Wednesday, 10 December 2014

Evidential Support is More Complex than 'For' or 'Against'

A naive view of probability pictures it as the result of a sort of tug-of-war between arguments for a statement and arguments against that statement.  If the arguments in favour of a proposition beat the arguments against, the probability will be high.  If it's the other way round, it'll be low.  Some critical thinking techniques, such as argument mapping or analysis of competing hypotheses, can promote this way of thinking, which is unfortunate because it's misleading.

When evaluating a hypothesis or scenario, the evidence cannot easily be split into 'for' and 'against' arguments for separate consideration.  Instead, all of the evidence needs to be considered as a whole.  The final probability of the target hypothesis is determined by the likelihood of all of the evidence conditioned under both that hypothesis and its alternatives, and is not straightforwardly a summation of parts of the evidence.

As an example, take these three statements:

A: "Jones lives in Eton College"
B: "Jones is more than twenty years old"
C: "Jones is female"

Taken alone, (A) is certainly evidence against (B).  Knowing that Jones is at Eton makes it highly likely that he's a boy or a young man.  But if you know (C), that Jones is female, (A) becomes very strong evidence in favour of (B), since it's highly likely she's a teacher or the wife of one.  

Items of evidence cannot, in other words, be treated in isolation from one another.  

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