Page:Popular Science Monthly Volume 9.djvu/245

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SCIENCE AND THE LOGICIANS.

nor is there even a more intelligent rendering of an old meaning. In our own opinion the distinction between the comprehension and the extension of propositions is important; but it is paraded with too much ostentation, and treated with too much prolixity. Hamilton's great virtue is his clearness of statement and exhaustiveness of treatment. His method is admirable. Sometimes, however, there is too much display of his own erudition.

But even in the domain of formal logic Hamilton is not the only one that has within the present century made important additions. Prominent among these is De Morgan. Especially valuable are his discussions upon the different values of the logical copula. Prof. Boole has also made important additions to the syllogism, and has most ably supported the theory of the common ground occupied by logic and the mathematics. Prof. Bain also, in pure logic, has made a most important generalization. Hamilton's three laws of thought, namely, identity, non-contradiction, and excluded middle, he has reduced to the single law or canon of consistency.

So much for the assertion that Hamilton was the only man in twenty-two centuries to make any important additions to the imperial science of logic. Like enough the doctor would exclude scientific method from the imperial science. Perhaps he regards formal logic alone fit to wear the purple. But even here we see that there can be no such claim set up. If, however, he could claim this distinction, it would afford no reason for receiving his definition of science without question. That should stand or fall wholly upon its own merits. The greatest of men are not without personal biases. It is well known that Hamilton had a metaphysical bias. In his work on metaphysics the first three lectures are occupied in attempting to prove the superiority of mental science over natural science. He quotes with much approval this ancient declaration, "On earth there is nothing great but man, in man there is nothing great but mind." This being his known bias, before examining the definition, an investigator of Nature, a believer in scientific method, might have thought that it was by no means certain that he "could afford" to take it simply on his authority. However, when we come to the definition itself, the matter of it is well enough. But we have the temerity to suggest that its form might be improved without changing the substance. It is too pedantic and prolix. It is not in a shape easily to be remembered. We would render it thus: Science is real knowledge logically classified. But, as Bain remarks, positive definition is not thorough enough. As he says in his second canon on definition, it is needful to assemble for comparison the particulars of the contrasting or opposed notion. We can never know distinctly what a notion is until we contrast it with its opposite. Knowing is discriminating. What is not science? What is the other notion that lies side by side with it—in contrast, but contained under the same genus? Now, if we