System of Logic.

Mill's System of Logic was published in 1843, and ran through many editions. The third (1850) and the eighth (1872) editions, especially, were thoroughly revised and supplemented with new and controversial material. It is his only systematic philosophical treatise. In spite of Hobbe's treatise, and of the suggestive discussions in the third book of Locke's Essay, the greater English philosophers almost seem to have conspired to neglect the theory of logic. Logic kept its place as an academic study, but on traditional lines; Aristotle was supposed to have said the last word on it, and that last word was enshrined in scholastic manuals. English thought, however, was beginning to emerge from this stage. Richard Whately had written a text-book, Elements of Logic (1826), which gave considerable impetus to the study, and Hamilton's more comprehensive researches had begun. Mill first worked out his theory of terms, propositions, and the syllogism; he then set the book aside for five years. When he returned to it and focused on the inductive process, he found material John Herschel's Discourse on the Study of Natural Philosophy (1830), and William Whewell's History of the Inductive Sciences (1837). After his theory of induction was substantially complete, he became acquainted with, and derived stimulus and assistance from, the first two volumes of Comte's Cours de Philosophie Positive (1830). These were the chief influences on his work.
The reputation of Mill's Logic was largely due to his analysis of inductive proof. He provided the empirical sciences with a set of formula and criteria which might serve the same purpose for them as the time-worn formulae of the syllogism had served for arguments that proceeded from general principles. Mill's work is not merely a logic in the limited sense of that term which had become customary in England. It is also a theory of knowledge such as Locke and Hume provide. Mill's account is made more precise by its reference to the question of proof or evidence. Mill formulates five guiding methods of inductionthe method of agreement, that of difference, the joint or double method of agreement and difference, the method of residues, and that of concomitant variations. The common feature of these methods, the one real method of scientific inquiry, is that of elimination. All the other methods are thus subordinate to the method of difference. Here we have a case of the occurrence of the phenomenon under investigation and a case of its nonoccurrence, these cases having every circumstance in common, save one, that one occurring only in the former; and we are warranted in concluding that this circumstance, in which alone the two cases differ, is either the cause or a necessary part of the cause of the phenomenon.
It is only in the simpler cases of casual connection, however, that we can apply these direct methods of observation and experiment. In the more complex cases, we have to employ the inductive method, which consists of three operations: induction, ratiocination or deduction, and verification.
To the Deductive Method, thus characterized in its three constituent partsInduction, Ratiocination, and Verificationthe human mind is indebted for its most conspicuous triumphs in the investigation of nature. To it we owe all the theories by which vast and complicated phenomena are embraced under a few simple laws, which, considered as the laws of those great phenomena, could never have been detected by their direct study. (Logic, Book III. Chapter XI. Section 3).
We deduce the law or cause of a complex effect from the laws of the separate causes whose concurrence gives rise to it. For example, "the mechanical and the organized body and the medium in which it subsists, together with the peculiar vital laws of the different tissues constituting the organic structure," afford the clue to "the laws on which the phenomena of life depend" (Logic, III. XI. I). But these "laws of the different causes" must first be ascertained by direct induction, and finally verified, as comparison with the facts of the case. Thus the entire process is based on induction.
To warrant reliance on the general conclusions arrived at by deduction, these conclusions must be found, on careful comparison, to accord with the results of direct observation wherever it can be had. . . Thus it was very reasonably deemed an essential requisite of any true theory of the causes of the celestial motions, that it should lead by deduction to Kepler's laws; which, accordingly, the Newtonian theory did. (Ibid, III. XI. 3).
