Numbers in Elementary Propositions

Abstract

It is often held that Wittgenstein had to introduce numbers in elementary propositions due to problems related to the so-called colour-exclusion problem. I argue in this paper that he had other reasons for introducing them, reasons that arise from an investigation of the continuity of visual space and what Wittgenstein refers to as ‘intensional infinity’. In addition, I argue that the introduction of numbers by this route was prior to introducing them via the colour-exclusion problem. To conclude, I discuss two problems that Wittgenstein faced in the writings before Some Remarks on Logical Form (1929), problems that are independent of the colour-exclusion problem but dependent on the introduction of numbers in elementary propositions.