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Induction and Experimental Method

From The Objective Standard, Vol. 2, No. 1.

Author’s note: The following is adapted from a chapter of my book in progress, “Induction in Physics and Philosophy.” The book is based on Leonard Peikoff’s lecture course of the same title.

The scientific revolution of the 17th century was made possible by the achievements of ancient Greece. The Greeks were the first to seek natural (as opposed to supernatural) explanations, offer comprehensive theories of the physical world, and develop both deductive logic and advanced mathematics. However, their progress in physical science was impeded by the widely held view that higher knowledge is passively received rather than actively acquired. For many Greek thinkers, perfection was found in the realm of “being,” an eternal and immutable realm of universal truths that can be grasped by the contemplative mind of the philosopher.

In contrast, the physical world of activity was often regarded as a realm of “becoming,” a ceaselessly changing realm that cannot be fully understood by anyone. The modern scientist views himself as an active investigator, but such an attitude was rare among the Greeks. This basic difference in mindset—contemplation versus investigation—is one of the great divides between the ancient and modern minds.

Modern science began with the full development of its own distinctive method of investigation: experiment. Experimentation is “the method of establishing causal relationships by means of controlling variables.” The experimenter does not merely observe nature; he manipulates it by holding some factor(s) constant while varying others and measuring the results. He knows that the tree of knowledge will not simply drop its fruit into his open mind; the fruit must be cultivated and picked, often with the help of instruments designed for the purpose.

Precisely what the Greeks were missing can be seen by examining their closest approach to modern experimental science, which was Claudius Ptolemy’s investigation of refraction. Ptolemy conducted a systematic study in which he measured the angular deflection of light at air/water, air/glass, and water/glass interfaces. This experiment, when eventually repeated in the 17th century, led Willebrord Snell to the sine law of refraction. But Ptolemy himself did not discover the law, even though he did the right experiment and possessed both the requisite mathematical knowledge and the means to collect sufficiently accurate data.

Ptolemy’s failure was caused primarily by his view of the relationship between experiment and theory. He did not regard experiment as the means of arriving at the correct theory; rather, the ideal theory is given in advance by intuition, and then experiment shows the deviations of the observed physical world from the ideal. This is precisely the Platonic approach he had taken in astronomy. The circle is the geometric figure possessing perfect symmetry, so Ptolemy and earlier Greek astronomers began with the intuition that celestial bodies orbit in circles at uniform speed. Observations then determined the deviations from the ideal, which Ptolemy modeled using mathematical contrivances unrelated to physical principles (deferents, epicycles, and equants). Similarly, in optics, he began with an a priori argument that the ratio of incident and refracted angles should be constant for a particular type of interface. When measurements indicated otherwise, he used an arithmetic progression to model the deviations from the ideal constant ratio.1

Plato had denigrated sense perception and the physical world, exhorting his followers to direct their attention inward to discover thereby the knowledge of the perfect ideas that have their source in a non-physical dimension. Unfortunately, Plato explained, these perfect ideas will correspond only approximately to the ceaselessly changing and imperfect physical world we observe.

Ptolemy’s science was superficially anti-Platonic in that he emphasized the role of careful observation. However, at a deeper level, his science was a logical application of Platonism; in astronomy and in optics, he started with the “perfect” model and then merely described without explanation the inherently unintelligible deviations from it. Thus Ptolemy regarded experiment not as a method of discovery but instead as the handmaiden of intuition; he used it to fill in details about a physical world that refuses to behave in perfect accordance with our predetermined ideas. This approach is a recipe for stagnation: The theory is imposed on rather than derived from sensory data; the math is detached from physical principles; and, without an understanding of causes, the scientist is left with no further questions to ask.

The birth of modern science required an opposite view: Experiment had to be regarded as the essential method of grasping causal connections. The unique power of this method is revealed by examining how it was used by the geniuses who created the scientific era. . . .

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1 “Ptolemy’s Search for a Law of Refraction,” Archive for History of Exact Sciences, vol. 26, 1982, pp. 221–40.

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2 Michael R. Matthews, Time for Science Education. (New York: Kluwer Academic/Plenum Publishers, 2000), p. 104.

3 Quoted in Matthews, Science Education, pp. 84–85.

4 Ibid., p. 82.

5 Stillman Drake, Galileo: Pioneer Scientist (Toronto: University of Toronto Press, 1990), p. 96.

6 Stillman Drake, Galileo at Work (Chicago: University of Chicago Press, 1978), p. 128.

7 Matthews, Science Education, p. 98.

8 Galileo: Dialogue Concerning the Two Chief World Systems, translated by Stillman Drake (Berkeley: University of California Press, 2nd ed., 1967), pp. 17–21.

9 Drake, Galileo at Work, pp. 387–388.

10 The Philosophical Writings of Descartes, Vol. 1, translated by John Cottingham, Robert Stoothoff, and Dugald Murdoch (New York: Cambridge University Press, 1985), p. 249.

11 I. Bernard Cohen and Richard S. Westfall. editors, Newton (New York: W. W. Norton & Company, 1995), p. 148.

12 J. E. McGuire and Martin Tamny, Certain Philosophic Questions: Newton’s Trinity Notebook (Cambridge: Cambridge University Press, 1983), p. 263.

13 Ibid., p. 389.

14 Richard S. Westfall, Never at Rest (Cambridge: Cambridge University Press, 1980), p. 164.

15 Newton’s Philosophy of Nature: Selections from His Writings, edited by H. S. Thayer (New York: Hafner Publishing Company, 1953), p. 6.

16 Ibid.

17 Ibid., pp. 7–8.

18 Newton restricted his inductive method and his rejection of arbitrary claims to the realm of science. He was devoutly religious, and hence he did not hold that all knowledge must be based on observation. However, in contrast to Descartes, who explicitly invoked God in his attempt to validate the laws of motion, Newton rarely allowed his religious views to affect his science (the crucial exception is his view of the nature of space and time).

19 Cohen and Westfall, Newton, pp. 148–149.

20 Leonard Peikoff, Induction in Physics and Philosophy, Lecture 2, available from The Ayn Rand Bookstore.

21 Morris Cohen and Ernest Nagel, An Introduction to Logic and Scientific Method (New York: Harcourt, Brace & World, 1934), p. 205.

22 Ibid., p. 266.

23 Ibid., p. 257.

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