- Towards a Semiotics of Mathematics
The author begins by noting that his approach is unlikely to create new mathematics and so unlikely to be of interest to mathematicians.
Of the referential, formal and psychological aspects of a code, each one in mathematics seems less than straightforward, and each suggests a different approach to the development of a semiotics: platonism, formalism or intuitionism.
Mathematics is a practice. In written papers, the indicative mood is bound up with the notion of proof and ‘truth’, but texts also contain the imperative mood, a set of instructions to be carried out within a known framework. These are largely to be acted upon by the reader, as the Subject who is the imagined, ahistorical reader, and as the Agent, a skeleton diagram of the subject who is imagined to execute certain actions, some of which (such as calculating an infinite sum) would be impossible for a real person to execute. These are both distinct from the Person who reads the mathematics in a certain time and place.
The Subject makes predictions about the results of an activity based on previous knowledge and generalisation. The Person however will tend to seek meta-interpretations such as the idea driving a proof, which lies outside the linguistic reserves made available to the Subject.
There follows a discussion of mathematical signifiers and the assumptions required for them to operate. Formalism, Intuitionism and (the much more dominant, among mathematicians) Platonism are discussed, and the author claims that mathematicians create mathematical reality through the language supposed to describe it.
This essay was written in the 1980s, and now suggests as further reading:
Jay Lemke 1998, Kay O’Halloran 1996, Edwin Coleman 1988, Sun-Joo Shin 1994, Mortensen and Roberts 1997, Paul Ernest 1998.