William Stanley Jevons

“ The hypothesis that there is a Creator at once all-powerful and all-benevolent is pressed, as it must seem to every candid investigator, with difficulties verging closely upon logical contradiction. The existence of the smallest amount of pain and evil would seem to show that He is either not perfectly benevolent, or not all-powerful. No one can have lived long without experiencing sorrowful events of which the significance is inexplicable. ”

“ It is of course by no means certain that everything which has been affirmed of a class is true of all objects afterwards referred to the class; for this would be a case of imperfect inference, which is never more than matter of probability. A definition can only make known a finite number of the qualities of an object, and it always remains possible that objects agreeing in those assigned qualities will differ in others. An individual cannot be defined, and can only be made known by the exhibition of the individual itself, or by a material specimen exactly representing it. ”

“ But in our logical system every term may be indifferently positive or negative, so that we express under the same form as many differences as agreements. It is impossible therefore that we should have any reason to disbelieve rather than to believe a statement about things of which we know nothing. We can hardly indeed invent a proposition concerning the truth of which we are absolutely ignorant, except when we are entirely ignorant of the terms used. ”

“ He who errs surely diverges from law, and it might be deemed hopeless out of error to draw truth. One of the most remarkable achievements of the human intellect is the establishment of a general theory which not only enables us among discrepant results to approximate to the truth, but to assign the degree of probability which fairly attaches to this conclusion. It would be a mistake indeed to suppose that this law is necessarily the best guide under all circumstances. Every measuring instrument and every form of experiment may have its own special law of error ”

“ But no one can suppose that patient labour alone will invariably lead to those conspicuous results which we attribute to genius. In every branch of science, literature, art, or industry, there are thousands of men and women who work with unceasing patience, and thereby ensure moderate success; but it would be absurd to suppose that equal amounts of intellectual labour yield equal results. A Newton may modestly attribute his discoveries to industry and patient thought, and there is reason to believe that genius is unconscious and unable to account for its own peculiar powers. ”

“ From science, modestly pursued, with a due consciousness of the extreme finitude of our intellectual powers, there can arise only nobler and wider notions of the purpose of Creation. Our philosophy will be an affirmative one, not the false and negative dogmas of Auguste Comte, which have usurped the name, and misrepresented the tendencies of a true positive philosophy. True science will not deny the existence of things because they cannot be weighed and measured. ”

“ Consciousness would almost seem to consist in the break between one state of mind and the next, just as an induced current of electricity arises from the beginning or the ending of the primary current. We are always engaged in discrimination; and the rudiment of thought which exists in the lower animals probably consists in their power of feeling difference and being agitated by it.
Yet had we the power of discrimination only, Science could not be created. To know that one feeling differs from another gives purely negative information. It cannot teach us what will happen. ”

“ In the second place an hypothesis must not be contradictory to what we believe to be true concerning Nature. It must not involve self-inconsistency which is opposed to the highest and simplest laws, namely, those of Logic. Neither ought it to be irreconcilable with the simple laws of motion, of gravity, of the conservation of energy, nor any parts of physical science which we consider to be established beyond reasonable doubt. ”

“ It must be the ground of all reasoning and inference that what is true of one thing will be true of its equivalent, and that under carefully ascertained conditions Nature repeats herself.
Were this indeed a Chaotic Universe, the powers of mind employed in science would be useless to us. Did Chance wholly take the place of order, and did all phenomena come out of an Infinite Lottery, to use Condorcet’s expression, there could be no reason to expect the like result in like circumstances. ”

“ Yet there is much to give us confidence in Science. The wider our experience, the more minute our examination of the globe, the greater the accumulation of well-reasoned knowledge,—the fewer in all probability will be the failures of inference compared with the successes. Exceptions to the prevalence of Law are gradually reduced to Law themselves. Certain deep similarities have been detected among the objects around us, and have never yet been found wanting. As the means of examining distant parts of the universe have been acquired, those similarities have been traced there as here. ”

“ In every act of inference or scientific method we are engaged about a certain identity, sameness, similarity, likeness, resemblance, analogy, equivalence or equality apparent between two objects. It is doubtful whether an entirely isolated phenomenon could present itself to our notice, since there must always be some points of similarity between object and object. But in any case an isolated phenomenon could be studied to no useful purpose. The whole value of science consists in the power which it confers upon us of applying to one object the knowledge acquired from like objects ”

“ When unexplained phenomena present themselves as objections to the theory, it will often demand the utmost judgment and sagacity to assign to them their proper place and force. The acceptance or rejection of a theory will depend upon discriminating the one insuperable contradictory fact from many, which, however singular and inexplicable at first sight, may afterwards be shown to be results of different causes, or possibly the most striking results of the very law with which they stand in apparent conflict. ”

“ The mathematician is only strong and true as long as he is logical, and if number rules the world, it is logic which rules number.
Nearly all writers have hitherto been strangely content to look upon numerical reasoning as something apart from logical inference. A long divorce has existed between quality and quantity, and it has not been uncommon to treat them as contrasted in nature and restricted to independent branches of thought. For my own part, I believe that all the sciences meet somewhere. No part of knowledge can stand wholly disconnected from other parts of the universe of thought ”

