Examination of Mill's Logic

J. N. Darby.

<32007E> 111 {file section c.}

{A System of Logic, by John Stuart Mill, 8th edition.

The reader must bear in mind that these are only MSS notes jotted down while reading the book.}

All he says as to mathematics is mere unintelligent materialism; as if, because his fingers and compass could not be absolutely true, his mental apprehension of it could not. His head is no wiser than his fingers. The certainty is no illusion. He supposes that mere materialism is all we have. But we exist in space and time, and space is divisible. What is material phenomenally exists in space, and the matter is not the subject of thought but that mode of existence, and this gives form and measure, and of this mathematics are cognisant and demonstrate the equality of dissimilar forms, etc. But his idea of a point, etc., is not only false, but wholly inapprehensive of the truth. A line is that at which divided space begins and ends, the limits of any such division, or of two which meet. And if I enter on existing matter, or the space it is in, I am not at the limit at all. Hence a line properly is a non-existent thing, as the limit of a thing, or of two spaces which meet, must be; but I necessarily so think from my nature. A point is the starting-point or end of the line, or any point where the mind divides it. A straight line is that whose direction is invariably to a fixed point. So surface is that where matter ceases or begins. If I pass into an existing thing, I am not on its surface. When we make lines physically, they are sufficient to represent them to the eye for the mind, but this is all. If I take what is physically marked, I have lost the idea of line. And we, as finite, living according to space and time, necessarily think in it. If the radii are not equal, it is that the circle is not a true one, not that equal radii are not true of any circle: if not, it is not a circle at all. And so far from a right angle never being true, it is necessarily true, and I cannot help thinking of an exact one if I think of it. Supposing a line so conceived as above, and for practical use any line drawn, let one cross another at any angle. Let one move round in the direction to enlarge the smaller of the two angles. I necessarily pass through all angles till the lines are identical, and at a given point a right angle; I must do it. The physical exactitude is a mere question of physical skill. In the case of a line one cannot form a mental picture of a line, for its essence is not to be a material existence at all, but the mode of existence of that of which I can form such a picture, that is, existence in divisible space; and it is his reducing all thought to mere objects, so as to apply the phenomenal facts as to that to all thought in the mind, which makes all his system false. Geometers just define it for practical use; but Mill never thinks nor gets beyond what he picks up to comment on. All human reasoning is built on hypothesis necessarily. The only difference of geometry is that, occupied with what actually exists in nature, the hypothesis is incontrovertible. Mere definition or axiomatic assertion may be well or ill founded, but the relations of space, quantity, inequality exist in the necessity of our thought; and geometry has only to discover what they are, and, as in all true deductive reasoning, the conclusion is necessary.

113 Some mathematical definitions are very stupid. "A straight line is the shortest line between two points." This may be and doubtless is true, but is no definition, not what a straight line is, but a quality of it. "Straight" is whatever never swerves from one direction towards a point fixed as regards the point from which it starts. Every basis of deduction is an assumed truth - and as to the nature of what is spoken of - only mathematics dealing with the forms and measures of space deal with that which exists as true in the nature we belong to. Man is mortal, or man is a rational animal, may give rise to a thousand questions other than such as belong immutably to the nature of space, the sphere or time, the condition in which we now exist.

His change as to equal magnitudes (p. 264) makes the whole thing false. There are equal magnitudes which cannot be so applied to one another as to coincide, though those which do are upon the face of it equal. I suppose "magnitudes equal to the same" to be a delusion in terms, even if convenient for practice. The magnitudes here are the same. I think the proposition that two straight lines cannot enclose a space may be demonstrated, for let them start from two separate points and these are not united by them. Let them start from the same point - either they are identical (only one line really) or perpetually diverge. The true definition of a straight line, one which never diverges from direction to one fixed point, makes all this simple. I dare say geometry may be more convenient as we have it; but what we want in it logically is to give right force to terms, and so to definitions. What we have said of straight lines is not (p. 266) an induction from the evidence of our senses (rather nonsense, by the bye) but is necessarily demonstrated from the meaning of "straight."

And this introduces another fallacy of Mill's, founded on his assertion of general propositions and ignorance of their nature. Of course they may be contested, but in all deductive reasoning are assumed. But as reasoning from particulars (Mill's theory) is clearly false on the face of it, and no reasoning at all - that is, no legitimate inference of any kind - so the universality of a general proposition is not all. That all men are mortal is a fact. They have been so in all known cases; but the induction goes farther, and involves, perhaps is even tacitly based on, another: Man is mortal, which affirms something of the nature of man which is other and more than the fact that all are involved in it. And this is the meaning of what is universal is necessary - that is, certainly must happen according to the nature. "Straight" is a line of a particular nature, one which never deviates in its direction; if it does, it is not straight. So a circle; it means a boundary line enclosing space whose distance from a point within is always equal. Now Mr. Mill's reasoning that it comes from observation is false upon the face of it; for he says there never was a perfect circle nor line seen, nor can there be, he declares. Hence it cannot be observation which has given me the idea of a perfect line or circle, for there is no such thing to be observed. It will be said, I correct its aberrations in my mind. Correct it by what? By the idea I have of it; that is, I have an idea to correct it by, not an idea in the sense of a mental image. I know what equal means. This I may have learned experimentally; but knowing what equal means, I know what circle means without seeing it or forming any image of it in my mind.

