J.S. Mill's logic. AI

Perplexity

John Stewart Mill's logic.

John Stuart Mill’s logic is an empiricist theory of reasoning that treats induction from experience as fundamental and regards deduction as ultimately grounded in inductive generalizations. It is laid out systematically in his 1843 work A System of Logic, Ratiocinative and Inductive.

Core aims

Mill’s logic aims to be a science of proof or evidence, not of belief or psychology. It restricts logic to the evaluation of inferences from already known truths, whether these are particular observations or general propositions. Logic, on this view, investigates what makes a given argument a genuine proof, and what relations must hold between premises and conclusions if they are to track real facts.

Logic and propositions

Mill distinguishes merely verbal propositions (true by meaning alone) from real propositions (which assert matters of fact). Real propositions, in his analysis, ultimately make claims about:

Existence

Order in place (spatial relations)

Order in time (temporal relations)

Causation

Resemblance

For Mill, only inferences involving real propositions advance knowledge, since they connect us to facts about the world rather than to linguistic conventions.

Deduction and its limits

Mill accepts syllogistic deduction but offers a deflationary account of its epistemic power. A deduction from a general premise to a particular conclusion does not yield new knowledge; the conclusion is already implicitly contained in the general premise. Hence, every syllogism, considered as a proof, involves a kind of petitio principii: the general premise is itself warranted only because of particular instances. Deduction is useful for organizing and displaying what follows from what, but not for generating new truths about the world.

Induction as real inference

Induction, for Mill, is the only genuinely ampliative or “real” form of inference, because it moves from observed cases to unobserved ones and thereby extends knowledge. The basic pattern is analogical: from some individual instances that share properties, one infers that similar instances will share further properties. Mill then asks what distinguishes successful from unsuccessful inductions and answers by tying good induction to the discovery of causal laws of nature.

Methods of experimental inquiry

To discipline induction, Mill formulates his well-known “canons” or methods of experimental inquiry, which are refinements of Baconian ideas:

Method of Agreement

Method of Difference

Joint Method of Agreement and Difference

Method of Residues

Method of Concomitant Variations

These are intended as general rules for identifying causal connections by comparing cases in which a phenomenon is present or absent and tracking which conditions vary with it. They are meant to articulate how empirical science can systematically move from observed regularities to laws of nature.

Place in Mill’s philosophy

Mill’s logic underpins his broader empiricist and utilitarian outlook. By insisting that all knowledge beyond immediate intuition rests on inductive evidence about the world, he opposes views that ground logic or mathematics in purely a priori necessity. His work helped shift “logic” from a narrow focus on syllogisms to a broader methodology of science, emphasizing causation, experiment, and the structure of empirical inquiry.