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useful in so far as it has stood in the way of the application of far truer theories whose work, since it began, has shown itself to be one of progressive simplification and progressive fruitfulness.

So, again, the Corpuscular Theory of Light was useful in so far as it made it possible to explain the phenomena of the reflection and refraction of light, and so provided a rallying-centre for the advance of optical theory. But, unfortunately, it had Newton's brain behind it, so that it received a development out of all proportion to its intrinsic merits, and a prestige which gave it an artificial lease of life and prevented the wave-theory, as developed by Young and others, from exercising its due effect on the mind of the time. The non-utility of a false hypothesis is thus evidenced by the fact that the more perfectly it is elaborated, the more surely does it prove a hindrance to the development of Science.

It is true that Bradley's explanation of the phenomenon of Aberration, according to which each fixed star appears, in the course of a year, to describe a small orbit about its true position, was developed on the basis of the Corpuscular Theory, and experts aver that the discovery could not so readily have been made had the wave theory been adopted, so that in this case an erroneous theory led to an important discovery.* At the same time it is hard to convince oneself that what was positively erroneous in the theory could have led to the discovery in question.

CHAPTER XXXIX.

XI. (iii.) GENERALIZATION.

GENERALIZATION is a process so distinctive of the very activity of thought that it is not easy to define it. To be observing a fact or 'particular' in the light of an idea or 'universal' is already to be breaking through its sense-isolation and winning it for thought. A fact is indeed meaningless except in so far as it is relevant to some interest, and rests upon some background, however indeterminate, of questioning mental activity. We start the generalization of a fact when we first realize it as a fact, when we first question its meaning for us and our interests, and so transform the sense-datum into a thought problem. We complete the generalization when the fact is, in all its relevant relations, adequately systematized. If the

* 'The curious inference may be drawn that, if the more correct modern notions of the nature of light had prevailed in Bradley's time, it must have been much more difficult, if not impracticable, for him to have thought of his explanation of the stellar motions which he was studying; and thus an erroneous theory led to a most important discovery' (Arthur Berry, A Short History of Astronomy,' p. 265).

process of generalization may be said to consist in the progressive idealization of fact, in the continuous revelation of fact as an ordered system, the guiding-idea of that process may be defined as the systematizing of fact in the simplest and most economical way, so as to bring the simplest thoughts to bear upon the widest range of facts.

The fundamental form which generalization takes is that of fixing the flux of facts, as immediately experienced, within the steadying and permanent form of a concept. This process is commonly referred to as the generalization of facts under concepts or notions. It consists in starting from the observation of concrete objects, and proceeding thence to a knowledge of classes. This is done by progressively omitting the attributes peculiar to this object or to that, and by retaining those which are attributes of all the objects considered. So viewed, Generalization involves more or less complex processes of Comparison and Abstraction, and culminates in Definition.

In those discussions on the nature of the virtues with which Socrates began the first European 'Philosophy of Morals,' his method was to proceed by critical comparison of a number of instances, to abstract the common or essential features, and then to formulate these in a definition.

'If you were in need of a dinner,' asked Socrates, 'would you apply to a shoemaker ? No, but to a cook. Again, if you were bestormed, and wished to make for a harbour, would you resort to the soldiers on board? Not so, but to the pilot.' After a batch of such questions the learner would be in a position to see that cook, pilot, and the rest shared a common quality in virtue of which, on the respective occasions, application was made to them rather than to others-namely, the quality of being technically qualified.

The process of generalizing facts under concepts is beset by two main difficulties, to which Dr. Venn calls attention in his 'Empirical Logic':

1. There is, first, the difficulty of clearly detecting the common quality in a number of given instances of a certain class. Thus, to take Dr. Venn's instance, 'let A, B, C be Sheffield grinders, a familiar and well-marked class. It had long been known that they were sickly and short-lived people, but the person who first clearly recognized the character of their symptoms, so as to bring the disease '-a sort of lung disease-' under one concept, had no easy task to perform.'*

2. The quality in question may be obvious enough, but the individuals A, B, C, in which the quality is recognized, may never have been classed together. We have then to bring them under one class-concept, the right one for our purpose. This will often

* Dr. Venn, 'The Principles of Empirical or Inductive Logic, ch. xiv., p. 347.

be a matter of great difficulty. Briefly, the detection of the property to be generalized and of the class over which this property is to be generalized is often the most difficult and important of the many operations involved in the establishment of a complete induction.

If the problem of generalizing facts under concepts connects itself with the problem of Definition, that of generalizing concepts under concepts gives rise to the problem of Classification, a problem with which the name of Aristotle is as closely associated as the name of Socrates with that of Definition. In Classification (vide Chapter V.) we have the natural development of the same generalizing tendencies which find their first resting-place in Definition. But the problem of Scientific Classification is far more complicated now than it was in Aristotle's day. Aristotle worked on the basis of certain simplifying assumptions, such as that of the fixity of species, which modern theories of causation and development have rendered more than problematic. As a consequence, the nature of the generalizing processes involved in Scientific Classification and Definition has been greatly modified in modern times. The simpler processes of comparing attributes and abstract points of agreement have given way more and more to the more complex processes of analysing relations and gathering variations around diagnostically defined types. And pari passu with this complication in the nature of the process itself we find that the whole problem of bringing concepts under concepts becomes ever more intimately connected with a further aspect of the generalization-problem. This concerns the bringing of facts under lawslaws of causal interaction and laws of development. The very variability of objects 'forces us beyond the statement of a fixed complex of perceptible characteristics, and obliges us to include causal relations or laws of development in our enumeration of the attributes by which one class of things is distinguished from all others. Quicksilver seems to admit of a simple statement of characteristics by means of which its attributes are expressed in a combination which belongs to no other object; but it is only at an ordinary temperature that it is such an easily recognizable object: it evaporates in heat and becomes solid in cold, it combines with other metals to form amalgams, and with sulphur to form cinnabar, and not until we have included these transformations in our concept can we claim to have stated what quicksilver is' (Sigwart, 'Logik,' vol. ii., part iii., ch. ii., § 77, 6; English Translation, II., p. 163).

