Announcement: Chris Langan has published a new paper, "An Introduction to Mathematical Metaphysics", in the journal Cosmos and History.
Syntax is the set of rules obeyed by a language. Each language has its own syntax. For example, a natural language like English has one syntax, while a programming language like Lisp has another syntax. See syntax at Wikipedia for background.
In the CTMU, according to the Principle of Linguistic Reducibility, reality itself is a language. Reality therefore has a syntax, consisting of the set of structural and functional rules governing its spatial structure and temporal evolution. In particular, reality is a Self-Configuring Self-Processing Language (SCSPL) whose syntax includes the laws of mathematics (S1) and physics (S2).
Human cognition and perception can also be viewed as languages, whose syntax is the Human Cognitive-Perceptual Syntax or HCS.