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The dominant figure of mid-nineteenth-century British political economics, John Stuart Mill exercised a lasting influence on philosophical thought. This compact statement of Mill's doctrines offers the essentials for understanding his scientific methods of reasoning.
Starting with an informative Introduction by editor Ernest Nagel, the text proceeds with extracts from A System of Logic that clarify Mill's processes of reasoning. The following five-part treatment draws upon the philosopher's major works to consider names and propositions; reasoning; induction; operations subsidiary to induction; and the logic of the moral sciences. Selections from An Examination of Sir William Hamilton's Philosophy conclude the text, along with an essay on the definition of political economy and its methods of investigation.

1. Is the syllogism a petitio principii?

We have shown what is the real nature of the truths with which the syllogism is conversant, incontradistinction to the more superficial manner in which their import is conceived in the commontheory, and what are the fundamental axioms on which its probative force or conclusiveness depends.We have now to inquire whether the
syllogistic process, that of reasoning from generals to particulars, isor is not a process of inference, a progress
from the known to the unknown, a means of coming to aknowledge of something which we did not know
before.

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.

Ernest Nagel

Ernest Nagel (November 16, 1901 – September 20, 1985) was an American philosopher of science.  Along with Rudolf Carnap, Hans Reichenbach, and Carl Hempel, he is sometimes seen as one of the major figures of the logical positivist movement.

His work concerned the philosophy of mathematical fields such as geometry and probability, quantum mechanics, and the status of reductive and inductive theories of science. His 1961 masterpiece, The Structure of Science, practically inaugurated the field of analytic philosophy of science. He expounded the different kinds of explanation in different fields, and was sceptical about attempts to unify the nature of scientific laws or explanations. He was the first to propose that by positing analytic equivalencies (or "bridge laws") between the terms of different sciences, one could eliminate all ontological commitments except those required by the most basic science. He also upheld the view that social sciences are scientific, and should adopt the same standards as natural sciences.

Nagel wrote An Introduction to Logic and the Scientific Method with Morris Raphael Cohen, his CCNY teacher in 1934. In 1958, he published with James R. Newman Gödel's proof, a short book explicating Gödel's incompleteness theorems to those not well trained in mathematical logic. He edited the Journal of Philosophy (1939–1956) and the Journal of Symbolic Logic (1940-1946).