, but jumped to the highest generalisations: and that his explanatory notions were taken not from nature, but from the ordinary traditions of mediaeval physical science. He deceived himself, in short, in thinking that he could throw aside tradition and start afresh from observation.

For example. He is struck by the phenomenon of bubbles on water: "It seemeth somewhat strange that the air should rise so swiftly, while it is in the water, and when it cometh to the top should be stayed by so weak a cover as that of the bubble is". The swift ascent of the air he explains as a "motion of percussion," the water descending and forcing up the air, and not a "motion of levity" in the air itself. "The cause of the enclosure of the bubble is for that the appetite to resist separation or discontinuance, which is strong in solids, is also in liquors, though fainter and weaker." "The same reason is of the roundness of the bubble, as well for the skin of water as for the air within. For the air likewise avoideth discontinuance, and therefore casteth itself into a round figure. And for the stop and arrest of the air a little while, it showeth that the air of itself hath little or no appetite of ascending."[3] These notions were not taken direct from the facts: they descended from Aristotle. He differs from Aristotle, however, in his explanation of the colours of birds' feathers.

"Aristotle giveth the cause vainly" that birds are more in the beams of the sun than beasts. "But that is manifestly untrue; for cattle are more in the sun than birds, that live commonly in the woods or in some covert. The true cause is that the excrementitious moisture of living creatures, which maketh as well the feathers in birds as the hair in beasts, passeth in birds through a finer and more delicate strainer than it doth in beasts. For feathers pass through quills, and hair through skin." It is an instance of percolation or filtering: other effects of the same cause being the gums of trees, which are but a fine passage or straining of the juice through the wood and bark, and Cornish Diamonds and Rock Rubies, which are in like manner "fine exudations of stone".[4]

These examples of Bacon's Inductions are taken from the _Sylva_ at random. But the example which best of all illustrates his attitude as a scientific investigator is the remark he makes in the _Novum Organum_ about the Copernican theory. Elsewhere he says that there is nothing to choose between it and the Ptolemaic; and in the _Novum Organum_ (lib. ii. 5) he remarks that "no one can hope to terminate the question whether in diurnal motion it is really the earth or the sky that rotates, unless he shall first have comprehended the nature of spontaneous rotation". That is, we must first find out the _forma_ or formal cause of spontaneous rotation. This is a veritable _instantia crucis_, as fixing Bacon's place in the mediaeval and not in the new world of scientific speculation.

Bacon, in short, in the practice of induction did not advance an inch beyond Aristotle. Rather he retrograded, inasmuch as he failed to draw so clear a line between the respective spheres of Inductive collection of facts and Explanation. There are two sources of general propositions, according to Aristotle, Induction and Nous. By Induction he meant the generalisation of facts open to sense, the summation of observed particulars, the _inductio per enumerationem simplicem_ of the schoolmen. By Nous he meant the Reason or Speculative Faculty, as exercised with trained sagacity by experts. Thus by Induction we gather that all horned animals ruminate. The explanation of this is furnished by the Nous, and the explanation that commended itself to the trained sagacity of his time was that Nature having but a limited amount of hard material and having spent this on the horns, had none left for teeth, and so provided four stomachs by way of compensation.

Bacon's guesses at causes are on the same scientific level with this, only he rather confused matters by speaking of them as if they were inductions from fact, instead of being merely fancies superinduced upon fact. His theory of interpretation, it is true, was so far an advance that he insisted on the necessity of verifying every hypothesis by further appeal to facts, though in practice he himself exercised no such patience and never realised the conditions of verification. Against this, again, must be set the fact that by calling his method induction, and laying so much stress on the collection of facts, he fostered, and, indeed, fixed in the public mind the erroneous idea that the whole work of science consists in observation. The goal of science, as Herschel said, is Explanation, though every explanation must be made to conform to fact, and explanation is only another term for attaining to higher generalisations, higher unities.

The truth is that Induction, if that is the name we use for scientific method, is not, as Reid conceived, an exception to the usual rule of arts in being the invention of one man. Bacon neither invented nor practised it. It was perfected gradually in the practice of men of science. The birthplace of it as a conscious method was in the discussions of the Royal Society of London, as the birthplace of the Aristotelian Logic was in the discussions of the Athenian schools. Its first great triumph was Newton's law of Gravitation. If we are to name it after its first illustrious practitioner, we must call it the Newtonian method, not the Baconian. Newton really stands to the Scientific Method of Explanation as Aristotle stands to the Method of Dialectic and Deduction. He partly made it explicit in his _Regulae Philosophandi_ (1685). Locke, his friend and fellow-member of the Royal Society, who applied the method to the facts of Mind in his _Essay Concerning Human Understanding_ (1691), made it still further explicit in the Fourth Book of that famous work.

It was, however, a century and a half later that an attempt was first made to incorporate scientific method with Logic under the name of Induction, and add it as a new wing to the old Aristotelian building.

This was the work of John Stuart Mill, whose System of Logic, Deductive and Inductive, was first published in 1843.

The genesis of Mill's System of Logic, as of other things, throws light upon its character. And in inquiries into the genesis of anything that man makes we may profitably follow Aristotle's division of causes. The Efficient Cause is the man himself, but we have also to find out the Final Cause, his object or purpose in making the thing, the Material Cause, the sources of his material, and the Formal Cause, the reason why he shaped it as he did. In the case of Mill's system we have to ask: What first moved him to formulate the methods of scientific investigation? Whence did he derive his materials? Why did he give his scientific method the form of a supplement to the old Aristotelian Logic? We cannot absolutely separate the three inquiries, but motive, matter and form each had a traceable influence on the leading features of his System.

