166 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



mathematics are assigned the analysis of the "formal" 

 mode of statements. Such statements "are tautologies, 

 analytic propositions, certified on account of their form 

 alone. They have no content, that is to say, assert nothing 

 as to the occurrence or non-occurrence of some state of 

 affairs. If to the statement: ' The (thing) A is black' we add 

 'or A is blue 1 the supplemented statement still conveys 

 some information though less than at first. If, however, we 

 replace the supplementary phrase previously chosen by ' or A 

 is not black' the compound statement no longer conveys 

 any information at all. It is a tautology, i.e., is verified 

 by all circumstances." 1 



But to consider a proposition formally is to consider it 

 linguistically . ' We will call ' formal ' such considerations or 

 assertions concerning a linguistic expression as are without 

 any reference to sense or meaning." 2 By a language is 

 meant the "system of the rules of speaking. Such a language- 

 system consists of two kinds of rules, which we will call 

 formation rules and transformation rules. The formation 

 rules of a certain language-system S determine how sentences 

 of the system S can be constructed out of the different kinds 

 of symbols." 3 "The transformation rules . . . determine 

 how given sentences may be transformed into others; in other 

 words: how from given sentences we may infer others." 4 

 "Given any language-system, or set of formation rules and 

 transformation rules, among the sentences of this language 

 there will be true and false sentences. But we cannot define 

 the terms 'true' and 'false' in syntax, because whether a 

 given sentence is true or false will generally depend not 

 only upon the syntactical form of the sentence, but also 

 upon experience; that is to say, upon something extra- 

 linguistic." 5 Formal propositions, however, are true or 

 false simply by virtue of the rules of language. 



These statements seem to justify an interpretation of 

 Carnap's position which affiliates him rather closely with 



1 Ibid., pp. 33-34. 



2 R. Carnap, Philosophy and Logical Syntax (London: Kegan Paul, 1935), p. 39. 



3 Ibid., p. 41. * Ibid., p. 43. 6 Ibid., p. 48. 



