When engineers or biologists use the word `information', they usually
in mind the work of Claud Shannon. But there are several other theories of
information, most notably that of Carnap and Bar-Hillel (semantic
information theory) and that of Scott and Strachey (domain theory).
This survey contrasts Shannon's approach with semantic information theory,
introduces domain theory, and sketches what the speaker believes to be the
main research problem in modern information theory.