[FOM] Foundations and Frege

Charles A Stewart cas at janeway.inf.tu-dresden.de
Tue Oct 14 03:19:43 EDT 2003

Dear William,

A few days ago you wrote, opining that Frege's contributions to foundations are overvalued, but
  His discovery of quantification 
  theory was important for the codification of logic and so ultimately 
  for foundations.

There was an invited talk at the recent FOL75 conference in Berlin by William Ewald
entitled "Frege, Hilbert, and the Discovery of Modern Logic" whose main thrust was to
  1. Frege was the first of several independent discoverers of the quantifiers; the
  discovery of quantification was in many respects waiting to happen.
  2. Frege didn't realise the importance of quantification as a discovery; he was
  more impressed by other features of his Begriffschrift.  In particular, when arguing
  for the superiority of his system over Boole's, the issue of multiple generality and
  relative expressiveness doesn't occur to Frege.
  3. Frege wasn't alone in not realising this: Pierce and Peano also didn't see the
  crucial significance of the quantifier.
  4. Frege's technical work in fact had close to no impact, both Peano and Pierce were
  far more influential.  
  5. The crucial importance of the quantifier was not commented upon until far later,
  by Quine.

(I summarise from memory, possibly my recollection is not entirely accurate).

If we agree with Ewald, then it looks as if Frege's technical influence on the development of
logic is rather slender.


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