90 THE FOUNDATIONS OF SCIENCE 



began our survey. Our experience gives us data 

 on which to reason ; particular instances to which we 

 may apply our intuitive knowledge of the relations 

 between universals. 



Our experience gives perceptions which suggest 

 the corresponding concepts of length, time, and 

 force, and from them we divine the secondary con- 

 cept of mass, related to force by the definition that 

 a mass (ra) is measured by the force (/) required to 

 give it unit acceleration. Hence we get the symbolic 



statement 



/= mxa. 



This relation is suggested by our experience of 

 the force required to set masses in motion, but, in 

 its accurate form, it is a consequence of our defini- 

 tion of mass. Thus, strictly, we can only know that 

 it applies to the conceptual world. Given our con- 

 cepts of length, time, and force, and our definition 

 of mass, the relation f= ma is a consequence of our 

 logical laws of thought, and gives only a necessary 

 relation between our ideal concepts of universals. 



But, as a matter of experience, we find that this 

 relation serves as a valid basis for the practical 

 science of dynamics. To build that science, we 

 need further experience of actual cases. Newton, 

 associating the fall of an apple with the fall of the 

 moon, makes the hypothesis of an attracting force 

 between masses to explain both. Deducing by 

 logical intuitive principles the consequence of the 



