¹ Philipp Frank, “The Place of the Philosophy of Science in the Curriculum of the Physics Student,” American Journal of Physics, 16, 214 (1947).

² R. B. Lindsay & H. Margenau, Foundations of Physics (John Wiley & Sons, N. Y., 1936), p. 29.

³ St. Thomas Aquinas, “Summa Theologica,” Q. 2, Art. 1, Reply Obj. 3, Basic Writings of St. Thomas Aquinas, ed. A. Pegis (Random House, N. Y., 1945), p. 20. “The existence of truth in general is self-evident, but the existence of a Primal Truth is not self-evident to us.” By Primal Truth we can understand St. Thomas to mean totality. We always get the notion in reading St. Thomas that he completely understands the significance of a physical boundary condition and the limitations it imposes upon a system. In Q.2, Art. 2, Reply Obj. 3, he again says (p. 21): “… we can demonstrate the existence of God from His effects; though from them we can not know God perfectly as He is in His Essence.”

⁴ St. Thomas, “Summa Theologica,” Q.1, Art. 1, Reply Obj. 2, Basic Writings, p. 5. “Sciences are diversified according to the diverse nature of their knowable objects. For the astronomer and the physicist both prove the same conclusion—that the earth, for instance, is round: the astronomer by means of mathematics (i.e., abstracting from matter), but the physicist by means of matter itself…” Aquinas is suggesting here that philosophical truth is arrived at by abstraction in contrast with experimental truth which is derived from experience.

⁵ Philipp Frank, op. cit., Amer. Jour. of Physics, 15, 214 (1947).

⁶ St. Thomas, “Summa Theologica,” Q.1, Art., Basic Writings, p. 18.

⁷ E. Gilson, Spirit of Medieval Philosophy (Chas. Scribner & Sons, N. Y., 1936), p. 365.

⁸ St. Thomas, “Summa Theologica,” Q. 1, Art. 1, Basic Writings, p. 5.

⁹ Ibid., Art. 2, Q. 7, p. 57. “We must consider therefore that a thing is called infinite because it is not finite. Now matter is in a way finite by form, and the form my matter. Matter is made finite by form inasmuch as matter, before it receives its form, is in potentiality to many forms; but on receiving a form, it is terminated by that one…” In the same article, Reply Obj. 3, he continues, “The term quantity is, as it were, its form, and this can be seen in the fact that a figure which consists in the termination of quantity is a kind of quantitative form. Hence the infinite of quantity is in the order of matter and such a kind of infinite cannot be attributed to God, as was said above.” Let us consider for a moment the electron—the most important consideration in all modern physics. Its number, if a real thing, may be infinite, but its electrostatic vector force field may never be.

¹⁰ Ibid., Q.7, Art. 3, p. 59.

¹¹ St. Thomas, “Summa Theologica,” Q. 10, Art. 4, Basic Writings, p. 78.

¹² Ibid., Q. 10, Art. 6, p. 82. “Now some say that there is only one time for all temporal things, because one number exists for all things numbered; and time is a number according to the Philosopher. This, however, is not a sufficient reason, because time is not a number as abstracted from the thing numbered, but as existing in the thing numbered; otherwise it would not be continuous. For the ells of cloth are continuous not by reason of number, but by reason of the thing numbered…”

¹³ R. B. Lindsay & H. Margenau, Foundations of Physics, p. 74.

¹⁴ E. Gilson, Spirit of Medieval Philosophy, p. 408.

¹⁵ R. B. Lindsay, Physical Mechanics (Van Nostrand, N. Y., 1933), p. 1.

¹⁶ A. N. Whitehead, Science in the Modern World (Macmillan, N. Y., 1925), p. 26.

¹⁷ St. Thomas, “Summa Theologica,” Q.1, Art. 1, Basic Writings, p. 5.

¹⁸ “Alles was geschieht (anhebt zu sein) setzt etwas voraus worauf es nach einer Regel folgt.” Quoted from Lindsay & Margenau, Foundations of Physics, p. 516.

¹⁹ Ibid., p. 522.

²⁰ St. Thomas, “Summa Theologica,” Q. 10, Art. 4, Basic Writings, p. 78.

²¹ LaPlace, Theorié Analytique des Probabilités (Paris, 3rd ed., 1820).

²² St. Thomas, “Summa Theologica,” Q. 3, Basic Writings, p. 25.

²³ LaPlace, op. cit., quoted from Lindsay & Margenau, Foundations of Physics, p. 517. The intelligence of LaPlace, the so-called daemon exists essentially in a man-made universe. Therefore we can substitute man for this daemon and we have an entirely causal universe in which the human mind has not only apprehended causality but all ultimate reality. We know that this was the ultimate aim of Scholasticism. We also know that it never has been achieved under any system.

²⁴ See, for example, H. Poincare, Foundations of Science (Science Press, N. Y., 1913) or Lindsay & Margenau, Foundations of Physics “The Meaning of a Physical Theory.”

²⁵ R. B. Lindsay & H. Margenau, Foundations of Physics, p. 520.

²⁶ Ibid., p. 521.

²⁷ Lindsay and Margenau, op. cit., p. 77. The authors present here the notions of G. I. Pokrowski in his article from Nature, 127, 667 (1931). Pokrowski proposes that we quantize time as we do to energy. We would therefore have to assign a basic “time-atom” and time would flow in discrete chunks of “time-atoms.” If a quanta is hv then the frequency of the chronon corresponding to this jump is mc ²/h and the period is h/mc ². Substitution of the mass of the proton for m yields a period of about 4.5 × 10^–24 seconds which is the period of the shortest known cosmic rays. As it is questionable whether or not the proton is the fundamental mass unit, we can not suggest much beyond this and are prevented from any serious consideration.

²⁸ LaGrange, Mecanique Analytique (Paris, 1788). LaGrange was so certain that the solutions of his famous equations would lead to an absolute causality and completely describe the universe and its state, that he abandoned all use of diagramtic thinking. On the frontispiece of his work he wrote: “There are no diagrams in this work.”

²⁹ See, for example, P. A. M. Dirac, Principles of Quantum Mechanics (Oxford, 1930). By the Newer Quantum Mechanics, we imply the method using operational techniques—i.e., the rediscovering of the Hamiltonian Operators, etc. This method applied with the use of the probability wave equations restores the causal character. Under the older quantum mechanics, the so-called “stationary state” had little explanation. Under the newer, these states appear to be the obvious results of boundary conditions in the solutions of second order differential equations. In this case the “stationary state” has come to represent the most probable statistical distribution of the electron. Again we must emphasise that this method was the culmination of pure abstraction and was never the result of the long years of spectroscopic experimentation.

³⁰ Frank, op. cit., Amer. Jour. of Physics, 15, 203 (1947).

³¹ Ibid., p. 204.

³² De Civ. Dei, ed. F. R. M. Hitchcock (Macmillan, N. Y., 1931).

³³ P. A. M. Dirac, Principles of Quantum Mechanics.