The Triumph of Force over Logic

In the debate between faith and science, irrational though the premise that they must be antagonistic might be, it is common for scientists to try to take the moral high ground and declare that logic is on their side. Of course, there is a world of difference between what a mathematician calls logical proof and the kind of ‘proof’ usually settled for by other branches of learning, especially in the biological sciences, but that is another story.

What I want to give here is possibly the first example of this high ground not being attained. And the protagonists here are mathematicians, who do know the meaning of rigorous proof. The ancient Greek Pythagoras is credited with being the man who put scientific and philosophical investigation of the world onto a sound foundation. His school, the Pythagorean Brotherhood, collected a vast body of mathematical knowledge and established the principles of logic by which the reliability of such knowledge could be made certain.

However, even Pythagoras failed to live up to his own ideals. He had spent his life establishing a view of the universe based on the harmony of natural numbers and fractions. When one of his students, Hippasus, showed him that a mysterious number, the square root of two, could not be written as a fraction, that it was in fact an irrational number, one might be excused for thinking that Pythagorus would share his delight that a whole new field of investigation was opening up before them. This was not to be the case.

To quote Simon Singh, in Fermat’s Last Theorem (or Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem):

The consequence of Hippasus’ insight should have been a period of discussion and contemplation during which Pythagoras ought to have come to terms with this new source of numbers. However, Pythagoras was unwilling to accept that he was wrong, but at the same time he was unable to destroy Hippasus’ argument by the power of logic. To his eternal shame he sentenced Hippasus to death by drowning.

The father of logic and the mathematical method had resort to force rather than admit he was wrong. Pythagoras’ denial of irrational numbers is his most disgraceful act and perhaps the greatest tragedy of Greek mathematics. It was only after his death that irrationals could be safely resurrected.

So, the so called ‘moral high ground’ of science actually started off in a bit of a valley. And these were mathematicians, who really do know what proof means, not biologists, chemists and other human scientists, for whom proof seems to be more like a blend of economics and politics.

This entry was posted in History of Science, Logic, Mathematics, Philosophy of Science and tagged , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.