LAWS OF NATURE 47 



essential part. Moreover, here again it is a means of testing ; for 

 we cannot combine incompatible, that is true and false, deductions. 

 At any rate, the attempt to combine them tends to sift the true 

 from the false. First we gather facts, as it were, into bundles by 



each of which includes a considerable range of phenomena ; but they are scarcely 

 what we understand by ' laws of nature.' A law is rather a description of a 

 uniformity in the way in which bodies affect one another ; or, in other words, 

 a description of the way in which they behave under uniform conditions. 

 Material bodies have properties or qualities which bring them into relation with 

 each other. From uniform relations, consequent on the possession of qualities 

 of like nature, uniform results follow. Thus, the statement that all material 

 bodies attract each other directly as their mass and inversely as the square of 

 their distance is unmistakably a law. A law is, in fact, a theory ; it describes 

 a uniformity in terms of causation (see 586) ; therefore it describes a uniformity 

 in the sequence of phenomena. It is a peculiarity of a natural law in the strict 

 scientific sense that we are able to deduce consequences from it, and so are able 

 not only to link up with it, and thereby ' explain ' phenomena not directly mentioned 

 in it, but we are able also in this way to test the truth of it. At any rate, a law 

 is valuable to us as a means of systematizing our facts in proportion as we are able 

 to make deductive inferences of consequences from it. No consequences worth 

 mentioning can be deduced from the uniformities that common primroses are 

 yellow, mammals have heads, and birds are bi-pedal. Here we do not describe 

 ways in which bodies affect one another. But any number of consequences can 

 be deduced from the law of gravitation. Here we do describe a way in which 

 bodies are affected by each other. We do not know why material bodies attract 

 each other, nor why they attract each other in the degrees that they do. But, 

 if the law of gravitation is a correct statement, if material bodies do attract each 

 other in the degrees stated in it, then, since contradictories cannot both be true, 

 given certain conditions, certain consequences must follow. Thus, given a planet 

 moving in accordance with the laws of motion with a certain momentum, at a 

 certain distance from the sun, then it must circle in a certain path round the sun ; 

 given the moon at a certain distance from the earth, then the tides of the ocean 

 must follow its course ; given lack of support, then stones must fall to the ground ; 

 given a fluid condition, then the surface of a body (e.g. water) must conform to 

 the general contour of the surface of the earth at the latitude in which it is situated ; 

 and so on. " Those ideas that hold good throughout the widest domains of 

 research and that supplement the greatest amount of experience are the most 

 scientific " (Mach, Principles of Mechanics, p. 490). Those sciences (e.g. physics 

 and mathematics) which are the most completely welded together by laws and 

 deductions from them, are the most completely scientific, the most completely 

 interpretative, the most completely intelligible. The fewer the laws necessary for 

 this process of welding the better ; for then the welding is the more perfect since 

 all the more is included within the range of each law. Those sciences (e.g. anatomy) 

 that are the least deductive, that are the least interpretative, are the least com- 

 pletely scientific (see 819 et seq.). If the reader devotes a moment's consideration 

 to the subject, he will perceive that nearly all thinking about heredity and evolu- 

 tion,|like much of the thinking in mathematics and physics, but unlike all thinking 

 in the ' systematic ' sciences (e.g. zoology and botany), consists in attempts to 

 explain the facts, or, in other words, to link them together in chains of causation. 

 When we link facts in this way, we join them by inferences. An inference is a 

 hypothesis. Hypotheses can be proved only by deductive appeals to reality. 

 A law is a hypothesis that has been fully established by such appeals. All the 