The validity of the entire inductive process is thus clearly seen to depend upon the validity of its underlying assumption, the law of causation itself. Assuming that every phenomenon has a cause, or invariable and unconditional antecedent, we investigate the problem of causation in detail. Is this fundamental assumption itself valid? Mill cannot avail himself of the theory that the law of universal causation is an intuition of reason or an a priori and transcendental principle. For him the only possible view is that
the belief we entertain in the university, throughout nature, of the law of cause and effect, is itself an instance of induction. . . We arrive at this universal law by generalization from many laws of inferior generality. We should never have had the notion of causation (in the philosophical meaning of the term) as a condition of all phenomena, unless many cases of causation, or, in other words, many partial uniformities of sequence, had previously become familiar. The more obvious of the particular uniformities suggest, and give evidence of, the general uniformity, once established, enables us to prove the remainder of the particular uniformities of which it is made up. (Logic, III. XXI. 4)
These early inductions, which result in the law of universal causation, cannot belong to the same type as those rigorous inductions which conform to the canons of scientific induction and presuppose the law of universal causation; they belong to "the loose and uncertain mode of induction per enumeration simplicem." How, then, can a process whose basis is thus loose and uncertain have any certain validity? Mill's answer is that induction by simple enumeration, or "generalisation of an observed fact from the mere absence of any known instance to the contrary," as contrasted with the critical induction of science, is a valid, though a fallible process, which must precede the less fallible forms of the inductive process, and that "the precariousness of the method of simple enumeration is in an inverse ratio to the largeness of the generalization."
As the sphere widens, this unscientific methods becomes less and less liable to mislead; and the most universal class of truths, the law of causation, for instance, and the principles of number and geometry, are duly and satisfactorily proved by that method alone, nor are they susceptible of any other proof.
The universality of the law of causation, as it is an induction from our experience, does not extend to "circumstances unknown to us, and beyond the possible range of our experience."
In distant parts of the stellar regions, where the phenomena may be entirely unlike those with which we are acquainted, it would be folly to affirm confidently that this general law prevails, any more than those special ones which we have found to hold universally on our own planet. The uniformity in the succession of events, otherwise called the law of causation, must by received, not as a law of the universe, by of that portion of it only which is within the range of our means of sure observation, with a reasonable degree of extension to adjacent cases. To extend it further is to make a supposition without evidence, and to which, in the absence of any ground from experience for estimating its degree of probability, it would be idle to attempt to assign any. (Logic, III. XXI. 4)
There is no difficulty in conceiving "that in someone, for instance, of the many firmaments into which sidereal astronomy now divides the universe, events may succeed one another at random without any fixed law; nor can anything in our experience, or in our mental nature, constitute a sufficient, or indeed any, reason for believing that this is nowhere the case" (Ibid., III. XXI. 4).
The appearance of paradox in the view that the law of causation is at once the presupposition and the result of induction disappears, according to Mill, with "the old theory of reasoning, which supposes the universal truth, or major premise, in a ratiocination, to be the real proof of the particular truths which are ostensibly inferred from it." His own view is that "the major premise is not the proof of the conclusion, but is itself proved, along with the conclusion, from the same evidence." The old theory implies that the syllogism is a petitio principii, since the conclusion the conclusion which is supposed to be proved is already contained in the major premise; if we know that all men are mortal, we know, and do not require to prove, that Socratesis mortal. "No reasoning from generals to particulars can, as such, prove anything, since from a general principle we cannot infer any particulars, but those which the principle itself assumes as known" (Ibid., II. III. 2). The only use of the syllogism is to convict your opponent of inconsistency; it cannot lead us from the known to the unknown. In reality the major premise is a register of previous inductions and a short formula for making more. "The conclusion is not an inference drawn from the formula, but an inference drawn according to the formula; the real logical antecedent or premise being the particular facts from which the general proposition was collected by induction" (Logic, II. III. 4). The major premise is merely a shorthand note, to assist the memory. "The inference is finished when we have asserted that all men are mortal. What remains to be performed afterwards is merely deciphering our own notes." The mistake of the traditional view is,
that of referring a person to his own notes for the origin of his knowledge. If a person is asked a question, and is at the moment unable to answer it, he may refresh his memory by turning to a memorandum which he carries about with him. But if he would scarcely answer, because it was set down in his notebook: unless the book was written, like the Koran, with a quill from the wing of the angel Gabriel. (Ibid., III. III. 3)
All inference is from particulars to particulars; the syllogistic process is only an interpretation of our notes of previous inferences. "If we had sufficiently capacious memories, and a sufficient power of maintaining order among a huge mass of details, the reasoning could go on without any general propositions; they are mere formulae for inferring particulars from particulars" (Ibid., III. IV. 3).
