It remains to speak of what I wrote during these years, which, independently of my contributions to newspapers, was considerable. In 1830 and 1831 I wrote the five Essays since published under the title of “Essays on some Unsettled Questions of Political Economy,” almost as they now stand, except that in 1833 I partially rewrote the fifth Essay. They were written with no immediate purpose of publication; and when, some years later, I offered them to a publisher, he declined them. They were only printed in 1844, after the success of the “System of Logic.” I also resumed my speculations on this last subject, and puzzled myself, like others before me, with the great paradox of the discovery of new truths by general reasoning. As to the fact, there could be no doubt. As little could it be doubted, that all reasoning is resolvable into syllogisms, and that in every syllogism the conclusion is actually contained and implied in the premises. How, being so contained and implied, it could be new truth, and how the theorems of geometry, so different in appearance from the definitions and axioms, could be all contained in these, was a difficulty which no one, I thought, had sufficiently felt, and which, at all events, no one had succeeded in clearing up. The explanations offered by Whately and others, though they might give a temporary satisfaction, always, in my mind, left a mist still hanging over the subject. At last, when reading a second or third time the chapters on Reasoning in the second volume of Dugald Stewart, interrogating myself on every point, and following out, as far as I knew how, every topic of thought which the book suggested, I came upon an idea of his respecting the use of axioms in ratiocination, which I did not remember to have before noticed, but which now, in meditating on it, seemed to me not only true of axioms, but of all general propositions whatever, and to be the key of the whole perplexity. From this germ grew the theory of the Syllogism propounded in the Second Book of the Logic; which I immediately fixed by writing it out. And now, with greatly increased hope of being able to produce a work on Logic, of some originality and value, I proceeded to write the First Book, from the rough and imperfect draft I had already made. What I now wrote became the basis of that part of the subsequent Treatise; except that it did not contain the Theory of Kinds, which was a later addition, suggested by otherwise inextricable difficulties which met me in my first attempt to work out the subject of some of the concluding chapters of the Third Book. At the point which I had now reached I made a halt, which lasted five years. I had come to the end of my tether; I could make nothing satisfactory of Induction, at this time. I continued to read any book which seemed to promise light on the subject, and appropriated, as well as I could, the results; but for a long time I found nothing which seemed to open to me any very important vein of meditation.
Note from KBJ: What perplexed Mill is how deduction can generate new knowledge. In a valid deductive argument, the conclusion contains no more information than the premises. Consider the syllogism "All men are mortal; Socrates is a man; therefore, Socrates is mortal." The conclusion says no more than the conjunction of the premises; indeed, it says less. Deduction purchases necessity at the cost of informativeness. Induction purchases informativeness at the cost of necessity. We would like to have both informativeness and necessity. We can't. We can have one or the other, but not both. I call this the tragedy of logic.
Keith Burgess-Jackson, J.D., Ph.D. 