A Short History of the Concept of Information
There is a long standing philosophical debate between the platonists and
the aristoteleans. The former emphasize the "world of the forms," whereas
the latter emphasize the "world of becoming." This talk will discuss the
history of the concept of information, starting with Plato (also ironically
Aristotle's contributions), and running quickly through the middle ages to
get to the late nineteenth century and Gottlob Frege's distinction between
"sense" (Sinn) and "reference" (Bedeutung). This distinction reflects itself in
the twentieth century in a more mathematical form via Rudolph Carnap's "
intension" and "extension." The former is shown to be an anticipation of the
even more abstract concept of "information" in Claude Shannon's "information
theory." I will discuss as well how the Carnapian idea is implicit in Stone's
representation theorems for Boolean algebras and distributive lattices, and
in the Jónsson-Tarski representation theorem for Boolean algebras with
operators (which in turn is implicit in the "Kripke semantics" for modal logic).
I will also briefly describe some recent generalizations of the Jónsson-Tarski
theorem due to myself (under the heading of "gaggle theory"). I shall close
with a perspective that grows from this that shows a kind of duality between
information and computation.