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always occupy several positions simultaneously, and accordingly possess spacial extension and figure.

There is a certain convenience in so distinguishing 'body' and matter' as to use the term 'body' to mean the distinct individuals of the genus 'matter.' A body is ordinarily regarded as that which moves as a unit; as whatever portion of matter may maintain the mutual positions of its parts unchanged, while their relations to other positions are changed. It is this capacity of an extended unit to be dislocated from its context, which is ordinarily regarded as defining its boundaries. And its identity would then be regarded as unaltered so long as this independence of internal on external relations continued. It is not evident, however, that the possibility of motion is necessary for the definition of an individual body. It is strictly necessary only that a region of space should be marked by some distinguishing character that remains unchanged through time. Matter, or physical being, on the other hand, would mean any complex containing something occupying both space and time. That which occupies space and time is indifferent; it is the space-time occupancy that constitutes its material or physical character.' Matter is commonly used also in a narrower but not incompatible sense, to exclude the strictly spacial and temporal properties. In this sense, matter would mean only whatever occupies the space and time, and not the whole complex.

Summarily expressed, then, we may say that 'physical' (bodily or material) connotes two sets of properties: spacial and temporal properties on the one hand; and, on the other hand, space-time-filling properties. The former are such as latitude and longitude, shape, date, and motion; the latter such as color, temperature, and sound. The

1 It will, I think, be generally agreed that neither ‘hardness' nor even 'impenetrability' is regarded by modern science as an essential property of matter. Cf. Sir Oliver Lodge: Life and Matler, pp. 24-34.

I do not mention the more general logical, arithmetical and algebraic properties, such as 'order,' 'number,' etc., because these are not distinctively physical. See below, pp. 108-109, 310-311.

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former may be said to be the fundamental physical properties, because the latter derive their physical character from their relation to the former. It follows that physical events — the immediate subject-matter of physical science, are of two general types. There is, first, the change of spacial-temporal properties; and second, the change of spacetime-filling properties: in short, change of place, and change of state. These events it is the task of science to explain.

$ 5. In what sense does science seek to explain'? Explanation is supposed to supply an answer to the ques

tion “Why?” But this interrogative pronoun Explanation and Description suggests several questions which, in the course in Science

of the development of science, have proved irrelevant to its special interest. For many minds, and, during a considerable period, even for the scientific mind, the demand for explanation has been satisfied by the reference of an event to a power, regarded as sufficient to produce it. Thus before Galileo's time, terrestrial motions were accounted for by attributing them to powers of "gravity" and "levity.” And similarly Kepler explained planetary motions by attributing them to celestial spirits." It seemed necessary to provide an agency having a capacity for effort as great as, or greater than, the effect; and immediately present to the effect, as the soul is present to the body it moves. But Galileo and Kepler have contributed to the advancement of science only because they have added to such explanation as this, an exact account of the process or form of terrestrial and planetary motions. Just how do bodies fall and planets move? This is the question which for scientific purposes must be answered; and only such answers have been incorporated into the growing body of scientific knowledge. Who or what moves bodies, in the sense of agency or potency, is for scientific purposes a negligible question; attempts to answer it have been, in the course of the development of science, not disproved, but disregarded. 1 Whewell: History of the Inductive Sciences, third edition, Vol. I, p. 315.

And the same is true of another sense of the interrogative 'why.' It is not infrequently taken to mean, “To what end?” “For what good?” Thus, we are said to 'understand' the beneficent works of nature, but to see no reason' for vermin, disease, and crime. Or, if we do seek a reason, we find it in some indirect beneficence that may be attributed to these things, despite appearances. This is the teleological or moral type of explanation. It appears in the ancient regard for 'perfect' numbers and forms, in the Platonic principle of the Good, and in the Christian notion of Providence. But this species of explanation, too, has been not disproved, but progressively disregarded by science. It has come to be the recognized aim of science to formulate what happens, whether for better or for worse; leaving out of account, as an extra-scientific concern, whatever bearing it may have on interest.

