impossibilities as these—that two and two should make five; that two straight lines should inclose a space; or that any thing should begin to exist without a cause. I can think of no definition of impossibility comprehensive enough to include all its varieties, except the one which I have given: viz., An impossibility is that, the truth of which would conflict with a complete induction, that is, with the most conclusive evidence which we possess of universal truth.
As to the reputed impossibilities which rest on no other grounds than our ignorance of any cause capable of producing the supposed effects; very few of them are certainly impossible, or permanently incredible. The facts of traveling seventy miles an hour, painless surgical operations, and conversing by instantaneous signals between London and New York, held a high place, not many years ago, among such impossibilities.
205 Not, however, as might at first sight appear, 999 times as much. A complete analysis of the cases shows that (always assuming the veracity of the witness to be ⁹⁄₁₀) in 10,000 drawings, the drawing of No. 79 will occur nine times, and be announced incorrectly once; the credibility, therefore, of the announcement of No. 79 is ⁹⁄₁₀; while the drawing of a white ball will occur nine times, and be announced incorrectly 999 times. The credibility, therefore, of the announcement of white is ⁹⁄₁₀₀₈, and the ratio of the two 1008:10; the one announcement being thus only about a hundred times more credible than the other, instead of 999 times.
206 Supra, book iii., chap. ii., § 3, 4, 5.
207 Mr. Bailey has given the best statement of this theory. “The general name,” he says, “raises up the image sometimes of one individual of the class formerly seen, sometimes of another, not unfrequently of many individuals in succession; and it sometimes suggests an image made up of elements from several different objects, by a latent process of which I am not conscious.” (Letters on the Philosophy of the Human Mind, 1st series, letter 22.) But Mr. Bailey must allow that we carry on inductions and ratiocinations respecting the class, by means of this idea or conception of some one individual in it.
This is all I require. The name of a class calls up some idea, through which we can, to all intents and purposes, think of the class as such, and not solely of an individual member of it.
208 I have entered rather fully into this question in chap. xvii. of _An Examination of Sir William Hamilton’s Philosophy_, headed “The Doctrine of Concepts or General Notions,” which contains my last views on the subject.
209 Other examples of inappropriate conceptions are given by Dr. Whewell (_Phil. Ind. Sc._ ii., 185) as follows: “Aristotle and his followers endeavored in vain to account for the mechanical relation of forces in the lever, by applying the _inappropriate_ geometrical conceptions of the properties of the circle: they failed in explaining the _form_ of the luminous spot made by the sun shining through a hole, because they applied the _inappropriate_ conception of a circular _quality_ in the sun’s light: they speculated to no purpose about the elementary composition of bodies, because they assumed the _inappropriate_ conception of _likeness_ between the elements and the compound, instead of the genuine notion of elements merely _determining_ the qualities of the compound.” But in these cases there is more than an inappropriate conception; there is a false conception; one which has no prototype in nature, nothing corresponding to it in facts. This is evident in the last two examples, and is equally true in the first; the “properties of the circle” which were referred to, being purely fantastical. There is, therefore, an error beyond the wrong choice of a principle of generalization; there is a false assumption of matters of fact. The attempt is made to resolve certain laws of nature into a more general law, that law not being one which, though real, is inappropriate, but one wholly imaginary.
210 Professor Bain.
211 This sentence having been erroneously understood as if I had meant to assert that belief is nothing but an irresistible association, I think it necessary to observe that I express no theory respecting the ultimate analysis either of reasoning or of belief, two of the most obscure points in analytical psychology. I am speaking not of the powers themselves, but of the previous conditions necessary to enable those powers to exert themselves: of which conditions I am contending that language is not one, senses and association being sufficient without it. The irresistible association theory of belief, and the difficulties connected with the subject, have been discussed at length in the notes to the new edition of Mr. James Mill’s _Analysis of the Phenomena of the Human Mind_.
212 Mr. Bailey agrees with me in thinking that whenever “from something actually present to my senses, conjoined with past experience, I feel satisfied that something has happened, or will happen, or is happening, beyond the sphere of my personal observation,” I may with strict propriety be said to reason: and of course to reason inductively, for demonstrative reasoning is excluded by the circumstances of the case. (_The Theory of Reasoning_, 2d ed., p.
27.)
216 “E, ex, extra, extraneus, étranger, stranger.”
Another etymological example sometimes cited is the derivation of the English _uncle_ from the Latin _avus_. It is scarcely possible for two words to bear fewer outward marks of relationship, yet there is but one step between them, _avus_, _avunculus_, _uncle_. So _pellegrino_, _pilgrim_. Professor Bain gives some apt examples of these transitions of meaning. “The word ‘damp’ primarily signified moist, humid, wet. But the property is often accompanied with the feeling of cold or chilliness, and hence the idea of cold is strongly suggested by the word. This is not all. Proceeding upon the superadded meaning, we speak of damping a man’s ardor, a metaphor where the cooling is the only circumstance concerned; we go on still further to designate the iron slide that shuts off the draft of a stove, ‘the damper,’ the primary meaning being now entirely dropped.
