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The Rules Of Philosophizing

AT the opening of his Third Book, Newton sets forth the Rules of Reasoning in Philosophy, which in England have been generally accepted with an almost unquestioning reverence. Yet Newton himself never professed them to be exhaustive ; and indeed, as Whewell remarks, they were obviously constructed with an intentional adaptation to the case with which he had to deal, — namely, the induction of universal gravitation, — and are meant to protect the reasonings before which they stand. It is not strange, therefore, that, when considered under other aspects, these Rules should prove to be defective both in precision and in range. Whewell has criticised them without hesitation. Instead of criticising, or defending them, I here propose certain Rules which, while including those of Newton (with such modifications as may bring them into closer accordance with my views), will serve also by their wider range to protect the reasonings which will follow in the course of this work. There may be some temerity in deviating from Newton, for it is with Newton as with Shakespeare, — the genuine reverence of the Few has become stiffened into the superstition of the Many ; and the formalism of superstition is always out-raged by a suggestion of dissent. Men who have seldom or never turned over the leaves of the Principia are exasperated when they hear that any one who has studied and been strengthened by that work ventures to hint at flaws in it. Never having slaked their own thirst at the Holy Well, they hear with impatience of drinkers who presume to reject the weeds and dead leaves which float in its pure water.

Newton is not, however, directly here in question. What the following Rules profess is no more than certain general results of philosophic reflection on the conduct of Research, which are offered to the attentive meditation of the student.

RULE I. — No problem to be mooted unless it be presented in terms of Experience, and be capable of empirical investigation.


The proper statement of a question often carries with it the answer. When the answer is not at once conspicuous, a proper statement limits the field of search by disengagement of the unknown elements, which are then examined in order to determine whether, 1°, they are unknown, and unknowable because metempirical; or, 2°, they are unknown only because the requisite conditions of knowledge lie beyond our present data. In the former case research ceases. In the latter case it proceeds, and is guided by the following rules :-

RULE II. — Any contradiction of fundamental experiences of Sense or Intuition' to be taken as evidence of some flaw either in the data or the calculation.


This seems a truism, yet it is a rule fatally disregarded, partly owing to impatience, which leads men to accept even logical contradiction rather than remain without an explanation ; partly to the conviction that many of the most certain results of science seem in contradiction with ordinary experience. But, in truth, what seems a contradiction proves to be due either to the contradictory mode of statement, or to an erroneous inference from experience; sometimes it is the substitution of a prejudice or tradition for experience.

The Rule simply asserts that since the direct experiences of Sense and Intuition (the perception of objects, and the perception of the relations of objects) have the highest possible validity, and form the basis and the test of all Demonstration, they cannot be contradicted by any real deduction from them ; so that, whenever our deductions or hypotheses involve this logical inconsistency, it is the indication of something somewhere wrong. Does the error lie in our assuming that the experience we declare to be fundamental is direct, whereas it proves by analysis to be indirect, derivative, and possibly imperfect ? Critical examination must decide. The question must be reduced to its components. Thus the old opinion respecting the sun's revolution round the earth seemed to be a fundamental experience which Copernicus contradicted. It was nothing of the kind. It was an inference from experience ; and what the Copernican hypothesis contradicted was not the visible fact, but the inference respecting the invisible cause of that visible fact. Although we believe that the earth revolves round the sun, and that this motion has the effect of making the sun seem to describe the circle, yet what we see is not the motion of the earth, and for most practical purposes the old hypothesis is still employed.

The application of this Rule requires great tact and accurate knowledge. It is violated in many theories which have gained a wide acceptance, and its value is great in keeping the mind open to new evidence, and warning us that any conclusion which violates it must be wrong. The notion of " action at a distance," which still finds energetic defenders, could never have gained acceptance had this Rule been clearly recognized.

RULE III. —" The qualities of bodies which admit neither of intension nor remission of degrees, and which are found to belong to all bodies within the reach. of our experiments, are to be esteemed the universal qualities of all bodies."


This is Newton's Third Rule. On it he remarks : " For since the qualities of bodies are only known to us by experiments, we are to hold for universal all such as universally agree with experiments, and such as are not liable to diminution can never be quite taken away. We are certainly not to relinquish the evidence of experiments for the sake of dreams and vain fictions of our own devising ; nor are we to recede from the analogy of Nature, which uses to be simple. and always consonant to itself. . We no otherways know the extension of bodies than by our senses, nor do these reach it in all bodies ; but because we perceive extension in all that is sensible, therefore we ascribe it to all others also. And this is the foundation of all philosophy."