Syllologistic reasoning is thus a circuitous way of reaching a conclusion which might have been reached directly, like going up a hill and down again when we might have traveled along the level road. There is no reason why we should be compelled to take the high priori road except by the arbitrary fiat of logicians. "Not only may we reason from particulars to particulars without passing through generals, but we perpetually do so reason. All our earliest inferences are of this nature" (Ibid., II. III. 3). Mill, however, acknowledges "the immense advantage, in point of security for correctness, which is gained by interposing this step between the real evidence and the conclusion," the importance of "the appeal to former experience in the major premise of the syllogism" (IBid., II. III. 6). When we say that Socrates is mortal because he is a man, and all men are mortal, we assert that because he resembles that other individuals in the attributes connoted by the term man, he resembles them further in the attribute morality. "Whether, from the attributes in which Socrates resembles those men who have heretofore died, it is allowable to infer that he resembles them also in being mortal, is a question of Induction" (Logic, II. III. 7). The major premise is the record and reminder that we have made that induction, and are therefore not merely warranted, but required, to apply it in particular case before us.
"The chief strength of this false philosophy {intuitionism} in morals, politics, and religion," Mill remarks in his Autobiography,
lies in the appeal which it is accustomed to make to the evidence of mathematics and of the cognate branches of physical science. To expel it from these, is to drive it from its stronghold: and because this had never been effectually done, the intuitive school, even after what my father had written in his Analysis of Mind, had in appearance, and as far as published writings were concerned, on the whole the best of the argument. In attempting to clear up the real nature of the evidence of mathematical and physical truths, the System of Logic met the intuitive philosophers on ground on which they had previously been deemed unassailable; and gave its own explanation, from experience and association, of that peculiar character of what are called necessary truths, which is adduced as proof that their evidence must come from a deeper source than experience. (Autobiography, P. 226)
The peculiar certainty and necessity attributed to these truths is, he argues, "an illusion, in order to sustain which, it is necessary to suppose that those truths relate to, and express the properties of purely imaginary objects." As a matter of fact, the truths of geometry do not hold, except approximately, of the real world, but only of that imaginary world which corresponds to its initial definitions. The truth is that geometry
is built on hypothesis; that it owes to this alone the peculiar certainty supposed to distinguish it; and that in any science whatever, by reasoning from a set of hypotheses, we may obtain a body of conclusions as certain as those of geometry, that is, as strictly in accordance with the hypotheses, and as irresistibly compelling assent, on condition that those hypotheses are true. (Logic, II. V. I)
As for the axioms which, together with the definition, form the basis of geometrical reasoning, they are in reality "experimental truths, generalizations from observation." The great argument for their a priori character is that their opposites are inconceivable. But conceivability "has very little to do with the possibility of the thing in itself, but is in truth very much an affair of accident, and depends on the past history and habits of our own minds" (Ibid., II. V. 6). It is the effect of habitual association, itself the result of our earliest and most widely based inductions from experience; it is an acquired incapacity which can hardly, but be mistaken for a natural one, an experimental truth which can hardly, but be mistaken for a necessary one.
It is in the application of the inductive and psychological method to social and political problems that Mill sees the crowning achievement of scientific investigation. This application has yet to be made; the "German Coleridgian school" were "the first (except a solitary thinker here and there) who inquired with any comprehensiveness or depth, into the inductive laws of the existence and growth of human society" (Dissertations, I. 425). To the consideration of this new science of Ethology, or the study of the causes influencing the formation of national character, the final book of the Logic is devoted. In thus seeking to inaugurate a scientific Sociology, Mill was undoubtedly influenced by Comte, but he was also proceeding on the familiar lines of the Utilitarians, who always regarded character as the product of circumstances, and looked to education to effect the transition from the present unsatisfactory state of things to one more in accordance with their social ideal. The indefinite modifiability of human nature by circumstances is the working hypothesis of the school; all that Mill adds is the demand that social life be conducted on scientific principles. It is significant that Mill finally abandoned the intention to construct the scheme of such a science, and devoted his energies to the writing of his Political Economy, published five years after the Logic, in 1848. It would be difficult to reconcile the view of the growth of character implied in the desiderated Ethology with his insistence upon the importance of individuality, and his protest against the interference of society with the liberty of the individual, in the essay on Liberty, published in 1859.