In this talk, we outline the prehistory of type theory up to 1910 and
its development between Russell and Whitehead's Principia Mathematica
(1910-1912) and Church's simply typed lambda-calculus of 1940. We
first argue that types have always been present in mathematics, though
nobody was incorporating them explicitly as such, before the end of
the 19th century. Then we proceed by describing how the logical
paradoxes entered the formal systems of Frege, Cantor and Peano
concentrating on Frege's Grundgesetze der Arithmetik for which Russell
derived his famous paradox that led him to introduce the first theory
of types, the Ramified Type Theory rtt. We discuss how Ramsey, Hilbert
and Ackermann removed the orders from rtt leading to the simple theory
of types stt upon which Church's simply typed lambda calculus is
based. This is joint work with Twan Laan and Rob Nederpelt.
Workshop on History of Logics, Types and Rewriting
Workshop on History of Logics, Types and Rewriting