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{Left margin, top of page: "Logic 4"}

of us, has received a severe training by its conclusions being constantly brought into comparison with experiential results. Nay, we not only have a reasoning instinct, but as I shall early show, we have an instinctive theory of reasoning, which gets corrected in the course of our experience. So, it would be most unreasonable to demand that the study of logic should supply an artificial method of doing the thinking that his regular business requires every man daily to do.

{Left margin, next to the paragraph below: "Logical Artifices."}

Nevertheless, as the progress of civilization renders our modes of life more and more artificial, occasions will now and then arise in which scientific logical contrivances may be introduced to advantage. Ang[...], or vulgar mathematics, is an example of such an artificial logical aid to natural ways of thinking. Of no use whatever for such simple problems as presented

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