The Duhem effect

From the best blog series ever (part III) comes this gem:

Popperian falsification is known in logic as modus tollens.

  • M: If A, then Y.
  • m: But not-Y
  • /.: not-A

But there is never just one A, so what we always have is:

  • M: If A and B, then Y.
  • m: But not-Y
  • /.: Either not-A or not-B

Thus, it is never evident on the face of it which of the prior assumptions -- and there will be more than two! -- has been falsified when Y fails of observation. The problem is, it's hard to know what unspoken assumptions you are assuming. The lack of stellar parallax was thought to falsify A (Earth goes round the sun) but it actually falsified B (the stars are millions of miles away). In fact, they are billions of miles away and the parallax is too small for eyesight to detect even with a 20x telescope. The stellar distance was believed to be fact, based on the brightness and diameter of stellar disks. But it turned out (in the 19th cent.!) that the "disks" were optical illusions caused by aberration, and the stars differed in intrinsic brightness.

In other words: we usually, literally don't know what we're talking about.

Fri, 11 Oct 2013 • permalink