

Counterfactual Thinking - danger
http://terrytao.wordpress.com/2010/10/18/the-no-self-defeating-object-argument-revisited/

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danger
Among others, I liked this quote:

This is not to say that counterfactual thinking is not encountered at all
outside of mathematics. For instance, an obvious source of counterfactual
thinking occurs in literary fiction, particularly in speculative fiction such
as science fiction, fantasy, or alternate history. Here, one can certainly
take one or more counterfactual hypotheses (e.g. “what if magic really
existed?”) and follow them to see what conclusions would result. The analogy
between this and mathematical counterfactual reasoning is not perfect, of
course: in fiction, consequences are usually not logically dictated by their
premises, but are instead driven by more contingent considerations, such as
the need to advance the plot, to entertain the reader, or to make some moral
or political point, and these types of narrative elements are almost
completely absent in mathematical writing). Nevertheless, the analogy can be
somewhat helpful when one is first coming to terms with mathematical
reasoning. For instance, the mathematical concept of a proof by contradiction
can be viewed as roughly analogous in some ways to such literary concepts as
satire, dark humour, or absurdist fiction, in which one takes a premise
specifically with the intent to derive absurd consequences from it. And if the
proof of (say) a lemma is analogous to a short story, then the statement of
that lemma can be viewed as analogous to the moral of that story.

