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In mathematics there's a type of book, bordering on the textbook but slightly different, that compiles examples to demonstrate the necessity of various conditions on theorems and the correct directions of implication. For example, to show that a connected space need not be path-connected one can construct the topologist's sine curve.

My question: are there any similar compilations in the philosophical literature? For instance, in epistemology the obvious set would be the Gettier cases (to show that JTB is an insufficient analysis), along with Armstrong's (?) barn facades and fake towns (to show that context seems to be important) and so on. In ethics we have Nozick's experience machine (the limits of hedonism).

Further, potentially-not-site-appropriate question: do people think such a compilation would be in any way valuble in philosophy?


Clarification: I used the term 'counterexamples' since that's the popular term in maths; I mean what I've hinted at in the examples above: a case which establishes a conditions or bounds for a theory.

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    The philosophical analogues of mathematical counterexamples are paradoxes. Just as an appropriate counterexample is usually quickest and slickest way to prove a mathematical statement false, paradoxes and dilemmas are the most poignant way to demonstrate a philosophy inadequate for analyzing the subject at hand. I don't know of even books off hand, but here's a whole MIT open course on Paradox: ocw.mit.edu/courses/linguistics-and-philosophy/… – David H May 14 '13 at 16:17
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I know of no such text, but I believe it would be invaluable--so this is a great idea. It should probably be restricted to philosophical topic, though, in the way that such mathematical texts are.

We're looking for long answers that provide some explanation and context. Don't just give a one-line answer; explain why your answer is right, ideally with citations. Answers that don't include explanations may be removed.

  • Could you expand on why this would be invaluable? – stoicfury May 18 '13 at 21:07

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