In the generalization of facts under laws, the first step is the formulation of what are commonly called 'empirical' laws. There are three essential marks which must be included in the definition of an Empirical Law. In the first place, it must have been gained through direct observation of facts. In the second place, it must not already have been explained as a particular case or specification of some law more fundamental than itself; it is a law, in fact, which has not itself been systematized. Thus Kepler's Laws of Planetary Motion were empirical in this sense until Newton showed that they were necessary deductions from his own principle of universal gravitation. They then became specifications or expressions of the Law of Gravitation. In the third place, the Empirical Law is not an explanatory law. It is a law descriptive of the behaviour of facts, without at the same time being explanatory, or descriptive of the mode of behaviour of a cause. For an explanatory law, as Science understands it, can mean no more (and no less) than a law which necessarily implies a reference to a cause, force, energy, or tendency, though it makes no attempt to explain the nature of that cause beyond defining the law according to which it works.

We may illustrate the meaning of an Empirical Law by means of certain instances which we borrow from Dr. Sigwart (ibid., § 96; E. T., pp. 362-366). We may take the law of falling bodies, which states that, whenever a body falls freely from rest, it describes spaces which are proportional to the squares of the times. This is a law in the sense that it describes the motion of a falling body by means of a formula (2s=gt2), but it is not a law in the causal or explanatory sense: it states the 'how, but not the 'why.' So, again, Kepler's first law tells us that planets move in ellipses about the Sun as focus, tells us how and not why they move as they do; whilst his second law-the law of equal areas-states in a formula the relation between the velocity of a planet and its distance from the sun, and is similarly descriptive and empirical. The law which states the connexion between changes in the height of the tide and the changing positions of sun and moon with respect to each other and the Earth is, again, 'only a descriptive law concerning the regular accompaniment of one change by the other, and it is essentially different from the causal explanation which deduces this connexion from the attraction of moon and sun upon the waters of the earth' (ibid., E. T., II., p. 365). These descriptive statements are particularly frequent and important in Natural History. Thus the following are empirical uniformities, mere laws of sequence and coexistence :

A Dicotyledonous seed, when sown in suitable soil under favourable conditions of moisture, temperature, etc., will commonly germinate. The embryo which it contains will protrude its radicle. This will grow downward, and from it will be developed the primary root which fixes the developing seedling in the soil. This root may branch repeatedly, and ultimately form a complex rootsystem. The two cotyledons will (in many cases) emerge from the seed-coat and develop into green leaves. The stem will grow upward. If an embryonic plumule is present, this will develop its rudimentary leaves into the first foliage-leaves of the growing plant. The stem, like the root, may branch repeatedly, and will give rise to more foliage-leaves, and ultimately to the reproductive shoots known as flowers. The latter will (in many genera) be bisexual, producing both ovules and pollen. If the pistil is pollinated, this will normally give rise to further processes which will lead to the maturing of the seeds. Each seed will contain an embryo capable of developing into a form similar to the parent-plant.

The essential limitation of the Empirical Law is that it cannot be relied on beyond the range of those facts of which it serves to register the behaviour. Thus Kepler's law of equal areas, prior to Newton's generalization of it, was a law of the movement of the planets round the sun. In Newton's hands it became a law of the movements of any rigid body revolving under the influence of any central force acting, as gravitation does, according to the inverse square of the distance. But such an extension of the empirical law was not possible in Kepler's day. It was only the generalization of Kepler's law under Newton's that made this extension intelligible. This further problem of the generalization of laws through their progressive development and simplification, of the generalization of laws under laws, is, however, substantially identical with that of the generalization of facts under laws through Analysis and Synthesis.

The essential means for passing from fact to law is Experimental Analysis; and the explanation which is based upon such analysis takes the form of Synthesis. Facts are, as a rule, complex, and the function of Inductive Explanation is, through analyses and synthetic reconstructions based upon these analyses, to transform the complexity we start from into a strictly relevant coherency. The resolution of the complex fact into its simple factors is the work of tentative analysis-which must try and test itself at every stepthe culmination of the generalizing process being reached in the formulation of the laws according to which these more general factors operate. The systematic reconstruction of the fact, in idea, through deductive processes which, proceeding from the ascertained laws of operation of the factors, show how these factors co-operate in producing the fact, is the work of Synthesis, a synthesis which finds its climax in successful Verification.

The distinction between Analysis and Synthesis may be stated in a somewhat different form by reference to the purposive idea within which the whole process of inductive inquiry takes place. The aim of Analysis, we may say, is to disengage from a given complex situation such elements and combinations of elements as are relevant to its purposive reconstruction. From this point of view Analysis is essentially a process of purposive Elimination, Synthesis a process of purposive Elaboration. Through Analysis we eliminate the irrelevant elements in a total complex datum; through Synthesis we elaborate the relevant residue of Analysis in the light of the idea which has dominated and controlled the whole process.

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