1 Mackenzie, D. (2001), Mechanizing Proof (Cambridge, MIT Press), 23.
2 Dowd, Kevin et al. (2008), ‘How Unlucky is 25-Sigma?’, Centre for Risk and Insurance Studies, Nottingham University Business School; https://www.nottingham.ac.uk/business/businesscentres/crbfs/documents/cris-reports/cris-paper-2008-3.pdf.
3 King, M. (2016), The End of Alchemy (London: Little, Brown), 193.
4 See the superb intellectual portrait in D. Mellor (1995), ‘Cambridge Philosophers I: F. P. Ramsey’, Philosophy, 70, 242–62. Mellor adds that Ramsey’s version of Wittgenstein here is an improvement on the original, because it sums up a major objection to the Tractatus, one which Wittgenstein (probably) came to endorse.
5 Keynes, J. M. (1937), ‘The General Theory’, Quarterly Journal of Economics, 51, 213–14.
6 Friedman, M., and Friedman, R. (1998), Two Lucky People (Chicago: University of Chicago Press), 146.
7 For this example and much more detail on the difference between bell-curve and scale-invariant phenomena see N. Taleb (2010), The Black Swan (London: Penguin), chapter 15.
8 BBC News, 15 September 2008: http://news.bbc.co.uk/1/hi/7616996.stm. Quoted in D. Orrell (2012), Economyths (London: Icon), 90.
9 Freedman D., and Stark, P. (2003), ‘What is the Chance of an Earthquake?’, Technical report 611, Department of Statistics, University of California, Berkeley. For an accessible introduction which has influenced my discussion here see D. Orrell, chapter 4.
10 I owe this example to J. Lancaster (2010), Whoops! (London: Penguin), 137.
11 Bernstein, P. (1998), Against the Gods (New York: Wiley), 250.
12 Wells, T. (2001), Wild Man: The Life and Times of Daniel Ellsberg (New York: Palgrave Macmillan), chapter 2.
13 Ibid., 128.
14 Ellsberg, D. (1961), ‘Risk, Ambiguity and the Savage Axioms’, Quarterly Journal of Economics, 75, 643–69.
15 See C. Zappia (2015), Daniel Ellsberg on the Ellsberg Paradox (University of Siena, Department of Economics), notes 13 and 15.
16 Taleb, 70.
17 Tversky, A., and Kahneman, D. (1983), ‘Extensional versus Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment’, Psychological Review, 90 (4), 293–315.
18 Greenspan, A., Statement to the House, Hearing of the Committee on Oversight and Government Reform, 23 October 2008.
19 Turner, A., ‘How to Tame Global Finance’, Prospect, 27 August 2009.
20 Mellor, D. H. (2007), ‘Acting under Risk’ in T. Lewens, Risk: Philosophical Perspectives, (London: Routledge).
21 Stern, N., ‘Ethics, Equity and the Economics of Climate Change Paper 1: Science and Philosophy’, Economics and Philosophy, 30 (3): 397–44, 423.
22 Aldred, J. (2009), ‘Ethics and Climate Change Cost-benefit Analysis’, New Political Economy, 14 (4), 469–88.
23 Jaeger, C., Schellnhuber, H., and Brovkin, V. (2008), ‘Stern’s Review and Adam’s Fallacy’, Climatic Change, 89, 207–18.
24 For further details on the ideas in this paragraph, see the postscript to Taleb.
25 Bernstein, P. (1998), Against the Gods (New York: Wiley), 219.
26 Englich, B., Mussweiler, T., and Strack, F. (2006), ‘Playing Dice with Criminal Sentences’, Personality and Social Psychology Bulletin, 32, 188–200.