114 Saying, too, I cannot reason about nonentities is false; for modes of existence (as time and space) are not entities, and I can, though with perhaps more difficulty, reason about them. And here the part which language takes is forgotten. I may have learned what "equal" is by observation (not by inference and inferring nothing from it); but I exist in space, and divisible space and time, and I know what number is, and I think in this order, and equal becomes an abstraction from the things I may have learned it by. I apply it to entities; but it is not an entity at all, yet it is a perfectly intelligible word. I have no mental image before me when I say equal or unequal, though modes of existence suppose for us that things exist; but they are not existing things imaged in the mind. This materialism has rendered all Mill's reasoning false. I have an idea of straight and circle, lines or forms, with certain qualities which exclude from them all lines and forms which have them not. And if nature or art does not, as Mill says, furnish such, then I say a true circle does not exist in nature, and art cannot make one, though what it makes is meant for it, and answers practically for deductive reasoning, because it is meant for it, and supposed to be it. I do not take Euclid's axioms; because they are taken as sufficient for mathematical purposes, not meant to have the precision necessary for logical discussion. Let us bear in mind that all syllogistic reasoning is on the assumption of the truth of premises - that is, hypothetical; and if true, the conclusion is always "must be," never really "is "; never truth affirmed in itself, but a conclusion, though always a necessary one. That two lines cannot include space is demonstrable, and no real axiom, but a necessary consequence of their nature, the meaning of "straight" being assumed, of which, whether I have ever seen an exactly straight thing or not, I have a perfectly clear thought.

115 As to the burden of proof (p. 267), it is a feeble defence, but Mill has proved it; for he tells us that no one has ever seen a true straight line or true circle. I have already said that the only difference of mathematics is that the truths we start with - space, divisible space, form, etc. - are in the certain nature of things, that is, our own mode of existence. Hence unless I know God and what "I am" means, in which there is no space or time, all thoughts, or rather attempts at thought, of what is eternal outside them are negative and cannot be otherwise - infinite, immense, and so on. I exist in what is divisible space and time, and with human power I cannot go beyond it. When I say I am, the thought has no past, no future - that is, is negative of finite time. It is the nearest to eternity I can come, and by a tacit negation. It is always now.* Hence, when used absolutely, it negatives time absolutely; when said of myself, it says, I exist now.

{*Everlasting only supposes continuous existence from now, ex parte post, so called, or ex parte ante.}

What Mr. Bain says is clearly false (p. 272), for we have no really straight objects to compare, and I cannot say "bent or crooked" without understanding what "straight" means, to which another object may be an approximation. That the knowledge which makes it understood suffices to verify it, is true; but for a very different reason. Straight means what does not deviate; but from what? All his reasoning in pages 274-5 is founded on different meanings of inconceivable. Whewell used it as tantamount to impossible, Mill as what the mind may or cannot apprehend, he having nothing but observation and experience to judge by, but the impossibility is in the nature of the things. Two are not three in the same sense, nor bent and straight. It is not simply that I cannot conceive two straight lines enclosing a space, but they cannot enclose it. It has nothing to do with the information of my mind or its habits, which is all Mill can speak of. The thing, according to our mode of existence and thought, cannot be. It is not merely that in my condition of mind it cannot de facto be thought: in my state of existence it is not thinkable. All his reasoning is not worth a straw. One is the effect of prejudice or education; the other is in the nature of the things. My having ascertained it or not is the state of my mind; the other is the state of two straight lines. And it is quite possible that, while my ascertaining the fact is a matter of scientific progress, I may learn, too, that, things being what they are (and so only can I think logically and as to nature), it could not be otherwise. Thus it took great progress to learn the uniform and universal laws of gravitation; but, once learned, the sun being an enormously greater mass, that principle being true, the earth, once set in motion, must go round the sun.

116 So with combinations in the reasoning of both these gentlemen. If things were not definitely combined (though experimentally learned), we could not have a kosmos, an ordered universe. There might have been another combination possible (but not according to that in which we live, hence not conceivable by us); but to have order and distinct bodies, there being diverse elements, they must be definitely combined to have these distinct bodies. Uniformity and order cannot exist without it. Whewell, on the main point, defends himself needlessly and to no purpose (page 283). The question is not, save for myself, if I conceived distinctly or not, nor do I trouble myself with actual axioms more or less correct; but is there such a thing as a straight line conceivable which is not a crooked one, and a circle which is itself not an ellipse nor a square? Necessary conclusions are those rightly drawn from admitted premises; necessary truths are those which follow necessarily from the facts certain in nature. They are also facts. I learn them perhaps by reasoning. Geometry proves the equal quantities of distinct forms. I join by a straight line two radii of a circle. I have an isosceles triangle; whatever may be deduced rightly from that necessarily follows, and may involve important discoveries. The uncultivated mind has no clear idea of what makes it impossible for him, therefore it is not so, of course. And though I cannot conceive a world with different chemical combinations, as I belong to this and am not a creator, I can conceive there may be; just as I may conceive there are a thousand chemical combinations yet undiscovered. But chaos man cannot conceive. It is combination in a definite way which comes into his mind, if any; but any particular combination must be for an ordered kosmos.

117 True axioms, then, are relationships which are in nature and for our existence always and necessarily true. When I define a thing in mathematics, I take a fact in the relations of space or number, not an existing object, but a relationship mentally conceived, one which is important for further reasoning, though there may be a thousand others; not, as Mr. Mill says, denying other attributes, but selecting that which makes it important. What I take necessarily and absolutely exists, not a physical object, an object of sense, but a relationship in the nature of things, say a right angle. Now all angles exist infinite in number. I take one where, two lines crossing each other, all the angles are equal. There must be such, for all angles exist (they are the mere relation or difference of direction of two lines from one point),* therefore this does: only I take it for further use. So there are infinite forms circumscribed by a continuous line, never straight, but returning to the same identical point. There is, therefore, one of which the circumscribing line is always equidistant from a point within, that is, all whose radii are equal. I take this one, because from this quality (there may be twenty others) all the system of trigonometry (its sines, cosines, versed sines, etc.) flows. But the existence of these relationships is in the nature of things, not objects (though if true they may become such), but as to which it is impossible that they should not be. I learn many consequences, as I do from the ellipse or other forms which in astronomy become of the greatest importance: consequences that are also true as relationships - say as Kepler's laws - much more certain and certainly accurate in mathematics than by observation. If facts, they may be observable of course, but their certainty is mathematical, that is, in their nature not experimental. I repeat, all deductive reasoning is hypothetical; that is, it assumes the truth of the premises.

