¹ Guy C. Omer, “A Nonhomogeneous Cosmological Model,” The Astrophysical Journal, CIX (January, 1949), 176.

² The phenomena may only be indirectly described or explained by a theory which directly explains the law or laws of the phenomena in question; and this process of successive explanation may be repeated indefinitely. However, the ultimate aim of any theory would seem to be that stated in the text.

After writing the above definition of a scientific theory, I noticed the following definition of “theory” in The Shorter Oxford English Dictionary (3rd ed., Vol. II): “3. A scheme or system of ideas or statements held as an explanation or account of a group of facts or phenomena; …”.

³ A principle may be thought of as a stable or recurring pattern of choice in a scientific investigation; such a pattern delimits the scope, or determines the presuppositions, or suggests the form of the inquiry. That such guiding principles are really an essential ingredient in scientific activity would seem to follow from the fact that the products of such activity must be systematic: the systematic character of a scientific theory derives from the systematic character—the relatively constant criteria of relevance, meaning, and logical structure—of the antecedent scientific activity.

⁴ Hans Reichenbach, Experience and Prediction (Chicago: The University of Chicago Press, 1938), p. 7.

⁵ Reichenbach, Philosophic Foundations of Quantum Mechanics (Berkeley and Los Angeles: University of California Press, 1946), p. 66.

⁶ See, for example, Herbert Dingle, The Special Theory of Relativity (London: Methuen and Co., 1940), p. vi: “… whereas McCrea's tendency is to present the world of experience as an exemplification of mathematical formulae, the theory is presented here as a mathematical formulation of relations first discovered in the world of experience. For example, McCrea deduces the Fitzgerald ‘contraction’ from the Lorentz transformation formulae, while here the transformation formulae are deduced from the Fitzgerald ‘contraction.’ Properly understood, of course, there is no incompatibility between the two procedures…”

⁷ The following exposition is based primarily on two of Einstein's writings: “Physics and Reality,” Journal of the Franklin Institute, CCXXI (March, 1936), and “On the Electrodynamics of Moving Bodies,” The Principle of Relativity, H. A. Lorentz et al. (London: Methuen and Co., 1923). The first of these contains Einstein's most systematic and detailed discussion of his own philosophy of science; the second constitutes Einstein's original (1905) formulation of the special theory of relativity.

⁸ “Physics and Reality,” p. 352.

⁹ Einstein is extremely emphatic on this point: “Considered logically this concept [of a bodily object] is not identical with the totality of sense impressions referred to; but it is an arbitrary creation of the human (or animal) mind” (ibid., p. 350).

¹⁰ Ibid., p. 351.

¹¹ Einstein, “Remarks Concerning the Essays Brought Together in This Co-operative Volume,” Albert Einstein: Philosopher-Scientist, ed. Paul Arthur Schilpp (Evanston: The Library of Living Philosophers, 1949), p. 679.

¹² “Physics and Reality,” p. 360.

¹³ “On the Electrodynamics of Moving Bodies,” p. 37.

¹⁴ Ibid., p. 38.

¹⁵ Einstein, The Meaning of Relativity (Princeton: Princeton University Press, 1946), p. 29.

¹⁶ Whitehead, An Enquiry Concerning the Principles of Natural Knowledge (Cambridge: Cambridge University Press, 1919), p. 3. Referred to hereafter as The Principles of Natural Knowledge.

¹⁷ An example of the former is the definition of force as mass times acceleration (which Whitehead criticizes in The Principles of Natural Knowledge, p. 19); an example of the latter is Einstein's definition of simultaneity (cf. p. 130).

¹⁸ Ibid., pp. 45–46.

¹⁹ Ibid., p. 56 (my italics).

²⁰ Whitehead, The Principle of Relativity (Cambridge: Cambridge University Press, 1922). p. 5.

²¹ Whitehead, Process and Reality (New York: The Macmillan Co., 1929), p. 5.

²² K-equal abstractive classes cover each other; this definition makes precise the notion of “equal convergence-properties.” One class of events is said to “cover” another when every member of the former extends over some member of the latter.

²³ This is the doctrine that every percipient event involves an essential reference to a “beyond” in space—this beyond being constituted by distant events known only as bare relata of the percipient event.

²⁴ As in Einstein's theory, the transformation equations are assumed to be linear in the four variables. This mathematical property corresponds, as we have already noted, to the physical hypothesis that space and time are homogeneous, i.e., that all points of space and time are equivalent from the point of view of the transformation.

²⁵ Whitehead, The Principles of Natural Knowledge, p. 159.

²⁶ Ibid., pp. 159–160.

²⁷ Ibid., p. 163.

²⁸ Ibid., p. 164.

²⁹ Ibid.

³⁰ Ibid.

³¹ Whitehead, The Concept of Nature (Cambridge: Cambridge University Press, 1920), p. 61.

³² Whitehead, Process and Reality, p. 496.

³³ For Whitehead, the external world and the extended world are one and the same (recall the constants of externality).

³⁴ The ground of the rejection is lack of “coherence”: “Incoherence is the arbitrary disconnection of first principles” (ibid., p. 9).

³⁵ “Important” is ambiguous here, since there are different kinds of importance for science, e.g., new theories, improved formulations of existing theories (superior elegance, rigor, etc.), and so on. As mentioned above, p. 116, each scientist would usually claim all of these virtues for his own approach.

³⁶ In fact, I distinguish these presupposed data from the axioms for space and time simply because Whitehead explicitly analyzes the concepts involved in the latter while he is content to accept without analysis the concepts involved in the former.

³⁷ Whitehead, The Concept of Nature, p. 173.

³⁸ Whitehead, The Principles of Natural Knowledge, p. 53.

³⁹ Whitehead, The Concept of Nature, p. 56.

⁴⁰ The general principle underlying all of these symmetry-properties has been stated as follows by Whitehead: “Two segments are congruent when there is a certain analogy between their functions in a systematic pattern of straight lines, which includes both of them” (Process and Reality, p. 505).

⁴¹ Whitehead, The Concept of Nature, p. 129.

⁴² Mathematically, this means that ⊘(v) = ⊘(–v) in Einstein's derivation of the Lorentz-Einstein equations—cf. p. 120 above.

⁴³ Whitehead, The Principles of Natural Knowledge, p. 161.

⁴⁴ Whitehead, The Principle of Relativity, pp. v-vi.

⁴⁵ Ibid., p. 65.

⁴⁶ Kant's view of the relation between the concepts of substance and matter seems to be an illustration of what I have in mind.

⁴⁷ Henri Poincaré, The Foundations of Science, trans. George Bruce Halsted (Lancaster, Pennsylvania: The Science Press, 1946), p. 135.

⁴⁸ Although it is true that both Einstein and Whitehead use the tensor calculus, their mathematical formulations nevertheless look quite different—e.g., the non-linear partial differential equations defining the gravitational field which are central in Einstein's theory do not appear in Whitehead's theory at all.