In mathematics we have demonstrably insoluble problems, one example being that of trisecting an arbitrary angle in elementary geometry. Every now and then, we encounter engineers and others who offer solutions of the insoluble and make some stir. To those who feel convinced of the demonstration of insolubility, these claimed solutions do not seem to deserve any serious considerations. In fact, such solutions have long since ceased to attract attention from mathematicians.

The situation in philosophy seems different. Here we do not possess demonstrations as clear and distinct as in mathematics. For example, it has been a fashion among philosophers for two centuries or so to answer Hume's scepticism concerning induction. Although, presumably, there never has been any answer or solution which is as widely accepted among philosophers as Hume's sceptical argument, yet philosophers continue to enjoy elaborating arguments for and against Hume's scepticism. And people who feel convinced by Hume's resaoning often find it difficult to understand why philosophers persist in trying to contradict Hume flatly instead of seeking for some more devious way out.