‘Dry,’ in like manner, through signifying the absence of moisture, water, or liquidity, is applied to sulphuric acid containing water, although not thereby ceasing to be a moist, wet, or liquid substance.” So in the phrases, dry sherry, or Champagne.
“‘Street,’ originally a paved way, with or without houses, has been extended to roads lined with houses, whether paved or unpaved.
‘Impertinent’ signified at first irrelevant, alien to the purpose in hand: through which it has come to mean, meddling, intrusive, 217 Pp. 226, 227.
220 Though no such evil consequences as take place in these instances are likely to arise from the modern freak of writing _sanatory_ instead of sanitary, it deserves notice as a charming specimen of pedantry ingrafted upon ignorance. Those who thus undertake to correct the spelling of the classical English writers, are not aware that the meaning of _sanatory_, if there were such a word in the language, would have reference not to the preservation of health, but to the cure of disease.
_ 223 History of Scientific Ideas_, ii., 111–113.
_ 225 History of Scientific Ideas_, ii., 120–122.
228 Dr. Whewell, in his reply (_Philosophy of Discovery_, p. 270) says that he “stopped short of, or rather passed by, the doctrine of a series of organized beings,” because he “thought it bad and narrow philosophy.” If he did, it was evidently without understanding this form of the doctrine; for he proceeds to quote a passage from his “History,” in which the doctrine he condemns is designated as that of “a mere linear progression in nature, which would place each genus in contact only with the preceding and succeeding ones.” Now the series treated of in the text agrees with this linear progression in nothing whatever but in being a progression.
229 Supra, p. 137.
232 The author of one of the Bridgewater Treatises has fallen, as it seems to me, into a similar fallacy when, after arguing in rather a curious way to prove that matter may exist without any of the known properties of matter, and may therefore be changeable, he concludes that it can not be eternal, because “eternal (passive) existence necessarily involves incapability of change.” I believe it would be difficult to point out any other connection between the facts of eternity and unchangeableness, than a strong association between the two ideas. Most of the _a priori_ arguments, both religious and anti-religious, on the origin of things, are fallacies drawn from the same source.
also _Examination of Sir William Hamilton’s Philosophy_, chap. vi.
and elsewhere.
234 It seems that this doctrine was, before the time I have mentioned, disputed by some thinkers. Dr. Ward mentions Scotus, Vasquez, Biel, Francis Lugo, and Valentia.
235 I quote this passage from Playfair’s celebrated _Dissertation on the Progress of Mathematical and Physical Science_.
236 This statement I must now correct, as too unqualified. The maxim in question was maintained with full conviction by no less an authority than Sir William Hamilton. See my _Examination_, chap. xxiv.
_ 237 Nouveaux Essais sur l’Entendement Humain—Avant-propos._ (Œuvres, 238 This doctrine also was accepted as true, and conclusions were grounded on it, by Sir William Hamilton. See _Examination_, chap.
xxiv.
239 Not that of Leibnitz, but the principle commonly appealed to under that name by mathematicians.
243 Supra, book iii., chap. vii., § 4.
244 It is hardly needful to remark that nothing is here intended to be said against the possibility at some future period of making gold—by first discovering it to be a compound, and putting together its different elements or ingredients. But this is a totally different idea from that of the seekers of the grand arcanum.
252 Ibid., p. 28.
253 Ibid., p. 62.
_ 256 Elements of the Philosophy of the Mind_, vol. ii., chap. 4, sect.
5.
257 “Thus Fourcroy,” says Dr. Paris, “explained the operation of mercury by its specific gravity, and the advocates of this doctrine favored the general introduction of the preparations of iron, especially in scirrhus of the spleen or liver, upon the same hypothetical principle; for, say they, whatever is most forcible in removing the obstruction must be the most proper instrument of cure: such is steel, which, besides the attenuating power with which it is furnished, has still a greater force in this case from the gravity of its particles, which, being seven times specifically heavier than any vegetable, acts in proportion with a stronger impulse, and therefore is a more powerful deobstruent. This may be taken as a specimen of the style in which these mechanical physicians reasoned sometimes guilty of the argument _à dicto secundum quid ad dictum simpliciter_: it is his business to do for his client all that his client might _honestly_ do for himself. Is not the word in italics frequently omitted? _Might_ any man honestly try to do for himself all that counsel frequently try to do for him? We are often reminded of the two men who stole the leg of mutton; one could swear he had not got it, the other that he had not taken it. The counsel is doing his duty by his client, the client has left the matter to his counsel. Between the unexecuted intention of the client, and the unintended execution of the counsel, there may be a wrong done, and, if we are to believe the usual maxims, no wrong-doer.”