“ Diversity may almost be said to constitute life, being to thought what motion is to a river. The perception of an object involves its discrimination from all other objects. But we may nevertheless be said to detect resemblance as often as we detect difference. We cannot, in fact, assert the existence of a difference, without at the same time implying the existence of an agreement.
If I compare mercury, for instance, with other metals, and decide that it is not solid, here is a difference between mercury and solid things, expressed in a negative proposition ”

“ The application of Scientific Method cannot be restricted to the sphere of lifeless objects. We must sooner or later have strict sciences of those mental and social phenomena, which, if comparison be possible, are of more interest to us than purely material phenomena. But it is the proper course of reasoning to proceed from the known to the unknown—from the evident to the obscure—from the material and palpable to the subtle and refined. ”

“ All induction is but the inverse application of deduction, and it is by the inexplicable action of a gifted mind that a multitude of heterogeneous facts are ranged in luminous order as the results of some uniformly acting law. So different, indeed, are the qualities of mind required in different branches of science, that it would be absurd to attempt to give an exhaustive description of the character of mind which leads to discovery. The labours of Newton could not have been accomplished except by a mind of the utmost mathematical genius ”

“ He will see that no theory can at first be reconciled with all objections, because there may be many interfering causes, and the very consequences of the theory may have a complexity which prolonged investigation by successive generations of men may not exhaust. If, then, a theory exhibit a number of striking coincidences with fact, it must not be thrown aside until at least one conclusive discordance is proved, regard being had to possible error in establishing that discordance. In science and philosophy something must be risked. ”

“ In reality even apparent equality is rarely to be expected. More commonly experiments will give only probable equality, that is results will come so near to each other that the difference may be ascribed to unimportant disturbing causes. Physicists often assume quantities to be equal provided that they fall within the limits of probable error of the processes employed. We cannot expect observations to agree with theory more closely than they agree with each other, as Newton remarked of his investigations concerning Halley’s Comet. ”

“ Nothing is more requisite than to distinguish carefully between the truth of a theory and the truthful application of the theory to actual circumstances. As a general rule, events in nature and art will present a complexity of relations exceeding our powers of treatment. The intricate action of the mind often intervenes and renders complete analysis hopeless. If, for instance, the probability that a marksman shall hit the target in a single shot be 1 in 10, we might seem to have no difficulty in calculating the probability of any succession of hits ”

“ An object may be said to be no where, when its parts are not so situated with respect to each other, as to form any figure or quantity; nor the whole with respect to other bodies so as to answer to our notions of contiguity or distance. Now this is evidently the case with all our perceptions and objects, except those of sight and feeling. A moral reflection cannot be placed on the right hand or on the left hand of a passion, nor can a smell or sound be either of a circular or a square figure. ”

“ The indestructibility of matter, and the conservation of energy, are very probable scientific hypotheses, which accord satisfactorily with experiments of scientific men during a few years past, but it would be gross misconception of scientific inference to suppose that they are certain in the sense that a proposition in geometry is certain. Philosophers no doubt hold that de nihilo nihil fit, that is to say, their senses give them no means of imagining to the mind how creation can take place. ”

“ A narrow and intense course of thought may sometimes lead to great results, but the adoption of a wrong theory at the outset is in such a mind irretrievable. The man of one idea has but a single chance of587 truth. The fertile discoverer, on the contrary, chooses between many theories, and is never wedded to any one, unless impartial and repeated comparison has convinced him of its validity. He does not choose and then compare; but he compares time after time, and then chooses.
Having once deliberately chosen, the philosopher may rightly entertain his theory with the strongest fidelity. ”

“ And Aristotle‍489 held a like opinion—Οὐδεμία δὲ τέχνη σκοπεȋ τὸ καθ’ ἕκαστον ... τὸ δὲ καθ’ ἕκαστον ἄπειρον καὶ οὐκ ἐπιστητόν. “No art treats of particular cases; for particulars are infinite and cannot be known.” No one who holds the doctrine that reasoning may be from particulars to particulars, can be supposed to have the most rudimentary notion of what constitutes reasoning and scíence.
At the same time there can be no doubt that practically what we find to be true of many similar objects will probably be true of the next similar object. ”

“ The Principia treats not of gravity so much as of forces in general, and the methods of reasoning about them. He investigates not one hypothesis only, but mechanical hypotheses in general. Nothing so much strikes the reader of the work as the exhaustiveness of his treatment, and the unbounded power of his insight. If he treats of central forces, it is not one law of force which he discusses, but many, or almost all imaginable laws, the results of each of which he sketches out in a few pregnant words. ”

“ It is true, indeed, that it requires much philosophy to observe things which are too near to us.
The high scientific importance attaching, then, to exceptions, renders it desirable that we should carefully consider the various modes in which an exception may be disposed of; while some new facts will be found to confirm the very laws to which they seem at first sight clearly opposed, others will cause us to limit the generality of our previous statements. In some cases the exception may be proved to be no exception; occasionally it will prove fatal to our previous most confident speculations ”

“ Some years of continuous labour would be required to ascertain the types of laws which may govern the combinations of only four things, and but a small part of such laws would be exemplified or capable of practical application in science. The purely logical inverse problem, whereby we pass from combinations to their laws, is solved in the preceding pages, as far as it is likely to be for a long time to come; and it is almost impossible that it should ever be carried more than a single step further. ”