Reason Hell: Absence of evidence is not evidence of absence

Reason Hell will be an occasional series on reasoning short cuts, fallacies and internet-sayings that pertain to modes of argument.

“Absence of evidence is not evidence of absence” it is a neat saying and a quick comeback but like many neat sayings it is too tidy. As it stands the aphorism is either a legitimate comment or a logical fallacy. This is a term that should be used with great care or not at all.

The first thing to note about the aphorism is that it pertains to evidence. Evidence is not the same as proof. There is no contradiction in saying that there is evidence for A and also evidence for not-A. Even a short treatment of the nature of evidence would be too long for this post and I will save that for a later post. However, it is fairly safe to say that evidence are facts that lend weight to regarding a proposition to be true or to be false. The strongest kind of evidence is a factual counter-example to a more general statement. A counter example is a kind of evidence that can amount to a formal proof that a proposition is false. For statements that are more hedged (most X are Y, many X are Y, frequently X’s are Y’s etc) a counter-example does not amount to a formal proof that the statement is false but clearly adds to a weight of evidence against it.

“Absence of evidence is not proof of absence” is a stronger statement. That there is no evidence of a deity does not prove there is no deity (the deity might be intentionally hiding and being omnipotent can ensure there is no evidence). This though is not aphorism. Applied to the case of a deity an absence of evidence for one would amount to evidence that there isn’t one because we would otherwise expect there to be evidence for a deity if one existed.

Put another way the existence of an X implies that there will be evidence of an X. Framed that way the aphorism looks like a logical fallacy in most cases – the exception being an X that has no material or observable impact on our world. If P implies Q and we can show not-Q then we can conclude not-P. With less the less tight logical implications of evidence, evidence for not-Q is evidence for not-P. Interestingly the reverse is less logically valid (i.e. evidence for Q implying P) but that also is a discussion for another time when I get to empiricism more generally.

Why then, is this aphorism so popular in discussion? Applied correctly it is not fallacious but it all very much depends on why there is an absence of evidence.

I am currently typing this on a train. Is there a man called James Smith on this train? As things stand I do have evidence that there are men on the train (I can see them) and my general knowledge about the country I am travelling in tells me that ‘James’ and ‘Smith’ would not be unusual names for a man on the train. However, apart from that I have no specific evidence on whether there is a James Smith on this train. Is this absence of evidence for James Smith on my train evidence that James Smith is absent from my train? Well, no or rather it isn’t very good evidence for one key reason: I haven’t actually looked.

What I should do if I really wish to establish whether there is a James Smith on the train is to seek him out. I could enter each carriage and call out “James Smith! I’m looking for James Smith!”. If a James Smith answers me then I have strong evidence that there was a James Smith on the train. If no James Smith answer then yes, this absence of evidence is evidence of absence. Not proof of course – James Smith may be hiding his true identity from the crazy person shouting on the train.

More generally absence of evidence is not evidence of absence when we either haven’t looked or we haven’t looked exhaustively or our experimental design or instrumentation may not have been sensitive enough.

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