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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 (20 May 1806 – 8 May 1873) was a British philosopher and civil servant. An influential contributor to social theory, political theory, and political economy, his conception of liberty justified the freedom of the individual in opposition to unlimited state control. He was a proponent of utilitarianism, an ethical theory developed by Jeremy Bentham, although his conception of it was very different from Bentham's. Hoping to remedy the problems found in an inductive approach to science, such as confirmation bias, he clearly set forth the premises of falsification as the key component in the scientific method. Mill was also a Member of Parliament and an important figure in liberal political philosophy.

He is also the author of On Liberty (1859), Utilitarianism (1861), and The Subjection of Women (1869).