Frege

Friedrich Ludwig Gottlob Frege

Born: 8 Nov 1848 in Wismar, Mecklenburg-Schwerin (now Germany)
Died: 26 July 1925 in Bad Kleinen, Germany

Gottlob Frege was one of the founders of modern symbolic logic putting forward the view that mathematics is reducible to logic.

Frege received his education at the universities of Jena (1869-71) and Göttingen (1871-1873) where he studied mathematics, physics and chemistry. He then taught at Jena in the department of mathematics where he remained, first as a lecturer and then a professor, for the rest of his working life.

Frege lectured on all branches of mathematics although his mathematical publications outside the field of logic are few. His writings on the philosophy of logic, philosophy of mathematics, and philosophy of language are of major importance. He once said

Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.

He was the first to fully develop the main thesis of logicism, that mathematics is reducible to logic. His works The Foundations of Arithmetic (1884) andThe Basic Laws of Arithmetic,Volume1 (1893) are devoted to this project.

His work was not particularly well received, mainly it was ignored. While volume 2 of The Basic Laws of Arithmetic was at the printers he received a letter (on June 16 1902) from Bertrand Russell. Russell pointed out, with great modesty, that the Russell paradox gave a contradiction in Frege's system of axioms. After many letters between the two Frege modified one of his axioms and explains in an appendix to the book that this was done to restore the consistency of the system. However with this modified axiom, many of the theorems of Volume 1 do not go through and Frege must have known this. He probably never realised that even with the modified axiom the system is inconsistent since this was not shown until after Frege's death by Leshniewski.

Frege was a major influence on Peano and Bertrand Russell.

References:

  1. Dictionary of Scientific Biography
  2. Biography in Encyclopaedia Britannica
  3. I Angelelli, Studies on Gottlob Frege and Traditional Philosophy (Dordrecht, 1967).
  4. J D B Walker, A Study of Frege (Oxford, 1965).
  5. E D Klemke (ed.), Essays on Frege (1968).
  6. D A Gillies, Frege, Dedekind, and Peano on the foundations of arithmetic (Assen, 1982).
  7. A Kenny, Frege (London, 1995).
  8. M Dummett, Frege : philosophy of mathematics (London, 1995).
  9. M D Resnik, Frege and the philosophy of mathematics (Ithaca, 1980).
  10. H D Sluga, Gottlob Frege (London, 1980).
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