128 ANIMAL BEHAVIOUR 



any one of the 52 cards may be exposed. We say that there were 

 a multitude of definite small causes which led to the disorder of 

 the cards — these were the unanalysable motions of the hands in 

 shuffling the cards. If we knew precisely all these small events 

 and if we knew precisely all the elements of the movements of 

 cutting the pack we could predict what card would be exposed. 

 In principle this is the same as saying that if we laid a penny 

 on the table head down we should know that when we turned 

 it up we should expose a head. That is, the relation between the 

 two events is had from our experience. 



So the effect of shuffling and cutting a pack of cards is not 

 unique but multiple and can be expressed as a series of more or 

 less probable events. Non-mathematical people say that these 

 effects are due to " chance " and can be predicted by the prob- 

 ability-equations of the mathematicians. The latter say that the 

 equations are valid because they are confirmed by experience ! 



Causality is therefore not an a priori, or elementary mental 

 operator, but comes a posteriori from experience. 



Hi. Substance. It is practically convenient to distinguish 

 between a thing and its properties, or attributes. The difflculty 

 is to imagine what remains when we divest a thing of its mass, 

 consistency, colour, odour, form and other properties that are 

 apparent in our perception of the thing. The " thing in itself," 

 that is, the substance underlying the properties, remains, said 

 Kant, though we cannot perceive this " noumenon," or thing-in- 

 itself. Thus the physics of a generation ago regarded the sub- 

 stance of the universe as being the ether of space. All material 

 bodies, all radiations and gravitation were modifications, or 

 motions, of this unknown ether which, as a thing-in-itself, could 

 not be perceived. But the ultra-modern mathematical physicists 

 are able to dispense with the notion of the ether and to regard 

 all things as relations. Thus 2-dimensional flat space is simply 

 the relation ds'^ — gn dx^"^ + 2^12 dx^ dx^ + ^22 ^-^2^ where 

 the g's are " potentials," that is values that, being inserted 

 into a certain, very complex differential equation, cause this to 

 have the value = O. Matter is just another system of " poten- 

 tials." Potentials are given from our knowledge of " intervals." 

 Intervals are observed by reading the scales of clocks and other 

 instruments. Clocks and scales are matter, and matter is just 

 a system of potentials, and so on. Here there is no substance, 