{*Angles are mere quantitative angular space, part of the whole circle of space round a point. A right angle is one of four equal ones which take in the whole space.}

118 (Pages 290, 293.) I come to numbers. Mr. Mill tells us that 1 = 1 is not certain, because a pound troy is not equal to a pound avoirdupois. This is a sample of Mill's logic. He says we must think of ten bodies, ten sounds, etc.; but I do not think of bodies or sounds at all, not even if such are before me, only of their relation in number. I think of ten. I can say ten is not nine, and think of no body or thing at all. Two and one is no definition of three at all; it merely states that, if I add one to two, it makes what I call three; but two and two making four, 3 + 1 making four, and so on, shew this has nothing to do with definitions. We cannot define numbers, because they enter as a primary idea into my condition of existence in the divisibility of quantity or the unity of an undivided object, as three parts, one sum. You cannot define colours for an analogous reason, nor sounds. They are primary sensations in the latter cases, the mode of my existence in the former. The word is merely the sign of it; but I am one, another person speaking to me is one, and we are two. When I say "two," it shews that it is not the object of sense, for the two are different, but unity or numerical quantity that I think of. The word "four," as applicable to all objects, represents none. It represents four, the number, a mode of separate existence. The objects are not the subject of thought, but the number of them, and therefore I can compute without referring to any object; the relations developed are relations of number, and nothing else. Nobody denies that objects are numbered, but thinking of number is not thinking of the objects. They exist in space, in time; but space and time are not the objects of sense that exist in them. To confound reasoning of "one" and "one pound," as if it were the same thing, shews an incapacity of mind which may not be impossible, but it is certainly "inconceivable" in one pretending to teach reasoning or logic: the difference is in the pounds, not in the one. But mathematical arguments as to quantity are just as certain. What have quantities, as man has combined them in commerce, to do with abstract relations of quantity? This is all child's play in logic.

I need not enter at any length into the question between Mr. Mill and Mr. Spencer. Both base their reasoning on exact experience, and both are all wrong. If, as Mr. Spencer says, I feel I am cold, and cannot conceive I am not, this is not past experience. Nor is it necessary to talk of the opposite being inconceivable. A present positive feeling is for him who has it certain. Mr. Mill's answer is simplest nonsense. He says, I can conceive not being cold; but Mr. S. evidently means that when I feel cold I cannot conceive being not cold then. But they are, in order to make experience the sole test of truth, making my conception of a thing the only question, not the thing itself If I have a toothache, the pain is something, though, of course, I conceive it; and in the cases we have been considering - circles, numbers, etc. - my conceiving it has nothing to do with it. The thing has the qualities; the form or number is what it is. There are numbers which convey no idea to the mind, but I can calculate them with as much certainty as if it were two or three: the certainty is in the numerical relation, not in any conception; and, be the circle big or little, the relations of sines, cosines, etc., are just the same. Conceiving depends on the conceiving power, not on the truth of the thing. "That what is inconceivable cannot be true," is as false as can possibly be; for conceivable depends on the capacity of the conceiver, not on truth or not. Besides, a man may be certain in his conception, and deceived - think himself made of glass, or Louis XVI; he is mad, no doubt, but just as certain. It is inconceivable for him that it should be otherwise. Mr. Mill distinguishes between inconceivable and impossible. I may use the former for the latter; but if the difference is made and it is just, I had already made it. The whole argument is not worth a rush. What is impossible cannot have been a matter of experience, and rests on the nature of the thing, not on conception or experience at all. And a thing may be impossible and yet supposed, or so far conceived, as that the square of the hypotenuse is not equal to the squares of the two sides. This is impossible to be true from the relation of the quantities. I may have to discover it, but it is in the nature of the thing always so.

119 As to contradiction or an excluded middle, I must add used in the same sense. Thus, snow is white; snow is not white. If snow is white, what is not white is not snow. What is red snow? It is in all its essential qualities what makes it snow, but it has been coloured in some way; and contradiction is simply such negatives that is, says the affirmation is not true, consequently the negative cannot be true if it is. But this supposes the term used in the same sense. A man is one single I, but there are body, soul, and spirit, which may be separated. But what Mill says is, as usual, wrong (p. 321); for an unmeaning proposition is none at all - is not true nor false, not as a proposition, but because it is not one at all. He is wrong, too, as to matter. What is infinitely divisible cannot be said to be not infinitely divisible. Whether matter exists or not has nothing to do with the question. The existence of matter is another proposition, the truth of which is assumed in the one we are treating of, as is always the case mentally. The incapacity of Mr. Mill in analysing is really astounding. Nor has sight or touch anything to do with it. Thus, if chemistry has shewn, as alleged in the atomic theory,* that divisibility cannot be carried farther, then the up to that divisible thing is not infinitely divisible. Infinite divisibility may be applied to space without matter in thought. If I get space, I get extension; and if I do, I can conceive part of it.

{*But this is merely physically. Mentally space is always divisible, because it has extension, or it is not space.}

120 In the quotations from Spencer we get the usual reference of everything to experience. Now as to phenomena I should insist on it. But reasoning has nothing to do with it. I know, without any phenomenon, that when I say a thing is not, I do not mean that it is, but to contradict it, that I am saying that the proposition is not true; if it is true, it is not true to say it is not. I have nothing to do here with the experience of objects, beyond which these men cannot get. I say, whales are mammals; it is said that whales are not mammals. If I use the word in the same sense both cannot be true, because one says the other is not, and it cannot be true and not true in the same sense. Yet I have no experience of whales - never saw one to examine it - only I know that in the usual ordinary sense of the term it is a great fish; but I have no experience of the matter; only I know what a proposition is, and what not means.

