Ockham's razor and chemistry

Bulletin de la Societe Chimique de France

Volumn 133, Issue 2, 1996, Pages 117-130

  Hoffmann, Roald ^a   Minkin, Vladimir I ^b   Carpenter, Barry K ^a  

^a Department of Population Medicine and Diagnostic Sciences   (United States)

^b SOUTHERN FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

Ockham's razor; Philosophy of chemistry; Reaction mechanism

Indexed keywords

EID: 33747015265     PISSN: 00378968     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (93)

1. The authoritative work on William of Ockham remains Baudry L, Guillaume d'Occam. Sa Vie, ses Oeuvres, ses Idées Sociales et Politiques (Etudes de Philosophie Médiévale, Vol. 39), Librairie Philosophique Vrin, Paris, 1950. See also Junghaus H, Ockham im Lichte der neueren Forschung, Lutherisches Verlagshaus, Berlin, 1968.
2. See the bibliography in Adams MM, William of Ockham, Vol 2, University of Notre Dame, Notre Dame, 1987.
3. Boehner P, Ockham Philosophical Writing, Nelson, Edinburgh, 1957, xii.
4. Eco U, The Name of the Rose, Harcourt Brace Jovanovich, San Diego, 1983.
5. Gál G, Franciscan Studies (1982) 42, 90-95. I am indebted to Brian Tierney for this reference.
6. Brian Tierney, personal communication. There is a substantial literature on William of Ockham's philosophy - here we cite only two leading references: Leff G, William of Ockham: The Metamorphosis of Scholastic Discourse, Manchester University, Manchester, 1975, and Vossenkuhl W, Schönberger R, Die Gegenwart Ockhams, VCH Acta Humaniora, Weinheim, 1990.
7. In Tractatus de successivis, 36-37; translated by Adams MM, ref 2, p 821.
8. Brian Tierney begins a paper on Ockham with the words 'William of Ockham was a difficult thinker.'
9. 9 Mary Reppy, personal communication.
10. Boehner P, Ockham. Philosophical Writings, Nelson, Edinburgh, 1957, pp xxx-xxxix.
11. These are quoted from Adams MM, (ref 2), Vol 1, pp 156-157, who provides the citations from Ockham where the formulations quoted may be found.
12. For instance, Odo Rigaldus, Commentatorium super sententias, MS Bruges 208, fol 150a, has 'Frustra fit per plura quod potest fieri per unum' (Boehner P, op cit, p xx). Odo Rigaldus was Archbishop of Rouen from 1248 to 1275.
13. Aristotle in De Caelo writes: 'Obviously then it would be better to assume a finite number of principles. They should, in fact, be as few as possible, consistently with proving what has to be proved. This is the common demand of the mathematicians who assume as principles things finite either in kind or in number.' (Aristotle, The Works of Aristotle Translated into English, Vol II, De Caelo, trans by Stocks JL, Ed Ross WD, Clarendon, Oxford, 1930, III, c. 4, (302b).
14. And Thomas Aquinas (1225-1274), in Summa Contra Gentiles: 'If a thing can be done adequately by means of one, it is superfluous to do it by means of several; for we observe that nature does not employ two instruments where one suffices.' (Trans by Pegis AC, Basic Writings of St Thomas Aquinas, Random House, New York, 1945, p 129.)
15. We owe these last two references to Ariew R, Franciscan Studies (1977) 37, 5-17. See also Leff G, William of Ockham, Manchester University, Manchester, 1975, p 35, note 141.
16. See the spirited account of Thorburn WM, Mind (NS) (1918) 27, 345-53.
17. Adams MM, (ref 2) Vol 1, p 157.
18. Rasoir des Nominaux: Etienne Bonnot de Condillac, Essai sur l'Origine des Connaissances Humaines, 1746, p 214. The English variant (Occam's Razor) apparently appears first in Sir William Rowan Hamilton, Discussions, 1852, 590. We owe these citations to Thorburn, op cit, (ref 13). But we may need a Mertonian analysis of the origins of this term...
19. For further discussions of Ockham's Razor, its utilization by Ockham and others, and its utility in philosophy, see: Brampton CK, Modern Schoolman (1964) 41(3), 273-82;
20. Maurer AA, Monist (1978) 61(3), 426-43;
21. Boler J, Franciscan Studies (1985) 45, 119-44;
22. Menger K, Synthèse (1961) 13(4), 331-49;
23. O'Hara G, Philosophical Studies (1963) 12, 125-39 (particularly good in discussing Bertrand Russell's use of Ockham's Razor).
24. Garner P, Rube Goldberg: A Retrospective, Delilah, New York, 1983;
25. Marzio PC, Rube Goldberg: His Life and Work, Harper & Row, New York, 1973.
26. de Maupertuis PLM, Mémoires de l'Academie Royale 423, (1744).
