Notes

  1. . In “Complementarity II” (Aristotelian Society: Supplementary Volume 32 [1958]: 105–22) I suggested that the logical notion underlying both physical and other uses of the term could be characterized as follows: “Two (or more) descriptions may be called logically complementary when (a) They purport to have a common reference (b) Each is in principle exhaustive, (in the sense that none of the entities or events comprising the common reference need be left unaccounted for), yet (c) They make different assertions, because (d) The logical preconditions of definition and/or of use (i.e., context) of concepts or relationships in each are mutually exclusive, so that significant aspects referred to in one are necessarily omitted from the othe” (pp. 114–15). In a, I would now delete the words “purport to.” The force of b here is of course permissive; if a description A does not claim to take account of certain of the entities comprising the situation described by B (as with the mathematical explanation of a computer's activity discussed in the section on “Hierarchic Complementarity” below), the corresponding features of B have no complementary correlate in A, but this does not prevent A from being complementary to the appropriate part of B. The point is that even where A does claim to take account of the total situation, in the sense that nothing would remain if all features named in A were removed, c and d can still apply. Some of the arguments in the present paper will be found amplified in “Complementarity II” and in my earlier papers, particularly “Complementary Descriptions” (Mind 66 [1957]: 390–94).
  2. . “Complementarity II”; also D. M. MacKay, “Complementary Measures of Scientific Information‐Content,” Methodos 7 (1955): 63–90.
  3. . Note that this stipulation does not require a neutral description of the common reference. All that is necessary is some acceptable means of identification. For example, if the lamps making up an advertising sign are flashing on and off, two observers reading the sign and studying the physics of the lamps, respectively, could help each other to be sure of the common reference by calling, “There it is,”“Now it's gone,”“Now it's there again,” until reasonable doubt was dispelled without ever producing a neutral description.
  4. . That the electronic description fails to mention those features that make it a signal does not make it less exhaustive in the above sense but only shows the need for another, complementary, description, which is not in the least rendered “otiose” by the exhaustiveness.
  5. . I pointed out the asymmetry between the complementary frames of reference of “actor” and “spectator” in “Mindlike Behaviour in Artefacts,” British Journal, for the Philosophy of Science 2 (1951): 118; for a recent lucid discussion of asymmetry between hierarchically related descriptions, see Michael Polanyi, “Life's Irreducible Structure,” Science 160 (1968): 1308–12.
  6. . In other words, the situation as it lies open to the inspection of anybody, regardless of what he makes of it. Of course, what one man is qualified to perceive in a situation may be imperceptible by another not so qualified, even though it is there to be perceived.
  7. . Polanyi.
  8. . See n. 2 above.
  9. . L. Brillouin, Science and Information Theory (New York: Academic Press, 1956), p.
  10. . The numerical value depends on the definition of “imprecision.” With a different definition, it is 1/2.
  11. . D.Gabor. Theory of Communication,Journal of the Institute of Electrical Engineers  93 (1946): 429.
  12. . Ibid.
  13. . E. L. Mascall, Christian Theology and Natural Science (London: Longmans, 1956), p. 133.
  14. . So far from being in “ideological conflict” with science, biblical doctrine seems to me to underwrite the scientist's confidence in the worthwhileness of his discipline. See my “The Sovereignty of God in the Natural World,” Scottish Journal of Theology 21 (1968): 13–26; Science and Christian Faith Today (London: Falcon Books, 1960); The Clockwork Image: A Christian Perspective on Science (London: Inter‐Varsity Press, 1974).
  15. . It is, of course, no part of my purpose to claim that scientific accounts are or ever will be in practice exhaustive in this sense. At best, they have to classify many events as “random” or “inexplicable” or “indistinguishable” and can claim to be exhaustive in principle only because of the existence of such categories in the official scientific scheme. My point, as before, is that exhaustiveness in scientific categories does not have to be denied to make room for a theistic account of the same happenings.
  16. . Mascall (n. 13 above), pp. 134–35.
  17. . W. G. Pollard, Chance and Providence (New York: Faber & Faber, 1958).
  18. . Matthew 6:26.
  19. . Genesis 50:20.
  20. . “Sovereignty of God” (n. 14 above).
  21. . D. M. MacKay, Freedom of Action in a Mechanistic Universe (Cambridge: Cambridge University Press, 1967).
  22. . “Sovereignty of God” (n. 14 above), p. 18.
  23. . M. A. Jeeves, Scientific Psychology and Christian Belief (London: Inter‐Varsity Press, 1967); see also D. M. MacKay, ed., Christianity in a Mechanistic Universe (London: Inter‐Varsity Press, 1965), chap. 2.
  24. . W. Sargent, Battle for the Mind (London: Heinemann, 1957).
  25. . H. Bedau and P. Oppenheim, “Complementarity in Quantum Mechanics: A Logical Analysis,” Synthese 13 (1961): 201–32, esp. n. 41.
  26. . Its other technical meanings (“complementary angles,”“complementary colors,”“complementary classes,” etc.) also exemplify the basic notion of “completing one another's deficiencies”; but the context of each is too specialized to justify taking any one of them as a normative model for complementary categories, descriptions, or explanations. The differences are important; but if “the common use” means what is common to all those examples, including Bohr's use of the term, then mine would seem to be as much in conformity with it as any.
  27. . D. M. MacKay, “Man as Observer‐Predictor,” in Man in His Relationships, ed. H. Westmann (London: Routledge, 1955), pp. 15–28, esp. 24–25.
  28. . D. M.MacKay. What Makes a Contradiction?Faith and Thought  97 (1968): 7–14.
  29. . P.Alexander. Complementary Descriptions,Mind  65 (1956): 145–65.
  30. . 2 Corinthians 5:19.
  31. . The following, written in 1953, still summarizes my attitude: “Whenever a new concept swims into philosophical ken there is a danger that it will be overworked by the Athenians on the one hand and abused by the Laodiceans on the other. Complementarity is no universal panacea, and it is a relationship that can be predicated of two descriptions only with careful safeguards against admitting nonsense. Indeed the difficult task is not to establish the possibility that two statements are logically complementary, but to find a rigorous way of detecting when they are not…. A good deal of consecrated hard work is needed on the part of Christians to develop a more coherent and more biblical picture of the relationship between the two…. But if once we recognize that at least most theological categories are not ‘in the same plane’ (in the same logical subspace) as most scientific categories, there is no longer any theological merit in hunting for gaps in the scientific pattern. Gaps there are in plenty. But it would seem to be the Christian's duty to allow‐indeed to help‐these gaps to fill or widen as they will, in humble and cheerful obedience to the truth as God reveals it through our scientific discipline, believing that to have theological stakes in scientific answers to scientific questions is to err in company with those unbelievers who do the like” (D. M. MacKay, “An Analogy and Its Limitations,” Christian Graduate 6 [December 1953]: 163–64).