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{Left margin, top of page: "Logic 3"}

understanding. But if you grant that it is a sound theory, it must have been prepared to do that, application or no application.

{Left margin, next to the paragraph below: "Useful even if not used."}

From this point of view, we can see that logic may be useful, apart from any direct application, but supplying us with modes of conception which are useful. These are few theories, if any, of which this is equally true.

{Left margin, next to the paragraph below: "No succedaneum for experience as training."}

For the most part, theories do little or nothing for everyday business. Nobody fit to be at large would recommend a carpenter who had to put up a pigsty or an ordinary cottage, to make an engineer's statical diagram of the structure. In particular, applications of theories would be worse than useless where they would interfere with the operation of trained instinct. Who could play billiards by analytic mechanics? Now we all have a natural instinct for right reasoning, which, within the special business of each

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