210 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



arrangeable on a scale through the numerical measures of 

 their wave lengths; chemical substances become arrange- 

 able in a table on the basis of atomic weights; circles, ellipses, 

 parabolas, and hyperbolas become related through a general 

 quadratic equation. As a result every symbol in the system 

 takes on important relations to other symbols, and signifi- 

 cant information about any symbol may be obtained merely 

 by exploring its intensional features. Definition plays a 

 predominant role, which replaces that of illustration in 

 descriptive science. For as the system takes on integration 

 the meaning of any symbol becomes increasingly a function 

 of its associated symbols, and decreasingly a function of its 

 referent. 



In view of this fact there arises a peculiar duplicity in the 

 meaning and truth of those descriptive propositions which 

 have been explained by the postulates. A descriptive 

 proposition has two very important relations, both of which 

 may be considered as contributing to its meaning and truth : 

 It has a relation to the fact which it describes, and it has a 

 relation to the postulate group from which it can be deduced 

 and by which it is explained. For example, the proposition 

 2 + 2 = 4 is descriptively true, since it states a fact about 

 stones, leaves, and other physical objects; but the proposi- 

 tion is also deductively true since it can be deduced from a 

 series of postulates constituting the logical foundations of the 

 number system. There is no difficulty here, since the proposi- 

 tion is true in both senses. But there are propositions which 

 are descriptively false yet deducible from postulate schemes, 

 and the question arises in such cases as to whether the 

 propositions are true or false. The answer is to be found in 

 considerations of the kind suggested in Chapter VII in the 

 discussion of analytic and synthetic propositions. 1 Whether 

 a proposition of the kind in question is to be considered as 

 true or false depends upon whether the intensional relations 

 are or are not to be taken as regulative over the extensional, 

 i.e., whether the deducibility of a proposition from a postu- 



» Pages 142-143. 



