 The demarcation between contingent propositions, which can be used to correctly or incorrectly represent parts of the world, and mathematical propositions, which can be decided in a purely formal, syntactical manner, is maintained by Wittgenstein until his death in 1951 (Zettel §701, 1947; PI II, 2001 edition, pp. 192–193e, 1949). Given linguistic and symbolic conventions, the truth-value of a contingent proposition is entirely a function of how the world is, whereas the “truth-value” of a mathematical proposition is entirely a function of its constituent symbols and the formal system of which it is a part. Thus, a second, closely related way of stating this demarcation is to say that mathematical propositions are decidable by purely formal means (e.g., calculations), while contingent propositions, being about the ‘external’ world, can only be decided, if at all, by determining whether or not a particular fact obtains (i.e., something external to the proposition and the language in which it resides) (2.223; 4.05).