Logic, Inductive and Deductive

by William Minto

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 mediæval 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 mediæval 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 Regulæ 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?"