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28. Feynman RP, Leighton RB, Sands M, The Feynman Lectures on Physics, Volume II, Addison-Wesley, Reading, 1964, Chap 19.
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30. Hückel W, Theoretische Grundlagen der Organischen Chemie, Akademische Verlagsgesellschaft, Leipzig, 1934. See also Wheland GW, Advanced Organic Chemistry, Wiley, New York, 1960.
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32. See the comprehensive reviews of Hine J, Adv Phys Org Chem (1977) 15, 1-19;
33. and Sinnott ML, Adv Phys Org Chem (1986) 24, 113-204.
34. See as well the comment, in the context of concerted reactions, by Berson JA, in de Mayo P, Ed. Rearrangements in Ground and Excited States, Vol 1, Academic, New York, 1980, p 375-76.
35. Korobov MS et al, J Chem Soc, Chem Commun (1982) 169-170.
36. Korobov MS et al, J Mol Struct (THEOCHEM) (1989) 200, 61-72.
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38. Jackson RA, Mechanism: An Introduction to the Study of Organic Reactions, Clarendon, Oxford, 1972.
39. Carpenter BK, Determination of Organic Reaction Mechanism, Wiley-Interscience, New York, 1984.
40. Russell B, The Problems of Philosophy, Oxford University, Oxford, 1980, p 97.
41. Oreskes N, Shrader-Frechette K, Belitz K, Science (1994) 263, 641-646, endnote 25.
42. Minkin VI, Nivoroshkin LE, Korobov MS, Russian Chem Rev, Uspekhi Khimii (1994) 303.
43. According to the original definition, pericyclic reactions are those 'in which all first order changes in bonding relationships take place in concert on a closed curve', Woodward RB and Hoffmann R, The Conservation of Orbital Symmetry, Verlag Chemie, Weinheim, 1970.
44. Houk KM, Li Y, Evanseck JD, Angew Chem Int Ed Engl (1992) 31, 682-707;
45. Dewar MJS, Jie C, Ace Chem Res (1992) 25, 537-543. Of special interest are the contradictory conclusions (in some cases) arising from ab initio vs or semiempirical methods of calculation. For an up-to-date and most readable account of this never-ending story see Houk KN, Gonzalez J, Li Y, Ace Chem Res (1995) 28, 81-90.
46. For a leading reference see Schwarz H, Angew Chem Int Ed Engl (1993) 32, 1412-1415.
47. Smalley RE, Acc Chem Res (1992) 25, 98-105;
48. Hunter JM et al, J Phys Chem (1994) 98, 1810; von Helden G et al, Nature (1993) 363, 60-63;
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50. Hunter JM et al, J Phys Chem (1994) 98, 1810;
51. Murry RL et al, Nature (1993) 366, 665;
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53. See also ref 34 and the work of Beiz T et al, Angew Chem Int Ed Engl (1994) 33, 1866.
54. See Smalley RE, in ref 35.
55. Quantum mechanical tunnelling is a widespread reaction mechanism responsible for occurrence of many proton and electron transfer reactions. Tunnelling also occurs, as we have only recently learned, for heavier atoms; Carpenter BK, J Am Chem Soc (1983) 105, 1700-1701.
56. Platt J, Science (1964) 146, 4642.
57. Of course it takes six for sex: Bjostad LB et al, J Chemical Ecology (1984) 10, 1309-1323;
58. Roelofs WL, Glover T, in Chemical Senses, Vol 3, Eds. Wysocki CJ, Kare MR, Dekker, New York, 1991;
59. Linn CE, Roelofs WL, to be published.
60. 40 The provisional nature of Ockham's Razor based arguments has been stressed by Kapp RO, British J Phil Science (1958) 8, 265-81.
61. The definition of the term "degrees of freedom" here differs from that commonly used in statistical mechanics.
62. 2 is computed for each model (y is the experimentally measured response of the system under study to a given value of x; ŷ is the response predicted by the model) and then divided by the appropriate number of degrees of freedom. This calculation provides the variance for each model. The ratio of the variances is compared with tabulated values that allow one to decide, with a specified level of confidence, whether the more complex model has made a statistically significant improvement to the fit. If it has not, one will generally opt for the simpler model because, again, it has the larger number of degrees of freedom.
63. See also the clear arguments here of Jeffreys H, Theory of Probability, Oxford University, Oxford, 1939; Jefferys WH, Berger JO, Am Sci (1992) 80, 64-72.
64. Malinowski ER, Howery DG, Factor Analysis in Chemistry, Wiley-Interscience, New York, 1990.
65. See also Gauch HJ Jr, Am Sci (1993) 81, 468.
66. Auf der Heyde T, S Afr Chem J (1993) 46, 45.
67. Katritzky AR et al, J Am Chem Soc (1989) 111, 7-15.