I deny altogether that all our knowledge comes from induction, or that induction gives us any truth at all. Induction gives us what we have to act on as men, in a multitude of cases; for Mill carefully leaves out belief in testimony. But induction only gives us a high degree of probability. Induction does not give us truth; testimony alone gives us truth. But he admits that what induction does is to discover and prove general propositions. He insists on ascertaining individual facts, but all this is sophistry.* Because I do not infer from some observed cases to one, unless it be the observation of all; for if not, you can draw no inference; it concludes from constant recurrence in all cases without other cause; it is true in all cases, hence in any given one; otherwise in none, unless that it is uncertain, for some are and some are not alike, or at least only probability. It never gives truth as such. "Observation of known cases" means of all known cases, or is quite false; but from all known cases universality is concluded. But this is the general proposition.

{*Indeed in page 331 he says, "In strictness, indeed, the result of the problem is a general proposition." To be sure it is, and must be - here in the case of mathematics.}

121 The inference is to a whole class, because it is true of the whole class in all observed cases. "It does not hold at all, or it holds in all cases." Just so; but my induction is from its having been so in all observed: if it has not, I cannot infer that it will; and of cases not yet observed I only infer it of one, because I infer it of all. Only, as I have said, it tacitly but really affirms the nature of the thing. "All men are mortal" is really a conclusion as to man's nature from having known all to die as to human knowledge. All diameters of a circle are equal is the nature of a circle having all its radii equal. But here again the cloven foot comes out, that the inquiry into a scientific principle or an individual fact is just the same induction. Now, a principle or the nature of things is a matter of induction from many or all observed facts, but an individual fact (save as identical with a scientific principle) is never a matter of induction, but of testimony. I know he reasons about it to shew that I believe by an induction as to credibility; but this, however much it has its place, does not in itself give any induction in believing the fact. I believe the testimony that the fact is, and infer nothing about anything. I may shew it is folly not to believe the testimony, and infer I ought; but that is reasoning or inferring as to the testimony, if I do this (not always the ground or belief, nor even of divine faith), not as to the fact. I believe on testimony, which is no induction at all; and this in the next pages he does not deny.

Page 329). The senses or testimony must decide on the individual fact. Inductions may, of course, then be made; but what he says about the syllogism is all false, as before. It is always and only deduction, and not induction. Even in practical affairs the inference to a particular case would not be just, unless true of all such cases, for if not, this one may be a similar exception; and so he admits in the first sentence in the next chapter. It is really wearisome to pursue such absence of all exactness of mind. This definition of induction? (p. 333) says all I have insisted on, as to the whole class or general proposition being its true character. But syllogism is not induction, but deduction. It does not give probability, however high, which is all induction can do, and therefore nothing certain, but a necessary and certain conclusion if the premises be true. The case Mr. Mill puts is induction, and of it syllogism says: Argumentum a particulari ad universalem nil valet, and for a deduction certain in its nature, that must be; it is an induction from given cases to a class which may or may not be well founded. It is an induction; there is a conclusion, namely that every A is B; whether it be fairly conclusive depends on circumstances. If this and that A are sufficiently numerous and none contradictory are known, then it is a fair induction, such as men have to act on. But it is not a syllogism - must be if the premises are.

122 Of the use of syllogism I have spoken; it connects with certainty, by means of a middle term, ideas or an idea not connected or contained in the subject as announced, and which is called in question. Every man is an animal; every animal lives (as such) by blood; therefore man lives by blood. The middle term animal connects life by blood with man, which is supposed to be in dispute. He is wrong in saying ascertained as to every individual in it. That is not it. It is ascertained as to every individual that has come under observation, and so I conclude as to one which has not. That is induction, the nature being really always introduced, though the process be not analysed in our minds. And this view of induction he admits to be true in pages 334, 335. But syllogism is wholly distinct in its nature, and gives on admitted premises a certain conclusion from them. The induction, if it be sufficient to prove the nature, is practically sufficient so far as phenomena go; but never in se certainty. But this point of the nature of things is of great importance, though it simplifies things much.

I need not follow the mass of useless verbiage in the controversy between Mill and Dr. Whewell. Mill sums it up in one sentence as to Kepler, but shews himself wrong therein; for, as is evident, Kepler's law was an induction, only one ready-made for him in the necessary rules of an ellipse. Having found a number of places and movements of Mars, he inferred all the rest: only the inference was ready-made for him. But as to the question of nature itself, what is in Mill (ground of induction) and Whately is vague and unsatisfactory, though there is a general presentiment of truth in it. Nature and its uniformity come up in three distinct ways. First, uniformity of relative existence, that is, of what is always true in nature as it subsists, as space and form, mathematical induction, which is really merely discovery of what is constantly so. Secondly, the effects of power in nature, which may or may not operate constantly, as gravitation or certain chemical affinities or effects. Thirdly, subjection to some law or power which operates universally. The second is probably the law of nature. I do not conclude because John and Peter have died that all will. Abel's death by violence, and all men's, save eight, by the flood, could not have proved it, because it was not the course of nature that all would have died by nature; but I conclude that John and Peter will die because all have. My reason is that the universality of it, without other external cause, makes it a law of man's nature; but as it is not in the subject itself apparently, but subjection to a law of necessity, I must shew its universality in the natural course of things, which practically proves its necessity in every cause. Yet it is not proof, that is, certainty, though quasi-certainty. He who believes scripture knows we shall not all die. It is what in a person or being in his normal state is contrary to his nature, for he lives. He is subjected to it, he may be even violently. Hence I can only conclude while that subjection continues. But in chemical affinities or gravitation it is in its normal state that it so acts; it is its nature. Seeing this, namely it is its nature, the law of it if you please, I reckon on its doing so in all cases, because it is its nature. This may be both learned and confirmed by observation, and, no doubt, possibly the generalisation induced; but from one clear adequate instance or many I have its nature.

