Journal of Philosophical Logic

, Volume 26, Issue 3, pp 237–239

Constructing Cantorian counterexamples


  • George Boolos
    • Department of Linguistics and PhilosophyMassachusetts Institute of Technology

DOI: 10.1023/A:1004209106100

Cite this article as:
Boolos, G. Journal of Philosophical Logic (1997) 26: 237. doi:10.1023/A:1004209106100


Cantor’s diagonal argument provides an indirect proof that there is no one-one function from the power set of a set A into A. This paper provides a somewhat more constructive proof of Cantor’s theorem, showing how, given a function f from the power set of A into A, one can explicitly define a counterexample to the thesis that f is one-one.

Cantordiagonal argumentset theory

Copyright information

© Kluwer Academic Publishers 1997