380 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



require definition through such operations are strictly mean- 

 ingless. This means, in effect, that "only those aspects of 

 the world have reality which are capable of showing them- 

 selves in some way to the observer." x The operational 

 theory insists "that the meaning of position amounts to a 

 specification of a method of reaching the particle." 2 Ref- 

 erence to this point of view has been made repeatedly in the 

 course of the preceding pages; according to this theory, for 

 example, motion means measured motion, scientific mass 

 means measured mass, and so on. Hence the meaning of any 

 quantitative notion in science involves explicit reference 

 to the techniques employed in obtaining the measured value 

 which is attached to it. 



What, then, on the basis of this theory is the meaning of 

 the mechanical principle which asserts a functional relation 

 between two states of a system — state being indicated by 

 position and velocity? Such an equation is meaningless 

 unless the processes to be employed in measuring a state can 

 actually be carried out. Rut according to the Heisenberg 

 principle this is just what cannot be done if the state in 

 question is that of an electron. For accurate measurement 

 of position is incompatible with accurate measurement of 

 velocity. The obvious conclusion is that the notion of state 

 is meaningless in such a case, and the law stating a relation 

 between states must also be meaningless. This seems a safe 

 conclusion on the grounds of the operational theory. If by 

 causal determination one means predictability, then causal 

 determination must be abandoned. For if one cannot know 

 both position and velocity — which are the sole grounds for 

 prediction — one cannot predict the behavior of any particle. 



Rut the objective indeterminist is not satisfied with this 

 somewhat conservative conclusion. He takes another step, 

 which is much more important in the determination of his 

 outlook. He insists that if a concept is meaningless it cannot 

 designate any natural entity. Hence there cannot be any 



1 A. H. Compton, The Freedom of Man (New Haven: Yale University, 1935), p. 40. 



2 R. B. Lindsay and H. Margenau, Foundations of Physics, pp. 80-81. 