123 In geometrical induction it is, as I said, discovery of the nature or essential qualities of one form; and these never vary, they are the qualities of that form. What he says of only proving that that circle is only so and-so is a mistake. It is what a circle, any circle, is. Colours do not give just ground for induction. They are not what the thing is - its nature. Black swans, however, were known - rara avis in terris, nigroque simillima cygno. What he says of abstraction is wrong. It abstracts a quality from all it may be found in, as whiteness; or a thing as a nature abstractedly from all in which the nature is found, as a man, or man; a circle, etc. It is not connecting known facts by common characters, but taking the characters apart from the facts. Man is so-and-so, whiteness dazzles. It is the quality of being in its nature apart from the objects in which a quality is, or individual instances of a being or an act: as "Reading much tries the mind": "Living by warm blood is the property of all beings who breathe through lungs." It is really that the nature of the thing has been discovered. In all cases it is, so far as one instance shews, the nature of the thing that the induction is sure (for mathematics is a discovered fact of relation of quantity). When it is only from all known instances (though adequately for human conclusions) and the nature of the thing not shewn, it is not, properly speaking, certain; as mortality is not the nature of man - that is, a living being; but subjection to something which produces it. But there is another kind of inference, not from cases or all cases to the one not observed, but to the cause of the case itself. This may be from other similar cases, but not necessarily. Thus if, having gone round part of an island, I find in a strait I have not surveyed the tide setting in strong through it, I conclude it is open at the other end, for the current could not so set through it under given circumstances if it were not. This is a legitimate induction to the cause of the phenomenon, and then to the state of things which allows the cause to operate and is its formal occasion.

124 But I deny wholly that belief in oracles, or Whately's popular superstition, is induction from experience. They may try and justify their opinion by experience. It is evidently the power of unseen things on the human mind. Its cause is not experience. What invented it? What set it up? I do not admit any proof in induction (page 352). When one man has died, the conception of being mortal is not arrived at at all. Nor is it properly a conception. I conceive death. Mortality is a moral judgment as to the condition of the living where that conception has no place. Nor is abstraction description. But I do not dwell on these points. But if generalisation from experience be induction, it cannot be proof. In material facts of the course of nature it may, but that is not really an induction from instances, but the discovery of the uniform law of the course of nature in which we exist. It does not assume the uniformity of the laws of nature, but discovers, and in that sense proves, it in the cases where it is so. I do not (from some cases of bodies falling, since nature is uniform) infer that other bodies will fall, but learn weight or gravity as a law of nature from all bodies (not hindered) falling. What I have discovered is the law (or uniformity) from all known cases, not some from an abstract idea of uniformity.

125 I have no contest with uniformity of laws of material nature; my question is about the inductive process. I admit habitual experience gives a general feeling of a uniform law in the order of nature. But even in this it is only present phenomena. The sun rises and sets, and I expect it to do so. But the most accurate science says this order must have begun, and it must end. I shall be told this is a mere general law; be it so (though it makes phenomenal induction a poor and foolish thing). But it proves that proof by induction from observed instances to others, on the assumption of uniformity in the course of nature, is no solid ground of reasoning. For this reason: the earth had a beginning, that is, as Mill admits, there was a change. That is, uniformity, which means no change, is not true.

If one boldly says beginning to exist is from a law (not to say that it is nonsense), where is the proof of it as a law? from what other causes is the induction made? What was the antecedent of which its existence is the sequence (called cause)? If I am told it was the effect of cast-off portions of a revolving sun and cooling mass, what was the antecedent of that? Whatever cooling of the sun may be affirmed, if matter be inert and has been set going, some force has set it going which is not in the inert matter. So, if the uniformity of the principle of weight is there, what put it there? This regards change and beginning, and motion is change. Where there is none, the case is even plainer. "Fire burns," he tells us, does not relate to time. Of course not, but "fire burns" is a statement of its nature, and what it is as such, what consequently it always as such does. There is no inference at all from cases known to cases unknown; it is known already and always that fire burns. He tells us (p. 254) that this uniformity of the course of nature, or government by general laws, "is an assumption involved in every case of induction." In page 255 again:" That the course of nature is uniform is the fundamental principle or general axiom of induction. It would yet be a great error to offer this large generalisation as any explanation of the inductive process. On the contrary, I hold it to be itself an instance of induction . . . . Far from being the first induction we make, it is one of the last." This is singular. It is an assumption involved in every case of induction, the fundamental principle or general axiom of induction; but then it is a late induction - that is, it is not an assumption at all, but an instance of induction, which of course must have been made without it, for it is one of the last inductions made-that is, it cannot have been assumed before. It is known by induction, the fruit of it; but the induction was made always by assuming it. It is always taken for granted to have proof by induction, but the induction must be made or it is not known; it is itself induction, in which it takes itself for granted.

126 His only answer to this is, for he admits it, that it is no more than the major of a syllogism. But this is no answer at all, for he admits that the major is necessary to prove the conclusion, though no part of the proof. What is necessary thus to prove all inductions is itself a matter of induction, when it is not there though necessary! But the answer is in itself unfounded. The major is part of the proof - ground I have already gone over. Thus man lives by blood, therefore man is mortal. Here is no proof whatever of anything. I say, Why so? I answer, which is the major, because everything that lives by blood is mortal. My minor only brought it into this class, the major proved it was mortal. He would say, Your major had to be proved. Of course it had. But that has nothing to do with the proof of the syllogism.

