 Consider now the proposition [Murgatroyd’s favourite number, which is an integer between 1 and 10, is prime], and let [Murgatroyd’s favourite number] be tagged as variable. Furthermore, let us restrict the class of permissible substituends by stipulating that (1) objectuality be preserved and (2) no two equivalent ideas be included. In this case, there will be eight permissible substitutions and, of these, four will result in true propositions. The ratio of the number of substitutions resulting in true propositions to the total number is accordingly equal to 1:2. Bolzano calls this the degree of validity of the proposition relative to the specified variables. He comments (TS, II: 81): “This ratio determines the degree of probability which the proposition takes on under certain circumstances.” Universal validity and universal invalidity are extreme cases, in which the ratio is respectively equal to 1:1 and 0:1.