When Mr. Mill commenced his labors, the only logic recognized was the syllogistic. Reasoning consisted solely, according to the then dominant school, in deducing from general propositions other propositions less general. It was even asserted confidently, that nothing more was to be expected,--that an inductive logic was impossible. This conception of logical science necessitated some general propositions to start with; and these general propositions being _ex hypothesi_ incapable of being proved from other propositions, it followed, that, if they were known to us at all, they must be original data of consciousness. Here was a perfect paradise of question begging. The ultimate major premise in every argument being assumed, it could of course be fashioned according to the particular conclusion it was called in to prove. Thus an 'artificial ignorance,' as Locke calls it, was produced, which had the effect of sanctifying prejudice by recognizing so-called necessities of thought as the only bases of reasoning. It is true, that outside of the logic of the schools great advances had been made in the rules of scientific investigation; but these rules were not only imperfect in themselves, but their connection with the law of causation was but imperfectly realized, and their true relation to syllogism hardly dreamt of. Mr. Mill altered all this. He demonstrated that the general type of reasoning is neither from generals to particulars, nor from particulars to generals, but from particulars to particulars. "If from our experience of John, Thomas, &c., who once were living, but are now dead, we are entitled to conclude that all human beings are mortal, we might surely, without any logical inconsequence, have concluded at once from those instances, that the Duke of Wellington is mortal. The mortality of John, Thomas, and others is, after all, the whole evidence we have for the mortality of the Duke of Wellington. Not one iota is added to the proof by interpolating a general proposition." We not only may, according to Mr. Mill, reason from some particular instances to others, but we frequently do so. As, however, the instances which are sufficient to prove one fresh instance must be sufficient to prove a general proposition, it is most convenient to at once infer that general proposition, which then becomes a formula according to which (but not from which) any number of particular inferences may be made. The work of deduction is the interpretation of these formulas, and therefore, strictly speaking, is not inferential at all. The real inference was accomplished when the universal proposition was arrived at.