A New Logic

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We cannot infer from Brutus killed Caesar to Brutus murdered Caesar, for murder is not, for the purpose of the argument, equivalent to, nor included, nor implied in killing. If there is no balm in Gilead, then we may legitimately infer that balm cannot be extracted out of Gilead ; and that there is no use in going to Gilead to get balm ; for these are implied in the postulate, though they are not equivalent to the postulate. These inferences are manifestly legitimate and valid. They commend the...mselves to the hearer, and carry their validity on the face of them. They cannot be doubted nor questioned ; but they cannot be reached by any of the processes of Inference, Immediate or Mediate, of Traditional Logic. That they are not Immediate Inferences is manifest. They are neither converses, obverses, contrapositives, nor inverses, and these are the only Immediate Inferences of Traditional Logic. Neither can they be reached through the syllogism. We might, indeed, construct a quasi-syllogism that would give us the conclusion.

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