Halliday & Matthiessen (1999: 416-7):
The modern split within the "transcendent" view is between what Barwise (1988:23) calls the world-oriented tradition and the mind-oriented tradition, which he interprets as public vs. private accounts of meaning… . The world-oriented tradition [e.g. formal semantics] interprets meaning by reference to (models of) the world; for example, the meaning of a proper noun would be an individual in the world… . The mind-oriented tradition [e.g. cognitive semantics] interprets meaning by reference to the mind; typically semantics is interpreted as that part of the cognitive system that can be “verbalised”.