Professor Challis calls this a golden rule. Whewell speaks slightingly of it ; and indeed it accords ill with his system. To me it seems absolute, if taken with the qualification involved in Rule X. When we generalize experience, and conclude what will be from what has been, it is obvious that our justification rests on the assumed homogeneity of the terms : the event predicted must be of the same nature as the event observed, otherwise the Rule cannot be fitly applied.

RULE IV. — No Agent to be admitted unless it. have a sensible basis ; nor any Agency unless it be verifiable or calculable.


This relates chiefly to Hypothesis. It permits the adoption of any conjecture as to Agent or Agency, provided such conjecture facilitates calculation. But so long as the verifiable nature of either is uncertain, the conjecture must be kept apart from all the positively ascertained data, and rigorously shut out from the final conclusion. In other words, the solution of an equation must always express the unknown quantity in terms of the known quantities ; and every interpretation of a phenomenon must be the interpretation of it in terms of Feeling.

RULE V. We are to admit no more causes of natural things than such as are both true, and sufficient to explain the appearances."


This is Newton's First Rule; and, though not expressed with perfect precision, is pregnant with wisdom. The objection may be raised that, inasmuch as causes avowedly not true can gain no acceptance, the whole question turns on the validity of the causes invoked. What is a vera causa? Newton obviously means by it an Agent or Agency already known to exist, and seen to be sufficient to account for the phenomena if its presence be admitted. Whewell objects that if we never look for a cause except among those already familiar, we shall never become acquainted with any new cause. This objection misses its mark. New Agents or Agencies, when discovered, may be seen to be the causes of phenomena hitherto unexplained ; but to attempt to explain by unknown causes is futile; and the Rule is directed against this very futility.

Curiously enough, Newton himself in his remark on the Rule violates it : " To this purpose the philosophers say that Nature does nothing in vain, and more is vain when less will serve ; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes." Now who shall say that Nature doing nothing in vain is a " true cause," or that Nature's " pleasure " can be known ?

The Rule is important by its exclusion of unknown causes, and by its correction of the tendency to multiply causes. We often find philosophers dissatisfied with an explanation which is sufficient, and seeking additional causes among data that are not given but assumed for the purpose. They fail to recognize that when we have discovered the law of a series, the form of a function, we have reached the limit of research.

RULE VI. —Each cause must always and everywhere have the same effect; and never more than this.


This will be much disputed, owing to the wavering interpretation assigned to the idea of cause. We often hear that different effects arise from the same cause, and that every cause has many effects : in this way Indigestion is said to be the effect of overwork of the brain or the effect of eating raw apples. This is utterly unscientific. Owing to the current laxity of conception even Newton has expressed himself timidly on this point in his enunciation of the Rule : " Therefore to the same natural effects we must as far as possible assign the said causes."

The unalterable rigor of the canon is necessary to the integrity of the conception of every phenomenon every process, every law. All experience, all science, would be a mere sand-heap without it. If the same cause could have different effects, or even slightly varying amounts of the 'same effect, prevision would be impossible. What we call the different effects, are the differences resulting from new combinations of causes. When I come to treat in detail the Problem of Cause, it will be made clear that whether we speak of complex or of simple phenomena there must necessarily be at least two factors for every product; hence, if we sum up the factors in the term Cause, and name the product Effect, it is obvious that the Effect is always the Procession of its Cause : the dynamical aspect of the statical conditions.

Not to enlarge on this point here, let us only remark that the Rule reminds us that no verified fact can be contradicted by any other fact : each has its own intrinsic validity. When two observations seem contradictory, or when the same facts present two different aspects to two observers, this is an indication of some alteration in the conditions, either of the fact itself, or of the observer's position. Under the same conditions phenomena are unalterable.

We may also see that no process can destroy another, although it may be so compounded with it that the result-ant of the two will present a different aspect from that of either of the components. Causes, like motions, may be superposed, each acting independently ; or combined, each acting as a factor: but whether superposed or fused, each cause is invariant; it is only the phenomena that are variable. Hence

RULE VII. — No proof can be valid beyond the range of its data; no conclusion is exact which shuts in what is not included in its premises.


