VERIFICATORY TECHNIQUES 219 



lem of prediction apparently lies simply in the derivation 

 of the required propositions, by means of the rules of logic, 

 from the body of propositions characterizing the theory. 

 But the problem is not so simple. What is important about 

 any hypothesis is not what it implies formally but what it 

 implies contentually. The formal implications of a postulate 

 system are those which can be drawn merely through the 

 applications of the principles of logic; they are not based 

 upon the content of the system, and are therefore independ- 

 ent of what the system is about specifically. They are 

 expressive only of the highly abstract features of events — 

 features which belong to all events indiscriminately, and 

 hence of no importance where reference is made to a limited 

 range of events. The contentual implications, on the other 

 hand, are those which are based on empirical generaliza- 

 tions; they are expressive of the content of the system, and 

 are therefore dependent upon what the system is about 

 specifically. They are expressive of the more concrete ways 

 in which particular kinds of events are associated in nature, 

 and they are true only of events correlated in these ways. 



As Carnap points out, 1 one must recognize the need in 

 physical science for drawing consequences of two different 

 kinds from a given proposition. On the one hand are the 

 transformations which are based on logical rules, such as 

 are found in Principia Mathematica. But one could add to 

 such a system "transformation rules of an extralogical char- 

 acter, for instance some physical laws as primitive sentences, 

 as, for example, Newton's principles of mechanics, Maxwell's 

 equations of electro-magnetics, the two principles of thermo- 

 dynamics, and such like." Carnap calls the former L-rules 

 and the latter P-rules, and the respective consequences 

 L-consequences and P -consequences, a distinction which may 

 be generalized here in terms of formal rules and consequences 

 and contentual rules and consequences. For example, the 

 proposition, " Matter is made up of molecules, and molecules 

 increase their rate of motion through the application of 



1 Philosophy and Logical Syntax, pp. 50-54. 



