The Logical Analysis of Existence

Abstract

Besides ‘existentialism’ whose elaboration of existence often represents, to be sure, absurd poetry of uncontrollably high standard, the neopositivistic ‘Vienna Circle’ and the analytic school of philosophy prevalent in England and America have also been concerned with ‘existence’. All these inquiries are based upon the existence concept of the Principia Mathematica of Whitehead and Russell.1 This comes about in the following way: If in connection with Gottlob Frege one considers a proposition such as, for example, ‘the rose is red’ as being composed of the predicate ‘is red’ and the argument ‘the rose’, then such a sentence possesses the form ‘f(a)’ in which ‘f’would symbolize a predicate of one digit and ‘a’ a determinate individual. In place of the symbol for a determinate, constant individual, it is possible to leave the space empty, thus obtaining the propositional form‘f()’ from the proposition. In order to emphasize the fact that something can be put into the empty space between the parentheses, it is also written ‘f(x)’. This variable 2 ‘x’ means nothing at all in itself but only indicates the place in which a constant can be put. Through such a substitution of a constant for a variable, a proposition again results from the propositional form. If, for example, ‘f’ denotes ‘is red’, ‘b’ ‘the tomato’ and ‘c’ ‘the lemon’, then ‘f(b)’ results in the true proposition ‘the tomato is red’ and ‘f(c)’ in the false proposition, ‘the lemon is red’.