[FOM] Frege, Russell and type theory

Alasdair Urquhart urquhart at cs.toronto.edu
Fri Oct 17 15:26:55 EDT 2003

I am completely in agreement with Giovanni Sambin
that prefigurations of type theory can be found
much earlier than Frege and Russell.  Alonzo Church
wrote a paper on Schroder's anticipation of the simple
theory of types, and Russell himself went out
of his way to emphasize the natural nature of type
restrictions, and similarities to traditional notions.

Nevertheless, I do think that the historical evidence
shows that Russell's thinking on the theory of types,
and especially type theory as a way out of the paradoxes,
begins from Frege's functional hierarchy.  I did not
mean in any way to make exaggerated claims for Frege
(in spite of my earlier tongue in cheek comments about defending
Frege from his detractors).  Putnam's article that I mentioned
earlier is an excellent corrective to the tendency to think
that Frege invented everything in modern logic (Whitehead
and Russell in fact tended to conceal their considerable
debt to the tradition of algebraic logic).

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