Provenly Unprovable

Solomon Feferman

• Incompleteness: The Proof and Paradox of Kurt Gödel by Rebecca Goldstein
  Norton, 224 pp, US $13.95, February 2006, ISBN 0 393 32760 4

Like Heisenberg’s uncertainty principle, Gödel’s incompleteness theorem has captured the public imagination, supposedly demonstrating that there are absolute limits to what can be known. More specifically, it is thought to tell us that there are mathematical truths which can never be proved. These are among the misconceptions that proliferate around Gödel’s theorem and its consequences. Incompleteness has been held to show, for example, that there cannot be a Theory of Everything, the so-called holy grail of modern physics. Some philosophers and mathematicians say it proves that minds can’t be modelled by machines, while others argue that they can be modelled but that Gödel’s theorem shows we can’t know this. Postmodernists have claimed to find support in it for the view that objective truth is chimerical. And in the Bibliography of Christianity and Mathematics (there really is such a publication) it is asserted that ‘theologians can be comforted in their failure to systematise revealed truth because mathematicians cannot grasp all mathematical truths in their systems either.’ The incompleteness theorem is also held to imply the existence of God, since only He can decide all truths.