[FOM] Re: Origins of type theory

Alasdair Urquhart urquhart at cs.toronto.edu
Tue Oct 21 16:12:40 EDT 2003

Just a brief followup to Allen Hazen's posting
on the history of type theory.  

The (rather complicated) history of 
The Principles of Mathematics is recounted by
Kenneth Blackwell in "Russell" N.S. Volume 4.
Appendices A and B were added to the book 
late in the day, when the main part of manuscript
was already in press.  

There is good evidence to show that Russell originally
hoped to solve the Contradiction in Appendix B (on
the theory of types), but in the published version,
he admits defeat.  The theory of Appendix B is 
basically the simple theory of types, as Allen Hazen
says, but it's contradictory because Russell refuses
to type propositions, and so gets a propositional
version of the Contradiction.  Hence, the theory
is Simple Theory of Types + Inconsistent theory
of untyped propositions.

Of course, the ramified theory of types emerges 
precisely through typing propositions.

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