The violation of this is seen when conclusions reached in one department of phenomena are. extended to departments wherein their premises are not the only premises. Although each science throws its light on every other, owing to the interdependence of phenomena and the community of Consciousness, yet no science can be con-trolled by the results of another, and this because phenomena are independent not less than interdependent. Mathematics cannot receive laws from Chemistry, nor Physics from Biology ; the phenomena studied in each are special. But underneath the special differences there are interdependencies, communities, whereby mathematical laws enter into chemical and biological explanations, physical laws into chemical, and chemical into biological. These laws are absolute at their points of intersection, but not beyond. That is to say, the mathematical law is absolute for the mathematical relations of the physical, chemical, or biological phenomenon, but not beyond ; and so of the others. The validity of each vanishes with its limit. In the development of an ovum, for instance, it is demonstrable that physical and chemical laws are involved, and that these are absolute in their order ; but more than these are involved, since by none of the laws hitherto detected in operation among inorganic phenomena is it possible to explain the biological laws of Nutrition, Evolution, Reproduction, and Decay. Should Molecular Dynamics one day be in a position to furnish such a deduction (which is probable), there would still remain the speciality of organic phenomena dependent on a speciality of concurrent causes, which would continue to separate biological from physical and chemical laws.

RULE VIII. — Because the significance of a phenomenon lies wholly in its relation to other phenomena we must never isolate it from this relativity, and draw conclusions respecting it per se.


It is the constant error of metaphysical speculation to attempt a real distinction corresponding with the analytical distinction of a thing from its relations. The thing is its relations, and although analytically we may separate them, attending now to this relation, now to that, we must never imagine the separation to be real.

RULE IX. — We are not to conclude the properties of elements from the properties of the groups they form; nor vice versa.


This, which is the direct consequence of Rule VIII., although obvious enough in many cases, often requires delicate tact in application. No one commits the mistake of supposing that either of the elements of water has when separate the properties of water ; no one supposes that the properties of each element combined in water could be deduced from the observed properties of the combination ; no one supposes that from the observed properties of oxygen and hydrogen, separately considered, the properties of water could be deduced. Yet analogous mistakes are often committed. Many philosophers assume that atoms, or the ultimate elements of Matter, must have the properties observed in masses; and still more assume that the properties of an object belong to it apart from the subject, not as elements of the combined object-subject, but as qualities of the thing per se; while still greater is the number of those who assign to one factor in a causation the character noted in a result due to several factors.

Every mathematician knows that there are numberless theorems true of integers which are not true of the fractions, the properties of the fractions often widely differing from the properties of the integers.

The mistake here pointed out often arises from not discriminating between component parts and constituent elements. What is true of the. mass is generally true of any part of that mass, the difference being only quantitative. A molecule of water has the properties of a gallon of water. But even this is true only of those properties not directly dependent on quantity ; for experiments on finely divided substances show that many a substance begins to lose its molar properties in becoming molecular, since some of the effects which depend on the individual molecules, and which in the mass were mutually balanced, then begin to manifest themselves, the balance being disturbed.

The distinction here indicated between Components and Constituents, or between Parts and Elements, will be seen hereafter to have its importance. All quantitative relations are componental ; all qualitative relations elemental. The combinations of the first issue in Result-ants, which may be analytically displayed; the combinations of the other issue in Emergents, which cannot be seen in the elements, nor deduced from them. A number is seen to be the sum of its units ; a direction of movement is seen to be the line which would. be occupied by the body if each of the incident forces had successively acted on it during an infinitesimal time; but a chemical or vital product is a combination of elements which cannot be seen in the elements. It emerges from them as a new phenomenon.

RULE X. -The validity of conclusions rests on the preservation of homogeneity in the terms and the identity of their ratios.