The same writer justly remarks (p. 251) that there is a converse fallacy, _à dicto simpliciter ad dictum secundum quid_, called by the scholastic logicians _fallacia accidentis_; and another which may be called _à dicto secundum quid ad dictum secundum alterum quid_ (p. 265). For apt instances of both, I must refer the reader to Mr. De Morgan’s able chapter on Fallacies.
263 An example of this fallacy is the popular error that _strong_ drink must be a cause of _strength_. There is here fallacy within fallacy; for granting that the words “strong” and “strength” were not (as they are) applied in a totally different sense to fermented liquors and to the human body, there would still be involved the error of supposing that an effect must be like its cause; that the conditions of a phenomenon are likely to resemble the phenomenon itself; which we have already treated of as an _a priori_ fallacy of the first rank. As well might it be supposed that a strong poison will make the person who takes it strong.
264 In his later editions, Archbishop Whately confines the name of Petitio Principii “to those cases in which one of the premises either is manifestly the same in sense with the conclusion, or is actually proved from it, or is such as the persons you are addressing are not likely to know, or to admit, except as an inference from the conclusion; as, _e.g._, if any one should infer the authenticity of a certain history, from its recording such and such facts, the reality of which rests on the evidence of that history.”
265 No longer even a probable hypothesis, since the establishment of the atomic theory; it being now certain that the integral particles of different substances gravitate unequally. It is true that these particles, though real _minima_ for the purposes of chemical combination, may not be the ultimate particles of the substance; and this doubt alone renders the hypothesis admissible, even as an hypothesis.
267 “And coxcombs vanquish Berkeley with a grin.”
268 Some arguments and explanations, supplementary to those in the text, will be found in _An Examination of Sir William Hamilton’s Philosophy_, chap. xxvi.
270 When this chapter was written, Professor Bain had not yet published even the first part (“The Senses and the Intellect”) of his profound Treatise on the Mind. In this the laws of association have been more comprehensively stated and more largely exemplified than by any previous writer; and the work, having been completed by the publication of “The Emotions and the Will,” may now be referred to as incomparably the most complete analytical exposition of the mental phenomena, on the basis of a legitimate Induction, which has yet been produced. More recently still, Mr. Bain has joined with me in appending to a new edition of the “Analysis,” notes intended to bring up the analytic science of Mind to its latest improvements.
Many striking applications of the laws of association to the explanation of complex mental phenomena are also to be found in Mr.
271 In the case of the moral sentiments the place of direct experiment is to a considerable extent supplied by historical experience, and we are able to trace with a tolerable approach to certainty the particular associations by which those sentiments are engendered.
This has been attempted, so far as respects the sentiment of justice, in a little work by the present author, entitled _Utilitarianism_.
272 The most favorable cases for making such approximate generalizations are what may be termed collective instances; where we are fortunately enabled to see the whole class respecting which we are inquiring in action at once, and, from the qualities displayed by the collective body, are able to judge what must be the qualities of the majority of the individuals composing it. Thus the character of a nation is shown in its acts as a nation; not so much in the acts of its government, for those are much influenced by other causes; but in the current popular maxims, and other marks of the general direction of public opinion; in the character of the persons or writings that are held in permanent esteem or admiration; in laws and institutions, so far as they are the work of the nation itself, or are acknowledged and supported by it; and so forth. But even here there is a large margin of doubt and uncertainty. These things are liable to be influenced by many circumstances; they are partially determined by the distinctive qualities of that nation or body of persons, but partly also by external causes which would influence any other body of persons in the same manner. In order, therefore, to make the experiment really complete, we ought to be able to try it without variation upon other nations: to try how Englishmen would act or feel if placed in the same circumstances in which we have supposed Frenchmen to be placed; to apply, in short, the Method of Differences as well as that of Agreement. Now these experiments we can not try, nor even approximate to.
273 “To which,” says Dr. Whewell, “we may add, that it is certain, from the history of the subject, that in that case the hypothesis would never have been framed at all.”
Dr. Whewell (_Philosophy of Discovery_, pp. 277–282) defends Bacon’s rule against the preceding strictures. But his defense consists only in asserting and exemplifying a proposition which I had myself stated, viz., that though the largest generalizations may be the earliest made, they are not at first seen in their entire generality, but acquire it by degrees, as they are found to explain one class after another of phenomena. The laws of motion, for example, were not known to extend to the celestial regions, until the motions of the celestial bodies had been deduced from them.
This, however, does not in any way affect the fact, that the middle principles of astronomy, the central force, for example, and the law of the inverse square, could not have been discovered, if the laws of motion, which are so much more universal, had not been known first. On Bacon’s system of step-by-step generalization, it would be impossible in any science to ascend higher than the empirical laws; a remark which Dr. Whewell’s own Inductive Tables, referred to by him in support of his argument, amply bear out.
