Abstract
According to Ian Hacking, Francis Bacon had “no concern with probability” and “does not aim at inference under uncertainty.”2 I believe this to be an important mistake, though such mistakes are rare in Hacking’s fascinating book. In fact Bacon, and later writers influenced by him, were very much concerned with probabilities, though not with probabilities structured in accordance with the mathematical calculus of chance. I shall call the latter “Pascalian probabilities,” in tribute to one of the great mathematical pioneers in this area; and my object will be to demonstrate not only Bacon’s own concern with a non-Pascalian probability, but also the existence of a long line of philosophical or methodological reflections about such a probability, stretching at least from the seventeenth into the nineteenth century.
Earlier versions of this paper were read at the XVth International Congress of the History of Science, in Edinburgh (August 1977); at the Royal Institution (History of Science Discussion Group) in London (February 1978); and at the IInd International Conference on History and Philosophy of Science in Pisa (September 1978). I am grateful to other participants at these meetings for helpful comments and criticisms.
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Notes
Earlier versions of this paper were read at the XVth International Congress of the History of Science, in Edinburgh (August 1977); at the Royal Institution (History of Science Discussion Group) in London (February 1978); and at the Ilnd International Conference on History and Philosophy of Science in Pisa ( September 1978 ). I am grateful to other participants at these meetings for helpful comments and criticisms.
I. Hacking, The Emergence of Probability (Cambridge, 1975), 76.
R. L. Ellis, “General Preface to Bacon’s Philosophical Works,” in The Works of Francis Bacon, ed. J. Spedding, R. Ellis, and D. N. Heath (London, 1879 ), 1, 23.
Op. cit.,27, from Novum Organum,Bk.I, sec.cxvii, in Works,I, 212.
Francis Bacon, Discovery and the Art of Discourse (Cambridge, 1974), 130.
De Augmentis Sciendarum Bk.III, sec.iv, in Works,I, 566–68.
Novum Organum,Bk.II, sec.iv, in Works,I, 230.
Ibid.,Bk.II, sec.xxxv, in Works,1, 261ff.
Ibid.,Bk.II, sec.xxxv, in Works,I, 291.
Ibid.,Bk.II, sec.ii, in Works,I, 228.
Ibid.,Bk.II, sec.xvii, in Works,I, 257–58.
Ibid.,Bk.II, sec.v, in Works, I, 230–31.
Instauratio Magna, Distributio Operis, in Works, I, 136–37, and Novum Organum, Bk.II, sec.civ, in Works,I, 205.
De Augmentis Scientiarum,Bk.III, sec.iv, in Works,I, 568.
A System of Logic, Ratiocinative and Inductive (London, 1896), Bk.III, ch.viii, sec.3, 256.
Novum Organism,Bk.II, sec.xxii, in Works,I, 268.
Works,I, 151.
A General Scheme, or Idea of the Present State of Natural Philosophy and How its Defects may be Remedied by a Methodical Proceeding in the making of Experiments and Collecting Observations, whereby to Compile a Natural History, as the Solid Basis for the Superstructure of True Philosophy,“ in The Posthumous Works of Robert Hooke,ed. R. Waller (London, 1705), 6.
Ibid.,7.
New Experiments Physico-mechanical touching the Spring of Air, and its Effects; made for the most part in a new Pneumatical Engine,“ in Works (London, 1744), 1, 199.
Ibid.,198.
Two Essays Concerning the Unsuccessfulness of Experiments,“ op. cit., 222. Boyle seems, however, not to have learned from Bacon how important it was to use adequate controls in assessing the efficacy of medicines that he gave to patients. Cf. L. S. King, ”Robert Boyle as an Amateur Physician,“ in C. W. Bodemer and L. S. King, Medical Investigation in Seventeenth-Century England (Los Angeles, 1968), 43
Scepsis Scientifica (London, 1665), introductory address.
Essays on Several Important Subjects in Philosophy and Religion (London, 1676),44.
