STEP-FUNCTIONS 7/9 



The presence of step-functions in an absolute system enables 

 both schools to be right, provided that those who maintain the 

 determination are speaking of the system which comprises all the 

 variables, while those who maintain the possibility of spontaneous 

 change are speaking of the main variables only. For the whole 

 system, which includes the step-functions, is absolute, has one field 

 only, and is completely state-determined (like Figure 7/8/1). But 

 the system of main variables may show as many different forms of 

 behaviour (like Figure 7/8/2, I and II) as the step-functions 

 possess combinations of values. And if the step-functions are not 

 accessible to observation, the change of the main variables from 

 one form of behaviour to another will seem to be spontaneous, for 

 no change or state in the main variables can be assigned as its 

 cause. 



The argument may seem plausible, but it is stronger than that. 

 It may be proved (S. 22/5) that if a 4 machine ', known to be 

 completely isolated and therefore absolute, produces several 

 characteristic forms of behaviour, i.e. possesses several fields, then 

 there must be, interacting with the observed variables and included 

 within the c machine ', some step-functions. 



89 



