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Before Mill wrote his System of Logic, the system of logic outlined by Aristotle in his Organon had been accepted as authoritative. Aristotle’s logic is a system of rules for creating syllogisms, arguments that start with a general premise and reach a conclusion about a particular instance, such as “All men are mortal. Socrates is a man. Therefore, Socrates is mortal.” Mill, however, was an empiricist and believed that all knowledge comes to us through our senses and that we only come to believe in any general principles by experiencing many particular instances that bear them out.
Although other empiricist philosophers, such as Locke, had argued that experience is the only basis of knowledge, no one before Mill had attempted to write a system of rules, comparable to Aristotle’s, for how we arrive at general principles by starting with particulars. Mill established a distinction between deductive logic, in which we extrapolate from general principles, and inductive logic, in which we draw conclusions from specific cases. Mill maintained that inductive logic is the true basis of knowledge.
Although Mill defines many different types of induction, the basic principles of his system are fairly straightforward. The inductive method is based on the idea of causation; the goal of induction is to determine what causes something. Mill considers various kinds of evidence and proof, but the essential method for establishing a cause is elimination. If an event happens in one set of circumstances but does not happen in other circumstances that are the same except for one thing, that one thing must be the cause of the event. Complicated phenomena involving a number of causes may be explained using a more elaborate inductive method in which separate causes are identified through deduction, and then their combination is identified through deduction.
For example, to explain what causes heart disease, we would use empirical evidence from experiments (i.e., induction) to establish many specific laws governing how diet, genetics, exercise, age, and other factors affect the heart, following which we would use deduction to arrive at a hypothesis for how these laws might work together. Finally, we would verify these hypotheses through induction (more experimentation and examination of empirical evidence).
Although Mill considered induction to be the basis of logic, today induction is not considered part of logic at all. The methods of evidence and proof that Mill wrote about are now considered part of the scientific method, whereas logic proper is limited to deduction.
