[FOM] Re: Papers of Poincare (Akihiro Kanamori)

[Colin McLarty]

Church was mistaken to think the 1908 version of these papers had 
"substantial additions". Rather, the papers were somewhat rearranged for 
the book.

The Dover translation of 1952 has very substantial deletions. It omits the 
most mathematical sections, and the most polemical arguments with the 
logicists - the parts deemed least interesting to the general public. These 
arguments are the funniest and meanest parts of the paper. I do not know if 
Ewald has a new translation or used the same abridged one.

Goldfarb discusses the papers from Russell's point of view and finds 
Poincare a decidedly incompetent logician. For example, Poincare believed 
that no axiomatization of arithmetic could ever be complete. Russell left 
the question open. This was long before Godel, and Poincare had no kind of 
proof of his claim. So you could take Poincare's view as a mere prejudice.

Poincare enthusiastically admired Hilbert's FOUNDATIONS OF GEOMETRY. He 
championed Cantor's set theory and was among the first mathematicians to 
actually use it. (He used it to study limit points of orbits in topological 
dynamics.)  So you can read him as much friendlier to logic than Russell 
and Goldfarb do. That way you can relate his philosophy of math more 
directly to his mathematical work. Poincare often tied his math to his 
philosophy but most of it is omitted from the abridged translation. I have 
written about this in "Poincaré: Mathematics & Logic & Intuition", 
Philosophia Mathematica (3) 5 (1997) 97-115.

best, Colin