In fact, moreover, universal laws of nature are not assumed. A universal law of gravity is discovered by observation, generalises withal by finding that it explains all the phenomena of movement in the universe, though gravity is only a name for the fact. But nothing of a universal law is assumed here. It is, as he admits, an induction, and an induction which could not yet be made. I find by experiment that water presses equally in every direction, another general law, but no assumption of universality. But when I find in every case coming before me that there are fixed principles of nature, and that it is in a general way necessary for the order which constitutes the kosmos, I accept it as a general principle of that kosmos--that is, in the physical order of things. It is a result of induction. But this proves the inaccuracy of Mill in saying that it is the basis in every induction; for it is not in any of these, by which it is ascertained. That is, his principle is wholly false. Nor does it go beyond material elements or physical nature; but we cannot expect Mill to get beyond materialism.

127 But then to assume it is a universal basis of induction because it is in material things is wholly unfounded. He may amuse himself with chemistry from Bain and Sir John Herschel, but this is superficial work, and shews a will. He says (p. 329): The validity of argument, when constructed, depends on principles, and must be tried by tests which are the same for all descriptions of inquiries. Now an inquiry whether alkalies neutralise acids is not tried by the same test as whether man is morally responsible to God, and what God is, what morality is. And Mill has shewn elsewhere the effect of this materialism in declaring his belief of an impotent God, partially good and unable to do better with the materials ready to His hand, whencesoever they came. Doubtless he had felt physical evil personally, and knew, as evidently he did not, nothing else, nothing of the truths involved in conscience. His theory is - we are to perfect what has been made imperfectly.

The induction by simple enumeration is true where it is the expression of nature, for that reason; one instance of an effect well ascertained to be attributable to a chemical agent is so for the same reason. When I cannot say it is nature, it is the highest probability where no other cause is, as ordinary mortality. Violence, disease, or not, men equally die as to animal life; phenomenally animals the same. I then say it is the present order of nature. When I say alkalies neutralise acids, or hydrogen and oxygen in given proportions make water, I get, as far as men can ascertain, their nature as to that. And I to not, however, draw an induction properly in this case. It is the nature of alkalies, and these gases so united make water. I do not predict, save to the ignorant. They do not resemble, as Mill would say; they are the same, not in corporate unity, which has nothing to do with the matter, in action. Alkalies do that, not "have done" nor will," though each be true; they do it. When I conclude from instances to instances, it may be more or less likely, because, if tolerably many, there is probably a common cause; but it is no proof of anything: but if I ascertain the nature of the thing, that is an induction, and so far practical proof. But this only applies to material nature, not to a law binding everything with a phenomenal kosmos. Consequences prove antecedents, but only where it is the nature of the thing; sequence in itself has nothing to do with it. He admits the fact; but if it does not in one instance, it is no proof in any.

128 Day follows night, that is, light darkness; but it is not of the nature of darkness to give light, or to cause it, and the sequence has nothing to do with causation, laws of nature, or induction. That is propter, quia post. Where a thing produces anything, then I pronounce on its nature, and it is always itself when not hindered. His chemical instances may be all very well as trivial illustrations of means to discover producing causes, though he never travels beyond materialism; very pretty experiments borrowed from others, which not only are confined to material things, but do not analyse the true principles even of them. They are mere means of scientific discovery, beyond which his mind cannot go. He does not see the difference I have noted. The black or white swan, or grey crow, says nothing as to nature; it is a mere fact, and swan or crow is merely a class made ill or well; and all the white swans in the world would not prove there was not a black one - has nothing to do with it. The only important principle evolved here is that he is obliged to rest all on testimony, as in all questions of fact we must. Most of the laws of nature are simply facts, and there is no induction whatever, but adequate ascertainment of a fact; as that hydrogen and oxygen make water: only in the details we must see that other causes do not come in to produce or have hindered.

As to cleverness in experiment, his cases may be all very well, but have nothing to do with the logic of causes. I cannot see any induction in ascertaining the laws of nature, though clever induction may shorten the work in guessing or probability (not proper invention). The fact is there, and the fact is learned. A clever mind may think of means to ascertain whether the fact is such; a well-informed mind knows what may eliminate, what would confuse. But if hydrogen and oxygen always make water, there is no induction. If a third element be there which hinders it, I have to ascertain where the true law or uniform fact is; but all this is mere ascertainment of facts by observation. As to the result, that is the fact. You have nothing to do with following them.

129 I quite admit cleverness and knowledge in the use of facts. When Leverrier or Adams discovered that Uranus's motions could not be accounted for, all the difference was that they could not see what caused it. The law of gravity was known: it was an instance of it. The irregular movement proved the presence of the object, just the same as sight would. The cause and result were identified.

The reason why testimony that there were black swans could be received was that colour does not alter the nature at all. Wearing heads under arms clearly ran counter to the natural structure of a man. You cannot say there can be none such, but it is too contrary to nature, and so to probability, to receive it. Experience would not help us with the swans. If colour had to do with nature, as the black spot from arsenic, it would at once affect our judgment.

As to his case of abuse of power, there is generalisation, but his conclusion is, as usual, a Tenterden steeple one. How does he know that education will ever elevate character, or destroy the love of power or its abuse? The only conclusion to be drawn is that no forms hinder the love and abuse of power found in man, and no system of education yet invented has corrected his nature (pages 354-372). He had before told us (p. 258) that mathematics were not certain: now their laws are rigorously universal.

