Misquoting Hume

The problem with words over math

In #articles

I recall a comment in E. T. Jaynes' book about Laplace, where he realized that most of the arguments against the claims of Laplace were arguments against things Laplace never said. Jaynes would habitually check the original source whenever he heard claims ascribed to Laplace, and found that Laplace was consistently misquoted. Recently, I have realized that the same can be said of Hume. I've written before about the claim that Hume believed we have "no good reason at all for thinking the sun will rise tomorrow" (spoiler alert: he didn't believe this).

So, I've seen this little pithy Hume quote:

"The evidence for the regular is always greater than that for the rare."

in various critiques of Hume on the web. The problem? Hume never says this. You can read Hume's actual statements about miracles in the two parts of his argument here: part 1 and part 2. The misquotes that I have seen are always from Christian apologists, so it isn't totally surprising.

I think one of the reasons this occurs is that Hume predates probability theory, so he uses verbose explanations where the modern reader can insert a single statement. For example, reading Hume's work on Miracles, it is clear to me that what he intends to say is simply

the prior probability for the regular is always greater than the rare

a bit less pithy, but more correct (although Hume doesn't phrase it quite like that either). This is at least a factual statement - before the data, we should believe the regular over the rare. That doesn't imply that data couldn't convince us of rare events, it only implies that it is more difficult for data to convince us of rare vs regular events (i.e. you need better evidence for the rare).

In an Unbelievable podcast interview with apologist Norman Geisler, Geisler uses the first "quote" of Hume above, and then argues that Hume must be wrong because science already accepts singular and rare events - the Big Bang, the origin of life, and macro evolution (this last one is, of course, neither singular nor rare). Geisler then concludes that miracles can exist! However, seen in the light of probability theory, it becomes clear.

The prior probability of the events is low: \begin{eqnarray} P(\mbox{Big Bang})\ll 1 \\ P(\mbox{Origin of Life})\ll 1 \\ P(\mbox{Macro Evolution})\ll 1 \\ P(\mbox{Miracles})\ll 1 \end{eqnarray} but with data, we have something quite different: \begin{eqnarray} P(\mbox{Big Bang}|{\rm data})\sim 1 \\ P(\mbox{Origin of Life}|{\rm data})\sim 1 \\ P(\mbox{Macro Evolution}|{\rm data})\sim 1 \\ P(\mbox{Miracles}|{\rm data})\sim 0 \end{eqnarray} where the data are

  • Big Bang - a long list
  • Origin of Life - a nice summary with RNA world, and autocatalysis
  • Macro Evolution - a term not used by biologists, but another long list for evolution
  • Miracles - nothing convincing to the scientific community

So, although all these things can occur, only a few of them actually have evidence strong enough to overcome their initial low prior probability. Hume recognized this for miracles, as was clear from his writings, although it would have been clearer had he had the benefit of probabilistic vocabulary. Don't take my word for it, go read Hume here, and here.