Interrogative Sentences (1934/1938)

Abstract

Let us replace the word ‘John’ in the sentence ‘John is a man’ by the letter‘x’ which has no meaning. The resulting expression will be ‘x is a man’. Since ‘x’ has no meaning, this expression is neither true nor false, hence it is not a sentence. It is, however, a formula from which a true or false sentence may be obtained, provided for the letter ‘X’ we substitute suitable meaningful expressions. viz. suitable terms. An expression which in place of a word contains a meaningless letter or letters and which turns into a sentence when for those letters suitable meaningful words are substituted, is known as a propositional formula or a propositional function. The meaningless letter which occurs in a propositional function is a variable. The following are examples of propositional functions: ‘x is a man’, ‘John R Peter’, ‘x + 5 = 7’, etc. It is obvious that the first of these expressions will be transformed into a sentence on replacement of ‘X’ by suitable names, the second will turn into a sentence on substitution of suitable functors for ‘R’ (sentence-forming functors like ‘likes’, ‘beats’, ‘saves’, etc.), the third on replacement of‘X’ by numerals.

Translated by Jenzy Giedymin. First published in Logiezne Podstawy Nauczania, Encyklopedia Wychownia. Warszawa 1934, reprinted 1938. Translation based on Jezyk iPoznenie, I, 278–286. Reprinted here by kind permission ol PWN.