If truth is investigated by evidence, neither induction nor logic is such at all. He naturally avoids all efficient causes, looking only to physical ones; in which, too, all is false, because he has confounded cause and sequence, and things apparently necessary with cause. It is the merest fallacy to call it causation where it is simply sequence. Be it that I learn what is a cause from it by eliminating other concomitants, but then it is a producing cause. Whether there be a constant sustaining will is another question: I believe it, but I may consider the ordered sequences apart as ordered. In that sense he is superficial and unanalytical still. Events, as we know them in the kosmos, have had not necessarily antecedents; this is not so, but causes. Gravity is not an antecedent of centripetal motion, nor impulse even of rectilinear. They act in the motion. What we call gravity is only the force so displayed. But the real cause is not all the antecedents where there are such. Poison kills one man, not another, the former being unhealthy, but the latter is not the cause. The poison destroyed the tissues, or corrupted the blood, etc;, that killed the man; in the other case there was adequate force to resist, which there was not in the first.

130 (Pages 378-9.) Language may be used carelessly, and occasion used for cause, and Mill's mind not get beyond this. We do so when, without the occasion, the result would not have happened; but this is only language. The man falling from the ladder broke his neck - suppose this was the cause of his death; but I say slipping from the ladder, because otherwise he would not thus have broken his neck, and his weight would not have done it at all. A stone falling to the bottom is caused by gravity simply, partially hindered by the medium. It is immaterial what might hinder. It is evident that it cannot come into the cause of what it is not hindered in. He is wrong as to the surprise. The absence of the sentinel did cause the surprise, not the attack; but it was the cause why that attack was a surprise on the others; and that is what causing a surprise means, not causing the fact, but causing that fact to be a surprise. Absence may be a cause. Absence or non-existence of light (darkness) makes me lose my way. There must be a way, and a man purposing to go it; but this has nothing to do with the cause of his losing it.

I may say, in common parlance, Faust died (p. 383), because he was a man; Mephistopheles not, because he was a spirit. But this does not say what was the cause of Faust's death. Poison killed Faust, his being a man did not. But the operation of the poison did not exist as to spirit. There was no cause at all at work. In comparing and saying why there was not, it is all well to say because, etc., but this has nothing to do with the cause. His whole system as to causation is wrong. To say that the existence of tissues is the cause of their destruction, because there must be tissues to destroy, is trifling nonsense, and that it is not alleged as a cause only, because taken for granted. The existence of tissues is no cause at all of their being destroyed. In page 383 he says this, in page 380 he says it is vicious tautology.

131 The movement of a projectile is the effect of the combination of two forces. More than one cause may be in operation, but the collection of all conditions being causes is unfounded. And he takes states of objects as causes, but this is all the grossest delusion. If a stone attracts the earth, that is not what makes it fall; were it big enough the earth would go to it. So colours are states of an object. There being causes of sensation in me is a wholly different matter. He has really a most incompetent mind.

The thing caused in my mind has nothing to do with the colour being a patient, but my senses. The action and passion refer to different objects in which the result is produced. If I give a blow and produce pain, I am in no way the patient. The whole of this in page 388 is utterly false, because the object is not agent in that in which it is patient, nor vice versa. The case of the scholar and teacher is sophistical in this, that in both mind is brought in. But even here, qua recipient from the teacher, the scholar is not active. It may set his mind working. Mill is all confusion, too, here.

In page 62 a substance or body is the external cause of our sensation. Hence, if I paint the wall white, the cause of my seeing whiteness is there. It is a simple direct cause, not an induction, at least if page 62 be just. Painting the wall is merely putting on that place what does so; the wall has nothing to do with it. Nor do I see that what he says of cause, or of conditions to define cause, is just. Cause means what produces an effect. Be it that Hume will have that we only know what is constantly antecedent. This is not true, as Reid's case of night and day shews. Mill adds unconditionally. But this is not true. His elaborate proof to shew that there is the condition that the sun must rise and set is absurd; for I have his experimentum crucis of the sun making daylight the cause of daylight - that is, the cause known by the effect. And if I say, accounting for the sequence, it is the rotation of the earth which causes the sequence, as it is, there is the condition of the sun or light being there, and even here, as much as before, the earth may cease to rotate, or the sun to give light. But the rotation is none the less de facto the cause of the sequence - I cannot say it will be for ever, but will be, nature being what it is: a necessary condition in every case. The man whose side was shot away led to experiments on the power of the gastric juice in digestion, the proportional ease of digestion of different edibles; but when they put the gastric juice into a vial, it was found that it did not digest save at the heat of the stomach. Here it was clear there was a condition, a certain degree of heat. But gastric juice digested the substance. If not, what did? Gastric juice in its normal condition, not else. Hydrogen and oxygen produce water by being mixed, but if mixed with a certain force the hottest fire; here is a condition, the absence of a certain degree of force in mixing them. It is not unconditionally that the mixture produces water, but the mixture of hydrogen and oxygen for all that is the cause of water. And, according to his own statement, in the case of the surprise of the army, non-existence cannot be a cause of anything. The absence of force is not existence; so that cannot be a cause. But even there he was wrong, because the army reckoned on the sentinel, and therefore it did not watch.

132 And now, let me ask, what sequence of antecedents and consequences, conditioned or unconditioned, makes me find the light of the sun by day an experimentum crucis that it is the cause of day? But further, this is merely an effort to insist on laws and nature's order. Supposing I make a lamp, what sequence, conditioned or unconditioned, is the cause of its existence? Every fact which has a beginning, he tells us (p. 376), has a cause. All right. And the invariable antecedent is termed the cause (page 377). The lamp had a beginning, consequently it had a cause. That is an invariable antecedent, and we learn farther on that it is always followed by the same consequent; whereas there is no invariable consequence in the lamp. The lamp is certainly an existing phenomenon. Between the phenomena which exist at any instant, and the phenomena which exist at any succeeding instant, there is an invariable order of succession. Now if his explanations and definitions apply only to one class of objects, and are untrue of all the rest, they are false as such. Thus every fact which has a beginning has a cause; that is, according to his definition, an invariable antecedent. Both these are clearly not true.

