The W’s article about Evidence of Absence is confusing. They have an anecdote:
A simple example of evidence of absence: A baker never fails to put finished pies on her windowsill, so if there is no pie on the windowsill, then no finished pies exist. This can be formulated as modus tollens in propositional logic: P implies Q, but Q is false, therefore P is false.
But then go on to say: “Per the traditional aphorism, ‘absence of evidence is not evidence of absence’, positive evidence of this kind is distinct from a lack of evidence or ignorance of that which should have been found already, had it existed.“
And at this point I go all ?????.
And then they continue with an Irving Copi quote: “In some circumstances it can be safely assumed that if a certain event had occurred, evidence of it could be discovered by qualified investigators. In such circumstances it is perfectly reasonable to take the absence of proof of its occurrence as positive proof of its non-occurrence.”
Alright so, trying to untangle this mess, they seem to want to make a qualitative distinction between “high-expectation evidence” and “low-expectation evidence.” Now, if you have read other stuff on this blog, like stuff about Bayes’ Theorem and the Bayesian definition of evidence and the many ways to look at probability and… Well, you must know by now that probability theory has no qualitative distinctions. Everything is quantitative. Any sharp divisions are strictly ad hoc and arbitrary and not natural clusters of conceptspace.
Thankfully, there is another quote in that W article that’s closer to the mark:
If someone were to assert that there is an elephant on the quad, then the failure to observe an elephant there would be good reason to think that there is no elephant there. But if someone were to assert that there is a flea on the quad, then one’s failure to observe it there would not constitute good evidence that there is no flea on the quad. The salient difference between these two cases is that in the one, but not the other, we should expect to see some evidence of the entity if in fact it existed. Moreover, the justification conferred in such cases will be proportional to the ratio between the amount of evidence that we do have and the amount that we should expect to have if the entity existed. If the ratio is small, then little justification is conferred on the belief that the entity does not exist. [For example] in the absence of evidence rendering the existence of some entity probable, we are justified in believing that it does not exist, provided that (1) it is not something that might leave no traces and (2) we have comprehensively surveyed the area where the evidence would be found if the entity existed…—J.P. Moreland and W.L. Craig, Philosophical Foundations for a Christian Worldview
This looks much more like Bayesian reasoning than the rest of that article did. But let’s delve deeper and see how to prove a negative.