Bain in the opinion that the resemblance of what we have not experienced to what we have, is, by a law of our nature, presumed through the mere energy of the idea, before experience has proved it. This _psychological_ truth, however, is not, as Dr. Ward when criticising Mr. Bain appears to think, inconsistent with the _logical_ truth that experience does prove it. The proof comes after the presumption, and consists in its invariable _verification_ by experience when the experience arrives. The fact which while it was future could not be observed, having as yet no existence, is always, when it becomes present and _can_ be observed, found conformable to the past.
Dr. M'Cosh maintains (_Examination of Mr. J. S. Mill's Philosophy_, p. 257) that the uniformity of the course of nature is a different thing from the law of causation; and while he allows that the former is only proved by a long continuance of experience, and that it is not inconceivable nor necessarily incredible that there may be worlds in which it does not prevail, he considers the law of causation to be known intuitively. There is, however, no other uniformity in the events of nature than that which arises from the law of causation: so long therefore as there remained any doubt that the course of nature was uniform throughout, at least when not modified by the intervention of a new (supernatural) cause, a doubt was necessarily implied, not indeed of the reality of causation, but of its universality. If the uniformity of the course of nature has any exceptions-if any events succeed one another without fixed laws-to that extent the law of causation fails; there are events which do not depend on causes.
189 Book i., chap. vii.
190 In some cases, a Kind is sufficiently identified by some one remarkable property: but most commonly several are required; each property considered singly, being a joint property of that and of other Kinds. The color and brightness of the diamond are common to it with the paste from which false diamonds are made; its octohedral form is common to it with alum, and magnetic iron ore; but the color and brightness and the form together, identify its Kind: that is, are a mark to us that it is combustible; that when burned it produces carbonic acid; that it can not be cut with any known substance; together with many other ascertained properties, and the fact that there exist an indefinite number still unascertained.
191 This doctrine of course assumes that the allotropic forms of what is chemically the same substance are so many different Kinds; and such, in the sense in which the word Kind is used in this treatise, they really are.
192 Professor Bain (Logic, ii., 13) mentions two empirical laws, which he considers to be, with the exception of the law connecting Gravity with Resistance to motion, "the two most widely operating laws as yet discovered whereby two distinct properties are conjoined throughout substances generally." The first is, "a law connecting Atomic Weight and Specific Heat by an inverse proportion. For equal weights of the simple bodies, the atomic weight multiplied by a number expressing the specific heat, gives a nearly uniform product.
The products, for all the elements, are near the constant number 6."
The other is a law which obtains "between the specific gravity of substances in the gaseous state, and the atomic weights. The relationship of the two numbers is in some instances equality; in other instances the one is a multiple of the other."
Neither of these generalizations has the smallest appearance of being an ultimate law. They point unmistakably to higher laws. Since the heat necessary to raise to a given temperature the same weight of different substances (called their specific heat) is inversely as their atomic weight, that is, directly as the number of atoms in a given weight of the substance, it follows that a single atom of every substance requires the same amount of heat to raise it to a given temperature; a most interesting and important law, but a law of causation. The other law mentioned by Mr. Bain points to the conclusion, that in the gaseous state all substances contain, in the same space, the same number of atoms; which, as the gaseous state suspends all cohesive force, might naturally be expected, though it could not have been positively assumed. This law may also be a result of the mode of action of causes, namely, of molecular motions. The cases in which one of the numbers is not identical with the other, but a multiple of it, may be explained on the nowise unlikely supposition, that in our present estimate of the atomic weights of some substances, we mistake two, or three, atoms for one, or one for several.
193 Dr. M'Cosh (p. 324 of his book) considers the laws of the chemical composition of bodies as not coming under the principle of Causation; and thinks it an omission in this work not to have provided special canons for their investigation and proof. But every case of chemical composition is, as I have explained, a case of causation. When it is said that water is composed of hydrogen and oxygen, the affirmation is that hydrogen and oxygen, by the action on one another which they exert under certain conditions, _generate_ the properties of water. The Canons of Induction, therefore, as laid down in this treatise, are applicable to the case. Such special adaptations as the Inductive methods may require in their application to chemistry, or any other science, are a proper subject for any one who treats of the logic of the special sciences, as Professor Bain has done in the latter part of his work; but they do not appertain to General Logic.
Dr. M'Cosh also complains (p. 325) that I have given no canons for those sciences in which "the end sought is not the discovery of Causes or of Composition, but of Classes; that is, Natural Classes."
Such canons could be no other than the principles and rules of Natural Classification, which I certainly thought that I had expounded at considerable length. But this is far from the only instance in which Dr. M'Cosh does not appear to be aware of the contents of the books he is criticising.
194 Mr. De Morgan, in his _Formal Logic_, makes the just remark, that from two such premises as Most A are B, and Most A are C, we may infer with certainty that some B are C. But this is the utmost limit of the conclusions which can be drawn from two approximate generalizations, when the precise degree of their approximation to universality is unknown or undefined.
_ 195 Rationale of Judicial Evidence_, vol. iii., p. 224.
196 The evaluation of the chances in this statement has been objected to by a mathematical friend. The correct mode, in his opinion, of setting out the possibilities is as follows. If the thing (let us call it T) which is both an A and a C, is a B, something is true which is only true twice in every thrice, and something else which is only true thrice in every four times. The first fact being true eight times in twelve, and the second being true six times in every eight, and consequently six times in those eight; both facts will be true only six times in twelve. On the other hand, if T, although it is both an A and a C, is not a B, something is true which is only true once in every thrice, and something else which is only true once in every four times. The former being true four times out of twelve, and the latter once in every four, and therefore once in those four; both are only true in one case out of twelve. So that T is a B six times in twelve, and T is not a B, only once: making the comparative probabilities, not eleven to one, as I had previously made them, but six to one.
