is what x would be if p were true. Examples: (1) John McCarthy if he had gone to Harvard rather than to Caltech as an undergraduate. (2) My car if it hadn't been backed into today. (3) The cake I would have baked if I had known you were coming. (4) What the world would be like today if Pickett's charge had been successful. (5) What would have happened if another car had come over the hill when you passed that Mercedes just now.
is an intrinsically approximate concept. How approximate depends on p and x. ``What if another car had come over the hill when you passed'' is much less approximate than``What if wishes were horses''. [CM99] treats useful counterfactual conditional sentences and gives many examples.
can serve as the foundation for other concepts, including counterfactual conditional sentences and statements of causality. [CM99] treats useful counterfactual conditional sentences and gives many examples.
Fiction provides an interesting class of approximate objects and theories, especially historical fiction, in which the author tries to fit his characters and their lives into a background of historical fact. Common sense knowledge tells us that Sherlock Holmes would have had a mother, but Conan Doyle does not provide us with a name. A definite address is given, but there was never a house there corresponding to Doyle's description. The author need only define his world to a point that lets the reader answer the questions the author wants the reader to ask.