[FOM] Russell's influence

Alasdair Urquhart urquhart at cs.toronto.edu
Mon Oct 20 11:04:31 EDT 2003

Dean Buckner's query:

"But then the question is how far did Russell
influence the actual development of anything, aside from being a (very good)
populariser of it?"

isn't hard to answer.  Principia Mathematica, for all its
faults, was THE treatise on mathematical logic right into
the 1920s.  Its influence on the Polish and American schools
of logic are so well known that I need not go into
details.  Its influence on the Hilbert school is less well
known, since Hilbert's work in the Russellian tradition appeared
only as unpublished lecture notes, but Wilfried Sieg, among
others, has been doing detailed historical work on this
little-known episode in Hilbert's career.  

It's only in the 1930s that the influence of the massive 
3-volume treatise begins to wane.   Here, for example, is
Kleene talking to John Crossley in 1974:

	CROSSLEY:  What did you do, Steve, when you first started
	in logic, you didn't have books, did you?

	KLEENE: Didn't have books?

	SACKS: Well, he had Principia (laughter).  Let's see,
	was there a book by Lewis on model theory?

	KLEENE:  Well, I never read Principia; of course I thumbed it a 
	little bit.  Rosser, I guess, started in logic that way,
	but I learned logic by learning Church's sytem, which 
	was subsequently proved inconsistent ...

	"Reminiscences of Logicians", Springer Lecture Notes 
	in Mathematics, # 450 "Algebra and Logic", p.1.

Kleene's mention of Rosser is interesting, because Rosser's
"Logic for Mathematicians" is perhaps the last logic book to be
written in the Principia Mathematica tradition.

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