Counterfactual Thinking

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.