Philosophers tried hard to repair the definition by conditioning on what they called “background factors” (another word for confounders), yielding the criterion P(Y | X, K = k) > P(Y | K = k), where K stands for some background variables. In fact, this criterion works for our ice-cream example if we treat temperature as a background variable. For example, if we look only at days when the temperature is ninety degrees (K = 90), we will find no residual association between ice-cream sales and crime. It’s only when we compare ninety-degree days to thirty-degree days that we get the illusion of a
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