68. See Minkin VI, Glukhovtsev MN, Simkin BY, Aromaticity und Antiaromaticity, Wiley, New York, 1994, for leading references.
69. Recently Katritzky et al's conclusion has been questioned by Schleyer PvR et al, Angew Chem Int Ed Engl (1995) 34, 337-340.
70. Murray-Rust R, Motherwell WDS, Acta Crystdlogr, Sect B (1978) 34, 2534.
71. Auf der Heyde TPE, Bürgi HB, Inorg Chem (1989) 28, 3960, 3970, 3982.
72. Basu G et al, J Am Chem Soc (1994) 116, 6307-15.
73. Fisher Michael E, personal communication.
74. 54 See 'toughness-tenderness' and 'juiciness' separated as important Principal Components, in an analysis of 69 beef roasts by Harris JM, Rhodes DN, Chrystall BB, J Texture Stud (1972) 3, 101, or the analysis of sensory characteristics of ham and their relationships with composition, visco-elasticity and strength: Nute GR et al, Int J Food Sci Tech (1987) 22, 461. Our source for these references on sensory properties and preferences of meat products is a perceptive overview by Einar Risvik, (Matforsk, Ås, Norway), to be published. For the use of PCA in the evaluation of 1976 Bordeaux wines see Nobel AC, Williams AA, Langdon SP, J Sci Food Agr (1984) 35, 88. Sivertsen HK, Risvik E (to be published) have carried out a detailed multivariate study of French wine profiles. They had eight panelists rate thirty wines for 17 specific and integrated sensory attributes. Two Principal Components accounted for 65% of the variation. The first of these was a fruity aroma axis, 'going from berry aromas to vegetative aromas and attributes representing a more ripened aroma, like "animal" and "vanilla". PC2 could be described as a mouthfeel and color axis, going from "suppleness" to "astringency", "color intensity", "potential", and "color tone".' Sivertsen and Risvik point to an amusing mapping of the wine varieties separating along these Principal Components onto the geography of France wine-producing regions.
75. Jeffreys H, Theory of Probability, Oxford University Press, Oxford, 1939.
76. See also articles by Gull SF, in Maximum Entropy and Bayesian Methods in Science and Engineering, Vol 1 Foundations, Erickson GJ, Smith CR, Eds, Kluwer, Dordrecht, pp 53-74, and in Maximum Entropy and Bayesian Methods, Cambridge 1988, Skilling J, Ed, Kluwer, Dordrecht, 1989, pp 53-71.
77. MacKay DJC, Neural Comput (1992) 4, 415-447.
78. Jefferys WH, Berger JO, Am Sci (1992) 80, 64-72; see also Gauch HG, Jr, Am Sci (1993) 81, 468-77.
79. Schuster HG, Deterministic Chaos, Verlag Chemie, Weinheim, 1984.
80. Hrovat DA, Morokuma K, Borden WT, J Am Chem Soc (1994) 116, 1072-1076.
81. See also Kozlowski PM, Dupuis M, Davidson ER, J Am Chem Soc (1995) 117, 774-778;
82. Jiao H, Schleyer PvR, Angew Chem Int Ed Engl (1995) 34, 334-337, and the account of Houk, González and Li in ref 33.
83. Carpenter BK, Acc Chem Res (1992) 25, 520-528.
84. Suckling CJ, Suckling RE, Suckling CW, Chemistry Through Models. Concepts and Applications of Modelling in Chemical Science, Technology and Industry, Cambridge University Press, Cambridge, 1980.
85. For a contrary view, see: Simon HA, The Sciences of the Artificial; 2nd ed, MIT Press, Cambridge, 1981.
86. Jammer M, The Conceptual Development of Quantum Mechanics; 2nd ed, American Institute of Physics, New York, 1989. Mehra J, Rechenberg H, The Historical Development of Quantum Theory, Springer, New York, 1982, Vol I, Part 1, p 150; see also Kuhn TS, Black-body Theory, and the Quantum Discontinuity, Oxford University Press, New York, 1978, Part 2, pp 616-17.
87. Hoffmann Hillel J, personal communication.
88. 66 Hoffmann R, The Same and Note the Same, Columbia University Press, New York, 1995.
89. Fisher Michael E, personal communication.
90. 68 It is not all that easy to define simplicity: 'The notion of simplicity, like truth, beauty and effective process is an intuitive one calling for a more objective characterization, ie, formalization, before we can even hope to agree about the relative complexities of different theories'; Casti JJ, Searching for Certainty, Morrow, New York, 1990.
91. Brian Tierney, personal communication.
92. 70 Newton I, Rules of Reasoning in Philosophy. We are grateful to L Pearce Williams for bringing this quote to our attention.
93. Einstein A, in Cohen JM, Cohen MJ, The Penguin Dictionary of Modern Quotations; 2nd ed, Penguin Press, London, 1971. We thank RH Crabtree for this reference.