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Volumes 7 and 8 comprise Mill’s landmark philosophical work A System of Logic, Ratiocinative and Inductive, in which Mill explores the basic principles of inductive reasoning. In this work Mill presents the five basic modes of induction, which are now known as Mill’s Methods: the method of agreement, the method of difference, the joint or double method of agreement, the method of residues, and that of concomitant variations. In contrast to Aristotle’s syllogisms, which are based on deductive reasoning, Logic provides an alternate path to knowledge and constitutes an important contribution to the development of the scientific method.

"One necessary part of the theory of Names and of Propositions remains to be treated of in this place: the theory of Definitions. As being the most important of the class of propositions which we have characterized as purely verbal, they have already received some notice in the chapter preceding the last. But their fuller treatment was at that time postponed, because definition is so closely connected with classification, that, until the nature of the latter process is in some measure understood, the former cannot be discussed to much purpose.
The simplest and most correct notion of a Definition is, a proposition declaratory of the meaning of a word; namely, either the meaning which it bears in common acceptation, or that which the speaker or writer, for the particular purposes of his discourse, intends to annex to it."

John Stuart Mill

John Stuart Mill (1806-1873), British philosopher, economist, moral and political theorist, and administrator, was the most influential English-speaking philosopher of the nineteenth century. His views are of continuing significance, and are generally recognized to be among the deepest and certainly the most effective defenses of empiricism and of a liberal political view of society and culture. The overall aim of his philosophy is to develop a positive view of the universe and the place of humans in it, one which contributes to the progress of human knowledge, individual freedom and human well-being. His views are not entirely original, having their roots in the British empiricism of John Locke, George Berkeley and David Hume, and in the utilitarianism of Jeremy Bentham. But he gave them a new depth, and his formulations were sufficiently articulate to gain for them a continuing influence among a broad public.