_ 274 Supra_, page 317 to the end of the chapter.
_ 277 Essays on some Unsettled Questions of Political Economy_, pp.
137–140.
278 The quotations in this paragraph are from a paper written by the author, and published in a periodical in 1834.
_ 279 Cours de Philosophie Positive_, iv., 325–29.
280 Since reprinted entire in _Dissertations and Discussions_, as the concluding paper of the first volume.
281 Written and first published in 1840.
282 This great generalization is often unfavorably criticised (as by Dr.
Whewell, for instance) under a misapprehension of its real import.
The doctrine, that the theological explanation of phenomena belongs only to the infancy of our knowledge of them, ought not to be construed as if it was equivalent to the assertion, that mankind, as their knowledge advances, will necessarily cease to believe in any kind of theology. This was M. Comte’s opinion; but it is by no means implied in his fundamental theorem. All that is implied is, that in an advanced state of human knowledge, no other Ruler of the World will be acknowledged than one who rules by universal laws, and does not at all, or does not unless in very peculiar cases, produce events by special interpositions. Originally all natural events were ascribed to such interpositions. At present every educated person rejects this explanation in regard to all classes of phenomena of which the laws have been fully ascertained; though some have not yet reached the point of referring all phenomena to the idea of Law, but believe that rain and sunshine, famine and pestilence, victory and defeat, death and life, are issues which the Creator does not leave to the operation of his general laws, but reserves to be decided by express acts of volition. M. Comte’s theory is the negation of this doctrine.
Dr. Whewell equally misunderstands M. Comte’s doctrine respecting the second or metaphysical stage of speculation. M. Comte did not mean that “discussions concerning ideas” are limited to an early stage of inquiry, and cease when science enters into the positive stage. (_Philosophy of Discovery_, pp. 226 et seq.) In all M.
Comte’s speculations as much stress is laid on the process of clearing up our conceptions as on the ascertainment of facts. When M. Comte speaks of the metaphysical stage of speculation, he means the stage in which men speak of “Nature” and other abstractions as if they were active forces, producing effects; when Nature is said to do this, or forbid that; when Nature’s horror of a vacuum, offered as explanations of phenomena; when the qualities of things were mistaken for real entities dwelling in the things; when the phenomena of living bodies were thought to be accounted for by being referred to a “vital force;” when, in short, the abstract names of phenomena were mistaken for the causes of their existence. In this sense of the word it can not be reasonably denied that the metaphysical explanation of phenomena, equally with the theological, gives way before the advance of real science.
That the final, or positive stage, as conceived by M. Comte, has been equally misunderstood, and that, notwithstanding some expressions open to just criticism, M. Comte never dreamed of denying the legitimacy of inquiry into all causes which are accessible to human investigation, I have pointed out in a former place.
284 I have been assured by an intimate friend of Mr. Buckle that he would not have withheld his assent from these remarks, and that he never intended to affirm or imply that mankind are not progressive in their moral as well as in their intellectual qualities. “In dealing with his problem, he availed himself of the artifice resorted to by the Political Economist, who leaves out of consideration the generous and benevolent sentiments, and founds his science on the proposition that mankind are actuated by acquisitive propensities alone,” not because such is the fact, but because it is necessary to begin by treating the principal influence as if it was the sole one, and make the due corrections afterward. “He desired to make abstraction of the intellect as the determining and dynamical element of the progression, eliminating the more dependent set of conditions, and treating the more active one as if it were an entirely independent variable.”
The same friend of Mr. Buckle states that when he used expressions which seemed to exaggerate the influence of general at the expense of special causes, and especially at the expense of the influence of individual minds, Mr. Buckle really intended no more than to affirm emphatically that the greatest men can not effect great changes in human affairs unless the general mind has been in some considerable degree prepared for them by the general circumstances of the age; a truth which, of course, no one thinks of denying. And there certainly are passages in Mr. Buckle’s writings which speak of the influence exercised by great individual intellects in as strong terms as could be desired.
285 Essay on Dryden, in Miscellaneous Writings, i., 186.
286 In the _Cornhill Magazine_ for June and July, 1861.
287 It is almost superfluous to observe, that there is another meaning of the word Art, in which it may be said to denote the poetical department or aspect of things in general, in contradistinction to the scientific. In the text, the word is used in its older, and I hope, not yet obsolete sense.
288 Professor Bain and others call the selection from the truths of science made for the purposes of an art, a Practical Science, and confine the name Art to the actual rules.
289 The word Teleology is also, but inconveniently and improperly, employed by some writers as a name for the attempt to explain the phenomena of the universe from final causes.
290 For an express discussion and vindication of this principle, see the little volume entitled “Utilitarianism.”