MILL, JOHN STUART

(b. London, England, 20 May 1806; d. Avignon, France, 8 May 1873),

philosophy, economics. For the original article on Mill see DSB, vol. 9.

Mill’s most important contribution to science was to provide an inductive methodology for it. He did so in his System of Logic, particularly in books three to five, where he defines induction as “the process by which we conclude that what is true of certain individuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times” (1843, p. 188). Mill believed that such inferences provide a crucial step in scientific inquiry. In typical scientific cases involving several hypotheses and various computations, Mill advocated what he called the deductive method, consisting of three steps: first, a set of inductions to the laws involved; second, ratiocination or calculation, involving combining the laws together with specific initial conditions so as to generate predictions; and third, verification of these predictions by observation and experiment.

Mill’s view of scientific method has had many severe critics, including William Whewell (1794–1866) and Charles Sanders Peirce (1839–1914) in the nineteenth century, and many philosophers of science in the twentieth century. Some claim that Mill was erroneously assuming a fallacious principle of induction by simple enumeration, according to which whenever all observed A’s have been B it is legitimate to infer that all A’s are B. Mill, however, was making no such assumption. He was simply offering a definition of induction or inductive generalization while allowing that some inductions are justified whereas others are not. Indeed, he devotes an entire section to when inductive generalizations are fallacious. His view is that the question is an empirical one, the answer to which varies depending on the kinds of instances and their properties. People may need only one observed instance of a chemical fact about a substance to validly generalize to all instances of that substance, whereas many observed instances of black crows are required to generalize about all crows. This is due to the empirical fact that instances of chemical properties of substances tend to be uniform, whereas bird coloration, even in the same species, tends not to be.

A related criticism is that Mill’s inductive philosophy ignores the idea of severely testing a hypothesis; for example, it fails to consider how the sample from which the induction was made was generated. But again this is a vast oversimplication. Mill emphasizes that the generalizations of concern to science are causal laws, and, in one of the most famous sections of his work, he offers “four methods of experimental inquiry” for determining causes. Mill writes:

When a fact has been observed a certain number of times to be true, and is not in any instance known to be false; if we at once affirm that fact as an universal truth or law of nature, without ever testing it by any of the four methods of induction, or deducing it from other known laws, we shall in general err grossly. (p. 373)

More generally, for Mill whether an inductive generalization from “these A’s are B” to “all A’s are B” is justified depends on a variety of empirical factors, including how the A’s were selected.

Some critics claim that Mill trivializes the scientific enterprise by restricting inductions to generalizations from facts ascertainable simply by opening one’s eyes and looking (for example, the fact that these crows are black); and that in so doing he did not allow inferences to more typical theoretical scientific conclusions. Again, this is an oversimplication. What Mill required is that inductions be made from known facts and that the latter be

established by observation and experiment (or from previously established inductions). But his view of what counts as established by observation and experiment is quite broad. He cites examples of inductions in astronomy and physics from empirically established facts about the magnitudes of particular planets in the Solar System, their mutual distances, the shape of the Earth and its rotation, and gravitational forces between the Sun and the planets. Mill did reject the claim of many physicists of his day that the wave theory of light had been empirically established. He did so not because light waves cannot be seen, but on the ground that no legitimate induction had yet been made to the existence of the vibrating luminiferous ether, though he allows that such an inference might be possible in the future from the experimental establishment of other facts.

Another major criticism, offered particularly by advocates of a hypothetico-deductive (H-D) account of science, is that Mill’s first step in his deductive method, the inductions to the laws, is not needed in science. Some, following Karl Popper (1902–1994), say that such a step is illegitimate, since, as David Hume (1711–1776) argued, inductive generalizations are never justified. For the hypothetico-deductivist, the scientist begins not by inductively inferring a hypothesis or law, but by making a guess or conjecture. Following this, H-D theorists say, agreeing with Mill, there is ratiocination and verification of predictions. If the predictions turn out to be true, then some HD theorists will conclude that the hypothesis is probably true, while others (following Popper) will reject this conclusion and say that we can conclude only that the hypothesis has not been shown to be false.

Mill rejected both ideas. From the fact that our hypotheses yield predictions that turn out to be true, we cannot conclude that our hypotheses are probably true, because of the competing hypotheses objection: there may well be hypotheses incompatible with ours which yield the same successful predictions. This can be so, Mill argues against Whewell, even if the predictions are novel and even if the system of hypotheses is simple and coherent. By contrast, from our successful predictions, if we simply conclude (with Popper) that our hypotheses have not been shown to be false, we are not satisfying one of the fundamental aims of science, which Mill regards as “discovering and proving general propositions” (p. 186). Only by including the inductive step, Mill insists, can one avoid the competing hypothesis objection and infer the probable truth of the hypotheses.

Finally, most critics have a field day with Mill’s principle of the uniformity of nature, which he claims warrants inductions, namely that “what happens once will, under a sufficient degree of similarity of circumstances, happen again … as often as the same circumstances recur.” Critics regard this as an unnecessary, unjustified, and vague assumption. Mill’s discussion of this principle is admittedly somewhat confusing. But perhaps a charitable if plausible interpretation is this: Instead of asserting boldly but vaguely that nature is uniform, Mill is claiming less boldly and less vaguely that there are uniformities in nature, that is, there are general laws governing various types of phenomena. This is an empirical claim. Some of these laws are initially arrived at inductively, without presupposing any particular laws or even that there are laws of nature. These can then be used to strengthen inductive inferences to the existence of other laws, which are inductively arrived at. For example, Newton used the inductively inferred fact that the motions of the moons of Jupiter are governed by a central inverse-square force exerted by Jupiter on those moons to strengthen the inductive inference that a central inverse-square force is exerted by Saturn on its moons to produce their similar motions.

SUPPLEMENTARY BIBLIOGRAPHY

WORKS BY MILL

A System of Logic: Ratiocinative and Inductive. London: Longmans, 1843 (1959).

OTHER SOURCES

Achinstein, Peter. Particles and Waves: Historical Essays in the Philosophy of Science. New York: Oxford University Press, 1991.

Peirce, Charles S. Collected Papers of Charles Sanders Peirce. Edited by Charles Hartshorne and Paul Weiss. Cambridge, MA: Belknap Press of Harvard University Press, 1960–1966.

Popper, Karl R. The Logic of Scientific Discovery. New York: Basic, 1959.

Skorupski, John. John Stuart Mill. London: Routledge, 1989. Snyder, Laura J. Reforming Philosophy: A Victorian Debate on Science and Society. Chicago: University of Chicago Press, 2006.

Whewell, William. The Philosophy of the Inductive Sciences, Founded upon Their History. 2nd ed. 2 vols. London: Parker, 1847.

Peter Achinstein