This extremely important Rule we shall often have to invoke. It will be brought prominently forward in the discussion of Necessary Truths. One of the commonest sources of error is that of unconsciously changing the terms of a proposition without at the same time making the corresponding change in the ratios. Valid generalization can only be effected by extending to many or to all what is positively true of some, it being therein assumed, or proved, that the many, or all, do not differ from the some in the characters ascribed. For example, when we generalize from masses to molecules, it is like passing from large numbers to small numbers, so long as the molecules are assumed, or proved, to possess all the characters known of masses ; but if we observe — and we often do observe — that the masses tend to lose their homogeneity in becoming molecular (which is the passage to their heterogeneity in becoming resolved into their constituent elements), our conclusions respecting their properties tend to become more and more uncertain. We cannot deduce the relative movements in a system from our observation of the movements of that system, — the movements of animals from the movement of the earth, — the rotation of the earth from the movement of the solar system; or, vice versa, the orbital movements of the earth from the relative movements of its bodies. Each problem has its equation of condition; and it is only by generalizing this, that is to say, preserving the homogeneity of its terms and ratios, that any conclusion can be established beyond the particular case.

RULE XI. —Science is built up from Abstractions, and these are built up from Concretes. No Abstraction must contain more than is warranted by its Concretes.

When the Abstraction expresses more than is given in the Concretes, it must be understood as the geometer understands a transcendent ; however useful in preserving the symmetry of expressions, it must never enter into the final equation. We may employ the abstraction Life to express all the concrete phenomena observed, and the unexplored remainder ; but it is only the former that we must admit into our theoretical explanation : the unexplored remainder must not be treated as if it had been explored and mastered. We may employ a fourth co-ordinate to facilitate calculation, but must never allow this symbol to be mistaken for the sign of a concrete reality.

RULE XII. — Carefully to discriminate between the abstract or analytical point of view and the concrete or synthetical point of view.

Experience is the registration of feelings and the relations of their correlative objects. Science is the explanation of these feelings, the analysis of these objects into their components and constituents, which are then held to be the factors of the facts. These factors are of various kinds, real and ideal, concrete and abstract, appreciable by Sense, and appreciable by In-tuition.

Considered subjectively, the real is what is either felt or perceived ; the ideal is what is either imaged — that is to say, the feeling reproduced in the absence of its external object — or conceived, i. e. the feeling represented in a symbol. The real is what is actually given in Feeling. The ideal is what is virtually given, when Inference anticipates what would be Feeling, were the objective causes in direct relation with Sense. Thus the direct experience of the one is supplemented by the indirect experience of the other : vision is completed by prevision : real observation by ideal construction. No sooner has the construction been verified, all its inferences reduced to sensations, all its inductions to deductions, and its deductions to intuitions (by a process we shall hereafter consider), than ideal factors take the place of real factors, prevision of vision, and the truths of ideal relations are recognized as having the same validity as the truths of real relations, for the ideas are virtual feelings. But the process of verification is both complex and delicate, so that whenever an ideal relation is inconsistent with the corresponding real relation, and prevision contradicts vision, the error must lie on the side of the ideal construction.

The starting-point is always Feeling, and Feeling is the final goal and test. Knowledge begins with indefinite Feeling, which is gradually rendered more and more definite as the chaos is condensed into objects, effected through a rudimentary analysis determined by the fundamental Signatures (Qualities) of Feeling, namely, Tension, Intension, Extension, Duration, Likeness, Unlikeness.

Each object is by a subsequent analysis resolved into its components; these again are resolved into their constituents ; and these in turn into their constituents, if the regressive analysis be practicable or serviceable. Thus water is a real object, a concrete fact of our' experience. We learn its properties, and we also learn that it is a mass of molecules, each molecule having the properties , of water, and that the weight or force of the mass is the sum of the molecules. Analysis of this mass will re-solve each of the molecules into its constituent elements, oxygen and hydrogen gas: these have their properties, not the properties of water, and they have their movements, which are not the movements of the molecules. Analysis is. still within the region of the sensible, for the water is only the molecule " writ large " ; but now it takes a further regressive step, and decomposes each molecule of the gases into constituent atoms, or ultimate elements. These are purely ideal. They can-not be presented to Sense, but are presented to In-tuition, and are seen by the mind, not as reals, but as logical postulates, symbols to assist calculation, Thus a curve is a real, but the infinitesimal straight lines into which it is ideally analyzed are symbols only, not reals.

Analysis is descriptive when it deals with components and genetic when it deals with constituents. The one is proximate, sensible, and generally certain ; the other re-mote, extra-sensible, and liable to error: it is always an attempt to explain the known by the less known, some-times by the unknown but hypothetical, consequently it must always have less validity than the synthesis it is invoked to explain. I mean that a fact must always be more certain than the factors by which we elucidate its origin.

