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billswift comments on Counterfactual resiliency test for non-causal models - Less Wrong
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Hum... That is one suggested way of going. But it does seem to ignore the fact that these non-causal models are claimed to be correct, without needing to know anything much about the underlying processes.
Maybe "small" should be calibrated by the claims of the model?
At least for the three examples you cited, I seem to remember them bring called approximations, not "correct".
What's the difference between a singularity, and an approximate singularity? :-)
In the former case, it progresses asymptotically, while in the latter, it progresses exponentially or super-exponentially but not asymptotically.