First, then, as to his motive. It is a mistake to suppose that Mill's object was to frame an organon that might assist men of science as ordinarily understood in making discoveries. Bacon, his secretary tells us, was wont to complain that he should be forced to be a Workman and a Labourer in science when he thought he deserved to be an Architect in this building. And men of science have sometimes rebuked Mill for his presumption in that, not being himself an investigator in any department of exact science, he should volunteer to teach them their business. But Mill was really guilty of no such presumption. His object, on the contrary, was to learn their method with a view to its application to subjects that had not yet undergone scientific treatment. Briefly stated, his purpose was to go to the practical workers in the exact sciences, Astronomy, Chemistry, Heat, Light, Electricity, Molar and Molecular Physics; ascertain, not so much how they made their discoveries as how they assured themselves and others that their conclusions were sound; and having ascertained their tests of truth and principles of proof, to formulate these tests so that they might be applied to propositions outside the range of the exact sciences, propositions in Politics, Ethics, History, Psychology.

More particularly he studied how scientific men verify, and when they accept as proved, propositions of causation, explanations of the causes of things. In effect, his survey of scientific method was designed to lead up to the Sixth Book in his System, the Logic of the Moral Sciences. There are multitudes of floating endoxes or current opinions concerning man and his concerns, assigning causes for the conduct and character of individuals and of communities. Mill showed himself quite aware that the same modes of investigation may not be practicable, and that it may not be possible, though men are always ready to assign causes with confidence, to ascertain causes with the same degree of certainty: but at least the conditions of exact verification should be the same, and it is necessary to see what they are in order to see how far they can be realised.

That such was Mill's design in the main is apparent on internal evidence, and it was the internal evidence that first struck me. But there is external evidence as well. We may first adduce some essays on the Spirit of the Age, published in the _Examiner_ in 1831, essays which drew from Carlyle the exclamation, "Here is a new Mystic!" These essays have never been republished, but they contain Mill's first public expression of the need for a method in social inquiries. He starts from the Platonic idea that no state can be stable in which the judgment of the wisest in political affairs is not supreme. He foresees danger in the prevalent anarchy of opinion. How is it to be averted? How are men to be brought to accept loyally the judgment of the expert in public affairs? They accept at once and without question the decisions of the specially skilled in the physical sciences. Why is this? For one reason, because there is complete agreement among experts. And why is there this complete agreement? Because all accept the same tests of truth, the same conditions of proof. Is it not possible to obtain among political investigators similar unanimity as to their methods of arriving at conclusions, so as to secure similar respect for their authority?

We need not stop to ask whether this was a vain dream, and whether it must not always be the case that to ensure confidence in a political or moral adviser more is needed than faith in his special knowledge and trained sagacity. Our point is that in 1831 Mill was in search of a method of reasoning in social questions. Opportunely soon after, early in 1832, was published Herschel's _Discourse on the Study of Natural Philosophy_, the first attempt by an eminent man of science to make the methods of science explicit. Mill reviewed this book in the _Examiner_, and there returns more definitely to the quest on which he was bent. "The uncertainty," he says, "that hangs over the very elements of moral and social philosophy proves that the means of arriving at the truth in those sciences are not yet properly understood. And whither can mankind so advantageously turn, in order to learn the proper means and to form their minds to the proper habits, as to that branch of knowledge in which by universal acknowledgment the greatest number of truths have been ascertained and the greatest possible degree of certainty arrived at?"

We learn from Mill himself that he made an attempt about this time, while his mind was full of Herschel's Discourse, to connect a scientific method with the body of the Old Logic. But he could not make the junction to his satisfaction, and abandoned the attempt in despair. A little later, in 1837, upon the appearance of Whewell's _History of the Inductive Sciences_, he renewed it, and this time with happier results. Whewell's _Philosophy of the Inductive Sciences_ was published in 1840, but by that time Mill's system was definitely shaped.

It was, then, to Herschel and Whewell, but especially to the former, that Mill owed the raw materials of his Inductive Method. But why did he desire to concatenate this with the old Logic? Probably because he considered that this also had its uses for the student of society, the political thinker. He had inherited a respect for the old Logic from his father. But it was the point at which he sought to connect the new material with the old, the point of junction between the two, that determined the form of his system. We find the explanation of this in the history of the old Logic. It so happened that Whately's Logic was in the ascendant, and Whately's treatment of Induction gives the key to Mill's.

Towards the end of the first quarter of this century there was a great revival of the study of Logic at Oxford. The study had become mechanical, Aldrich's Compendium, an intelligent but exceedingly brief abstract of the Scholastic Logic, being the text-book beyond which no tutor cared to go. The man who seems to have given new life to the study was a tutor who subsequently became Bishop of Llandaff, Edward Copleston. The first public fruits of the revival begun by him was Whately's article on Logic in the _Encyclopaedia Metropolitana_, published as a separate book in 1827. Curiously enough, one of Whately's most active collaborators in the work was John Henry Newman, so that the common room of Oriel, which Mr. Froude describes as the centre from which emanated the High Church Movement, may also be said to have been the centre from which emanated the movement that culminated in the revolution of Logic.

The publication of Whately's Logic made a great stir. It was reviewed by Mill, then a young man of twenty-one, in the _Westminster Review_ (1828), and by Hamilton, then forty-five years of age, in the _Edinburgh_ (1833). There can be no doubt that it awakened Mill's interest in the subject. A society formed for the discussion of philosophical questions, and called the Speculative Society, met at Grote's house in 1825, and for some years following. Of this society young Mill was a member, and their continuous topic in 1827 was Logic, Whately's treatise being used as a sort of text-book.