220 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



heat," formally implies a number of propositions. It implies, 

 "Matter is made up of molecules," "Molecules increase 

 their rate of motion through the application of heat," 

 "Matter is made up of molecules or of atoms," "Molecules 

 increase or decrease their rate of motion through the ap- 

 plication of heat." But none of these propositions conveys 

 any very important new information about molecules. They 

 are all possible by virtue of the fact that the proposition 

 in question has the form "jo and 9," from which the proposi- 

 tions "jo," "g," "jo or r," and "g or s" follow without regard 

 to content. The contentual implications of the proposition 

 in question, however, are somewhat more informative. If 

 the application of heat to bodies increases the speed with 

 which the molecules are moving, it follows that bodies will 

 expand when heated. If matter is made up of molecules in 

 motion, it follows that gases placed in the same container 

 should diffuse, and that certain solids immersed in fluids 

 should dissolve. Only implications of this kind have any 

 value as instruments of verification; they follow from the 

 particular assumption about the molecular character of mat- 

 ter, and would not, presumably, follow from any alternative 

 theory. Hence they are implications which permit decision 

 to be made as to the adequacy or inadequacy of a theory. 

 Formal implications permit no such decisions to be made. 



But whereas formal implications are of no great use in 

 verification, they are the only techniques for which there 

 are rules. There are no rules for the drawing of contentual 

 implications. No formal analysis of the notion of molecules 

 would enable one to predict what empirical phenomena 

 would exist if there were such things as molecules. The 

 only justification for a contentual implication is an empirical 

 generalization. 'Man' implies 'mortality' because all 

 men are mortal; "metal" implies "conductor of electricity' 

 because all metals are conductors of electricity; "increase in 

 pressure of a gas" implies "decrease in volume" because all 

 increases of pressure are accompanied by decreases in volume. 

 One proposition contentually implies another because the 



