 An interest in probability lay behind one of Łukasiewicz’s two monographs published before the war, namely Logical Foundations of Probability Theory, which was written and published not in Polish but in German. In 1908 and 1909 Łukasiewicz visited Graz where both Alexius Meinong and Ernst Mally were also working on probability theory at this time, so it is likely that the book was written in German because their language of discussion was German, and also in order to ensure a wider audience. Łukasiewicz’s theory makes constructive use of ideas plucked from elsewhere: from Frege he took the idea of a truth-value, from Whitehead and Russell the idea of an indefinite proposition, and from Bolzano the idea of the ratio of true values to all values for a proposition. Consider the classical urn example, where an urn contains m black balls and n white balls. Let the indefinite proposition ‘\(x\) is a black ball in this urn’ be such that the variable ‘\(x\)’ may take as value any expression naming a ball in the urn: the variable is then said to range over the individual balls, and different expressions naming the same ball to have the same value. (Note that Łukasiewicz indeed uses the terminology, later associated with Quine, of a variable taking values, here expressions, and ranging over objects designated by said expressions.) An indefinite proposition is said to be true if it yields a true proposition (Łukasiewicz says ‘judgement’ for a definite proposition) for all values of its variables, it is false if it yields a false judgement for all values, and is neither true nor false if it yields true judgements for some values and false judgements for others. The ratio true values/all values is then called by Łukasiewicz the truth-value of the indefinite proposition. For true indefinites it is 1, for false indefinites it is 0, and for others it is a rational number between 0 and 1 (rational because only finite domains are considered). In our urn case the truth-value of the indefinite proposition ‘x is a black ball in this urn’ is \(\frac{m}{m+n}\).