Analysis always requires the verification of synthesis. Having taken an object to pieces, we cannot be sure that we have in the pieces all the components or constituents unless we can, really or ideally, build up again the object from those pieces. The failure to re-build indicates the oversight of one or more of the constituents.

RULE XIII. — Philosophy, being the harmony between the concrete and abstract, the synthetic and its explanatory analytic, demands that everywhere the abstract be subordinate to the concrete in respect to validity, though it is superior in point of dignity.


This is insisting on the subordination of means to ends. The purpose of knowledge being the guidance of primitive Impulses for the satisfaction of Desires, obviously Speculation must be subordinated to the Practice which it is intended to serve ; and all conceptions of Reason, however lofty, must have perception and action for their final aim : they are intermediates between the feeling which is. an impulse and the feeling which is the result of that. impulse in action.

But although the end is more important than the means, and although Feeling is final, and Thought has only validity in accordance with Feeling, in point of dignity (that is, of governing value) Thought is supreme, and abstract conceptions are of far higher moment than concrete perceptions. The animal life is higher in dignity than the vegetal ; the social life is higher than the individual. Yet the animal functions depend on the vegetal, the social on the animal. Theories which embody multitudes of relations are more dignified than facts which embody particular relations ; but the theories are subordinate to the facts. The Nation is of more importance than any one Family; and the Family than one of its members nevertheless the dependence of the Family on its members, and of the Nation on its Families, is absolute.

Hence the fallacy must be guarded against which assumes that general laws, or axioms, because of their superior dignity, have a deeper validity than particular truths. Connected with this is the fallacy that laws rule phenomena, determine them ; whereas they only express the phenomena in a formula.

One consequence of this fallacy, which has many, is the error of deducing from averages conclusions which are not of average but of particular relations, — e. g. when the average amount of food consumed by a hundred men is taken as the guide for the rations of the individuals, each man being taken as if he were a unit of the average ; whereas, in fact, each man is markedly different from every other, and the average eliminates the differences.

On the other hand, the Law, or abstract formula o the concretes, is valid when once verified ; any contradiction to such a law must be assigned either to a misinterpretation of its terms, or to a misapplication of it to the case in point. An example of misinterpretation is the common opposition to Mr. Buckle's statement that the number of marriages in a community is regulated by the price of corn, and not at all by the inclinations of the sexes. He has expressed this law so unguardedly that readers in general have rejected it with indignation. But if we reflect that the inclinations of the sexes are constant factors which would determine the marriage of all men and women, were their inclinations left unopposed, and if we recognize among the grounds of opposition none at once so general and so imperative as the need of sufficient food, we see that food must be the variable factor determining the variation in the number of the unmarried, which variation it is that the statistical law formulates. Mr. Buckle was injudicious and wrong' in saying that the inclinations have nothing to do with marriage ; what they have nothing to do with is the variable number of the unmarried, a number expressive of the perturbations to which sexual unions are subjected.

RULE XIV. —"In experimental philosophy we are to look upon propositions collected by general induction from phenomena as accurately or very nearly true, notwithstanding, any contrary hypotheses that may be imagined, till such time as other phenomena occur by which they may be made more accurate or liable to exceptions."


This is Newton's Fourth Rule, and he remarks that we must follow it in order that the argument of induction may not be invaded by hypothesis ; in other words, without too confidently relying on the universality of an induction, we must always prefer it to any reasoning not founded on an inductive basis.

RULE XV. —" Always to prefer the simplest hypothesis compatible with all the observed facts."


This is Comte's first law of Primary Philosophy ; and however self-evident it may appear, is very frequently disregarded, because the scientific use of Hypothesis is so little understood.

That many more rules might be added is indisputable ; but these fifteen are all that I deem necessary for my present purpose. They will be implied throughout the following investigations, and from time to time specially invoked.

( Originally Published 1874 )

Problems of Life and Mind:
The Method Of Science And Its Application To Metaphysics

The Method Of Science And Its Application To Metaphysics

The Method Of Science And Its Application To Metaphysics

The Method Of Science And Its Application To Metaphysics

The Method Of Science And Its Application To Metaphysics

The Rules Of Philosophizing

Psychological Principles

The Limitations Of Knowledge

The Sensational And A Priori Hypotheses

The Sensible, Extra-sensible, And Supra-sensible

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