It appears, in other words, that the common distinction between explanation and 'mere description' will not strictly hold in the case of scientific procedure. For science, to explain is to describe - provided only that the description satisfies certain conditions.2

$6. There are two specific conditions which description must fulfil, if it is to be sufficient in the scientific sense. In Conditions of

the first place, scientific description must reveal Scientific De- the general and constant features of its subjectscription

matter. It is a truism that thought tends to unify. The bare quale of phenomena, their peculiar individuality, gives way to certain underlying identities. Or, since natural science deals primarily with changes, bare novelty gives way to an underlying permanence. In other words, scientific thought is interested in what is the same, despite difference, or in what persists, despite change.'

1 For this purely theoretical motive in science, cf. above, pp. 25-28.

2 Cf. E. Mach: “The Economical Nature of Physical Inquiry” in his Popular Scientific Lectures, trans. by T. J. McCormack, p. 186.

As we shall presently see, this does not mean that science forces identity and permanence upon an alien chaos or flux, but only that science is interested in laying bare what identity and permanence is there.

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Furthermore, science is interested in relating the difference to the identity, and the change to the permanence; showing, so far as possible, that the former is a determinate variation of the latter.

And this brings us to the second condition which scientific description must fulfil. It must be analytical or exact in its final form. This does not mean imposing such a form upon nature arbitrarily. Bodies, as we have seen, are primarily spacial and temporal, and both space and time possess what is called 'extensive' magnitude, such as number,' 'length,' 'breadth,' 'volume,' 'interval,' etc. Furthermore, the space-time-filling properties of bodies have a form of magnitude called 'intensive' magnitude, such as 'intensity of light,' 'degree of temperature, etc. Changes of magnitude, whether extensive or intensive, can be exactly described only in mathematical terms. And underlying the strictly quantitative characters of bodies are certain more abstract characters, such as 'relation,' 'order,' 'continuity,' an exact description of which leads likewise to a mathematical or logical formulation. Where such descriptions have been obtained, as in the case of physics, we speak of 'exact science. And such science serves as the model of scientific procedure in general.

Scientific description, then, is governed by two motives, on the one hand, unity, parsimony, or simplicity, the reduction of variety and change to as few terms as possible; and, on the other hand, exact formulation. When a scientific description satisfying these conditions is experimentally verified, it is said to be a law. And it is certain that nothing more is required for purposes of scientific explanation than the discovery of the law. Whether this is a sign of the degeneracy of science, or of its logical refinement, it will be our task presently to inquire. But we shall be better prepared to raise this question, and we shall better understand what has gone before, if we now turn to a brief examination of certain samples of scientific

1 See below, pp. 93-100

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procedure. The philosophical interpretation of science turns not so much upon special scientific laws, as upon the general character common to all scientific laws. And this character is most evident in the case of certain mechanical laws, which are at the same time relatively simple and relatively fundamental. I shall therefore attempt to show briefly what is meant by 'acceleration,' 'mass,''gravitation,' and 'energy,' in relation to the empirical facts which they are intended to describe.

& 7. It has been said that modern science came "down from heaven to earth along the inclined plane of Gali

Galileo's importance lies not only in his specific contributions to mechanics, but in the example of

his method — the analytical description of Illustrations of Scientific motion. In order to understand the concept Method. Galileo's Con

of acceleration, which Galileo employed for ception of Ac- the description of a body's fall to the earth, celeration

let us begin with the simpler concepts which it implies. Motion, as we have seen, means a continuous change of place through a period (also continuous) of time. In other words, a body is said to move when a certain constant space-time-filling property is correlated with a continuously varying distance (d), measured from the point of origin, and a continuously varying period

(t), measured from the moment of origin. The scientist, seeking to discover constancy even where it does not at first appear, and to relate the constancy to the variability, is led to conceive of a constant proportion among these variables. It may be, e.g., that whereas d and t change, the fraction d/t remains the same. In other words, whereas the distance and the time vary severally, it may be that the ratio, 'velocity' (v), is uniform. This does not

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1 Bergson: Creative Evolution, trans. by A. Mitchell, p. 335. The best account of Galileo's services to science is to be found in Mach's Science of Mechanics (translated by T. J. McCormack). This book, W. Ostwald's Natural Philosophy, trans. by T. Seltzer, and K. Pearson's Grammar of Science, may be consulted for a more detailed statement of scientific concepts.

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