I admit, every one admits, that as a general principle the course of nature proceeds according to established laws. It would not be a course of nature if it did not. This does not preclude the possibility of interference, but it is there to be interfered with if it be. But Mr. Mill's theory of causation is wholly false and wrong. But further, every fact which has a beginning has a cause. Now in the course of nature there is no beginning phenomenally, or it would not be a course. Particular effects may begin, as the procession of the equinoxes returning on their course; but this is really a continuous effect, a regular thing. Thus there is no beginning of anything, consequently no cause of anything at all, save petty details man can make by his activities. Nothing ever began, and nothing ever was caused. A thunderstorm begins, but it is the regular course really of the operation of electricity and heat. It is as regular a course of nature really as the sunrise. But what made electricity have this course?

133 In truth Mr. Mill merely states a phenomenal course, but cause is no real word for it; hence, to slip out of the difficulty, he confines himself to course of nature where general laws are admitted, and avowedly confines himself to phenomena, by which he means merely the visible or discovered course of nature around us, where nothing phenomenal had a beginning, that is, now apparent as apparent, or it would not be an established law; for if established now (or any time), something established it, and there is an efficient, not a mere phenomenal, cause. If constantly in operation, it has not a beginning. The whole theory is utterly shallow.

If we are to believe Thompson, the earth must have had a beginning; so that there was a cause when it was not. But that is another question of fact. Phenomenal laws do not begin, and there is no beginning at all, or, in Mr. Mill's definition, a cause before the beginning of phenomenal laws. An established law now going on is not a beginning, but a going on; and he shirks the whole real question, falsifying all the principles he lays down himself. So he says (p. 397): - The beginning of a phenomenon is what implies a cause, and causation is the law of succession of phenomena. This is a contradiction in terms, or reduces phenomena to the subjective perception by me. The light of the sun causes day - his own example - but that is merely my seeing it, for it is always light; day is merely that I see it. As the moon always reflects the light, the waxing and waning and lunar months, etc., are merely a question of my seeing it. The moment I have a law, I have what always is, that is, no beginning and no cause, on his shewing of what "cause" is. But this involves most important principles. A course of nature phenomenally is clearly not beginning. It is not a law nor known phenomenally as a law till it acts, and has acted regularly, as such. If learned by experience, it is going on (though if the nature of the cause be ascertained, I may conclude to its being so from one instance). That is, the fact of beginning, implying a cause, and a law of nature or regular sequences (cause meaning no more), as ascertained by experience, are contradictory to one another.

134 Hence of two things, one: either the course of nature began, and then I have a cause, that is, an efficient cause, outside and before that course; or it went on eternally without any cause at all. Not merely matter existed (we do not know matter unformed and whose state is uncaused, and no part of the kosmos), but the whole perfectly ordered system (with the force that governs it in its movements, regular as no man could devise it - scarce discover, and multiform as no man can think) is perfectly uncaused and invented itself before it existed; for invented somehow it is. Matter, we are told, is inert; but it moves with a speed thought cannot realise, yet nothing has made it do so! It is here we may say Credat Judaeus Apella. Mill says he is not obliged to treat this question. But all his theory is false without it, because regular phenomena going on by established laws are not beginning. Day begins, no doubt, that is, I see the sun at a given time; but nothing is really beginning: the rotation of the earth is, as a law of nature, perpetual. If he says it is no law of nature, as it may naturally terminate, so begin, what gave the impulse? He cannot avoid efficient causes, for there are no other real ones. The attempt to reduce phenomenal causes to efficient ones was the intuitive sense that there must be such; the discovery of regular laws gradually did not falsify this, but merely the place they sought them in.

Discovery of gravity, a few general laws in chemistry - as the law of general proportions, etc., - proved it was not in essences of things efficient cause was to be sought (though there is more truth in it than in the denial of it). His changing conditions into causes is false as to causation. But the necessity of a cause somewhere is evident, and Mr. Mill admits it elsewhere, only an impotent one that could not make things better than they are, and we are to perfect the poor result! And the fact of general laws leads us up to a general or single cause which caused the course of nature to begin, and consequently was not of it (in the beginning was the Word and by Him all things began to be, or took place. Das Wort war, und durch ihn alles ward). But this, then, was by a will. Hence they can only continue by a will, the same that formed and gave the impulse. If the impulse was necessary to move originally, that only could cause the movement, and that will only can cause it to be now. By Him all things consist.

135 This is the only possible conclusion. Descartes may have gone wrong so far as not allowing secondary wills, as man's, which in their allowed spheres may be causes. All Sir W. Hamilton's reasoning (p. 417) is just nil. Is the steam not the cause of propulsion, because there are cranks and condensers, etc.? The intermediate instrumentality has nothing to do with the cause or efficient power which produces the effect. All Mill's statement refers, with his usual want of sagacity, not to the point itself, but to the means of ascertaining it. Supposing I learn it by experience - a dog, without learning anything, or using any reflex action of mind at all, moves his foot as much and as well as, or better than, I do. The cause of his action or moving is the same as mine. Foolish man may reason as to matter not acting on matter, or mind not acting on matter; but I and the dog do will, and do move our legs because we do will it. The case of paralysis proves nothing. It only shews that the machinery is out of order which communicates to a certain - say, as they do - distant lump of matter. Does it shew that steam is not a motive power if the crank be broken? The ascription of life by savages to sun and moon, because they had motion marking a plan, was a mistake as to the fact; but supposing it caused, as Mill and Reid say, which is only partially true, it was at the utmost a wrong deduction from too widely generalising a true fact; and this is their account of the matter. That is, they had always experienced that will in themselves gave rise to motion when so willed.