Ibid.,46. On the distinction in seventeenth-century England between different kinds of certainty (mathematical, sensory, religious, natural-scientific, etc.) cf. H. G. van Leeuwen, The Problem of Certainty in English Thought 1630–1690 (The Hague, 1970): this distinction does not concern us here.
An Essay on the Principles of Evidence and their Application to Subjects of Judicial Enquiry (Edinburgh, 1820), 653.
A Treatise of Human Nature (London, 1739), Introduction: ed. L. A. Selby-Bigge (Oxford, 1888), xx-xxi.
Ibid.,Bk.1, pt.1II, sec.XV, 173–76.
Ibid.,Bk.I, pt.III, sec.VI, 125ff.
Ibid.,Bk.I, pt.111, sec.XII, 134f. 31.Ibid.,135.
An Essay Concerning Human Understanding,5th ed. (London, 1706), Bk.IV, ch.XVI, sec.12.
Hume, op. cit.,142.
Op. cit.,Bk.III, ch.XX, sec. I, 367. Mill severely criticized Sir William Hamilton for ignoring these links: cf. J. S. Mill, An Examination of Sir William Hamilton’s Philosophy and of the Principal Philosophical Questions Discussed in his Writings (London, 1865), 420f.
Op. cit.,Bk.III, ch.XX, sec.3, 367.
The argument for the non-additivity of Baconian probability is developed at greater length in L. Jonathan Cohen, The Probable and the Provable (Oxford, 1977), 226ff.
London, 1830.
Ibid., 217.
Ibid., 148.
Ibid.,155. Another nineteenth-century Baconian who seems to have used both Pascalian and non-Pascalian concepts of probability, though without clearly distinguishing between them, is F. Oersterlen; cf. his Medical Logic,trans. G. Whitley (London, 1855), 287: “Our calculation of probability,equally with our hypotheses and conjectures, will gain in certainty the clearer our perception of the occurrences and circumstances with which we have to deal becomes” (my italics). An earlier and much more famous German philosopher who used both concepts without distinguishing them was Leibniz. Leibniz’s discussions of Pascalian probability are well-known. But his remarks to Conring (in a letter of March 19, 1678) have a decidedly Baconian flavor. He says nothing there about the partitioning of possibilities, but remarks instead that a hypothesis is more probable (“probabilior”) in proportion as it is intellectually simpler though more powerful, i.e., capable of explaining more phenomena on fewer assumptions: Die philosophischen Schriften von Gottfried Wilhelm Leibniz,ed. C. J. Gerhardt (Berlin, 1875), I, 195–96. In this passage Leibniz endorses, as Bacon had often done (e.g., Novum Organum Bk.1, sec.ciii, cvi, cxvii, in Works,I, 204, 206, 212, respectively), the importance of a hypothesis’ generating novel predictions. It is possible to show how this importance is a necessary consequence of adopting Baconian patterns of inductive reasoning: cf. L. Jonathan Cohen, op. cit.,159–60.
For the details see L. Jonathan Cohen, op. cit.,188ff. and 229ff., and also The Implications of Induction (London, 1970), 207ff. I am attributing to Bacon only the germs of the logic of controlled experiment that I have developed in these two books. Obviously his own formulations leave many critical issues unresolved.
L. Jonathan Cohen, The Probable and the Provable,49–120.
Ibid.,13–47.
It was only after writing this paper that I had an opportunity to read Glenn Shafer, “Non-Additive Probabilities in the Work of Bernoulli and Lambert;” Archive for History of Exact Sciences 19 (1978), 309–70. In his interesting paper Shafer has shown that both Bernoulli and Lambert investigated the mathematics of non-complementational probabilities (called by Shafer “non-additive probabilities”). But they did so, I think, within a framework of assumptions about the additivity (i.e., quantitative measurability) of evidential values which were quite rightly not shared by the classical Baconians (except J. S. Mill) in their concern with the evidence of controlled experimentation.
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Cohen, L.J. (2002). Some Historical Remarks on the Baconian Conception of Probability. In: Knowledge and Language. Boston Studies in the Philosophy of Science, vol 227. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2020-5_16
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