In the last edition I accepted this reasoning as conclusive. More attentive consideration, however, has convinced me that it contains a fallacy.
The objector argues, that the fact of A's being a B is true eight times in twelve, and the fact of C's being a B six times in eight, and consequently six times in those eight; both facts, therefore, are true only six times in every twelve. That is, he concludes that because among As taken indiscriminately only eight out of twelve are Bs and the remaining four are not, it must equally hold that four out of twelve are not Bs when the twelve are taken from the select portion of As which are also Cs. And by this assumption he arrives at the strange result, that there are fewer Bs among things which are both As and Cs than there are among either As or Cs taken indiscriminately; so that a thing which has both chances of being a B, is less likely to be so than if it had only the one chance or only the other.
The objector (as has been acutely remarked by another correspondent) applies to the problem under consideration, a mode of calculation only suited to the reverse problem. Had the question been-If two of every three Bs are As and three out of every four Bs are Cs, how many Bs will be both As and Cs, his reasoning would have been correct. For the Bs that are both As and Cs must be fewer than either the Bs that are As or the Bs that are Cs, and to find their number we must abate either of these numbers in the ratio due to the other. But when the problem is to find, not how many Bs are both As and Cs, but how many things that are both As and Cs are Bs, it is evident that among these the proportion of Bs must be not less, but greater, than among things which are only A, or among things which are only B.
The true theory of the chances is best found by going back to the scientific grounds on which the proportions rest. The degree of frequency of a coincidence depends on, and is a measure of, the frequency, combined with the efficacy, of the causes in operation that are favorable to it. If out of every twelve As taken indiscriminately eight are Bs and four are not, it is implied that there are causes operating on A which tend to make it a B, and that these causes are sufficiently constant and sufficiently powerful to succeed in eight out of twelve cases, but fail in the remaining four. So if of twelve Cs, nine are Bs and three are not, there must be causes of the same tendency operating on C, which succeed in nine cases and fail in three. Now suppose twelve cases which are both As and Cs. The whole twelve are now under the operation of both sets of causes. One set is sufficient to prevail in eight of the twelve cases, the other in nine. The analysis of the cases shows that six of the twelve will be Bs through the operation of both sets of causes; two more in virtue of the causes operating on A; and three more through those operating on C, and that there will be only one case in which all the causes will be inoperative. The total number, therefore, which are Bs will be eleven in twelve, and the evaluation in the text is correct.
197 Supra, book i., chap. v.
198 Supra, book i., chap. v., -- 1, and book ii., chap, v., -- 5.
199 The axiom, "Equals subtracted from equals leave equal differences,"
may be demonstrated from the two axioms in the text. If A = _a_ and B = _b_, A-B = _a-b_. For if not, let A-B = _a-b+c_. Then since B = _b_, adding equals to equals, A = _a+c_. But A = _a_. Therefore _a = a+c_, which is impossible.
This proposition having been demonstrated, we may, by means of it, demonstrate the following: "If equals be added to unequals, the sums are unequal." If A = _a_ and B not = _b_, A+B is not = _a+b_. For suppose it to be so. Then, since A = _a_ and A+B = _a+b_, subtracting equals from equals, B = _b_; which is contrary to the hypothesis.
So again, it may be proved that two things, one of which is equal and the other unequal to a third thing, are unequal to one another.
If A = _a_ and A not = B, neither is _a_ = B. For suppose it to be equal. Then since A = _a_ and _a_ = B, and since things equal to the same thing are equal to one another A = B; which is contrary to the hypothesis.
200 Geometers have usually preferred to define parallel lines by the property of being in the same plane and never meeting. This, however, has rendered it necessary for them to assume, as an additional axiom, some other property of parallel lines; and the unsatisfactory manner in which properties for that purpose have been selected by Euclid and others has always been deemed the opprobrium of elementary geometry. Even as a verbal definition, equidistance is a fitter property to characterize parallels by, since it is the attribute really involved in the signification of the name. If to be in the same plane and never to meet were all that is meant by being parallel, we should feel no incongruity in speaking of a curve as parallel to its asymptote. The meaning of parallel lines is, lines which pursue exactly the same direction, and which, therefore, neither draw nearer nor go farther from one another; a conception suggested at once by the contemplation of nature. That the lines will never meet is of course included in the more comprehensive proposition that they are everywhere equally distant. And that any straight lines which are in the same plane and not equidistant will certainly meet, may be demonstrated in the most rigorous manner from the fundamental property of straight lines assumed in the text, viz., that if they set out from the same point, they diverge more and more without limit.
_ 201 Philosophie Positive_, iii., 414-416.
202 See the two remarkable notes (A) and (F), appended to his _Inquiry into the Relation of Cause and Effect_.
203 Supra, p. 413.
204 A writer to whom I have several times referred, gives as the definition of an impossibility, that which there exists in the world no cause adequate to produce. This definition does not take in such 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.)
_ 213 Novum Organum Renovatum_, pp. 35-37.
_ 214 Novum Organum Renovatum_, pp. 39, 40.
215 P. 217, 4to edition.
216 "E, ex, extra, extraneus, etranger, 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 _pilgrim_, from _ager_: _per agrum_, _peragrinus_, _peregrinus_, _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, unmannerly, insolent." (_Logic_, ii., 173, 174.)
217 Pp. 226, 227.
_ 218 Essays_, p. 214.
_ 219 Essays_, p. 215.
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.
_ 221 Historical Introduction_, vol. i., pp. 66-68.