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THE SCIENCE OF DYNAMICS 55 

definition, certain processes of nature as closely as possible. 
Thus our "dynamical world" may be called a model of 
reality, and must not be confused with the reality itself. 

That this model of reality is constructed solely out of logical 
conceptions will result from our conclusion that mathematics 
is based on logic, and on logic alone ; that such a model is 
possible is really surprising on reflection. The need for 
completing facts of nature in thought was, no doubt, first felt 
as a practical need the need that arises because we feel it 
convenient to be able to predict certain kinds of future events. 
Thus, with a purely mathematical model of the solar system, 
we can tell, with an approximation which depends upon the 
completeness of the model, the relative positions of the sun, 
stars, and planets several years ahead of time ; this it is that 
enables us to publish the Nautical Almanac, and makes up to 
us, in some degree, for our inability "to grasp this sorry 
scheme of things entire . . . and re-mould it nearer to the 
heart's desire." 

Now, what is called "mechanics" deals with a very 
important part of the structure of this modeL We spoke of a 
billiard ball just now. Everybody gets into the way, at an 
early age, of abstracting from the colour, roughness, and so on, 
of the ball, and forming for himself the conception of a sphere. 
A sphere can be exactly described ; and so can what we call a 
" square," a " circle " and an " ellipse," in terms of certain 
conceptions such as those called " point," " distance," " straight 
line," and so on. Not so easily describable are certain other 
things, like a person or an emotion. In the world of moving 
and what we roughly class as inanimate objects that is to 
say, objects whose behaviour is not perceptibly complicated by 
the phenomena of what we call " life " and " will," people have 
sought from very ancient times, and with increasing success, to 
discover rules for the motions and rest of given systems of 
objects (such as a lever or a wedge) under given circumstances 
(pulls, pressures, and so on), Now, this discovery means : 
The discovery of an ideal, exactly describable motion which 
should approximate as nearly as possible to a natural motion 
or class of motions. Thus Galileo (15641642) discovered 
the approximate law of bodies falling freely, or on an inclined 
plane, near the earth's surface; and Newton (1642-1727) the