[FOM] Origins of type theory

[giovanni sambin]

>Roger Jones asks:
>
>
>	> The idea of logical types itself is a descendant
>	> of Frege's hierarchy of functions.
>
>	Can you tell us on what evidence this conclusion
>	is based?

Urquhart replies:

>I think this is fairly clear from the Frege/Russell
>correspondence of 1902.

Just a short piece of information: if you read the book by Bochenski 
on the history of logic (sorry, I don't have a copy at home to be 
able to give the page number), under type theory you find an excerpt 
from Paulus Venetus (wrongly translated in English as Paul of Venice, 
it shoud be Paul the Venetic). Paul is quite clearly thinking of 
types, in a sense very close to our our modern one.
He lived here in Padua and in Siena in the XV century, and wrote two 
books (Logica Parva and Logica Magna) which were textbooks used all 
over Europe for a long time.
Unfortunately this is all I know about the history of type theory 
before Frege, but -in my opinion- it is enough to understand that 
taking Frege as the starting point of types (and sometimes of 
everything in logic) is a too narrow perspective.

Giovanni Sambin
Professor of Mathematical Logic
University of Padua