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Ifs and Newcombs

Published online by Cambridge University Press:  02 January 2020

Arthur E. Falk
Arthur E. Falk*
Affiliation:
Western Michigan University, Kalamazoo, Michigan49008
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Extract

‘Ifs’ come washed or unwashed. The washed ifs are embedded in precise theories: the constantly strict implication of deductive inference, the variably strict implication of ‘nearness’ conditionals, and statements of conditional probability. By a nearness conditional I mean the common part of Stalnaker's and D. Lewis's theory of counterfactual conditionals, which depends on a notion that possible worlds are more or less near to each other, as a measure of their over-all similarity to each other.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 15 , Issue 3 , September 1985 , pp. 449 - 481
Copyright
Copyright © The Authors 1985

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References

1 Stalnaker, Robert ‘A Theory Of Conditionals,’ in Rescher, Nicholas ed., Studies in Logical Theory (Oxford: Basil Blackwell 1968) 98–112;Google Scholar Lewis, David Counterfactuals (Cambridge, MA: Harvard University Press 1973).Google Scholar ‘Nearness conditional’ is Allan Gibbard's term.

2 Some philosophers believe that Newcomb's problem is controversial only because it is stated incompletely or inconsistently, e.g., Mackie, J.L. ‘Newcomb's Paradox and the Direction of Causation,’ Canadian Journal of Philosophy, 7 (1977) 213–25.CrossRefGoogle Scholar I disagree. Even when the conditions of the problem are stated completely and consistently, the solution is still controversial. In these paragraphs and footnote 19 I specify all the points a solution depends on.

3 Nozick, Robert ‘Newcomb's Problem and Two Principles of Choice,’ in Rescher, Nicholas ed., Essays in Honor of Carl Hempel (Dordrecht: D. Reidel 1969) 114–46CrossRefGoogle Scholar

4 Gardner, Martin ‘Free Will Revisited with a Mind-Bending Prediction Paradox by William Newcomb,’ Scientific American, 229 (July 1973) 104–8,CrossRefGoogle Scholar and his column in Scientific American, 230 (March 1974), actually written by Robert Nozick, ‘Reflections on Newcomb's Problem: a Prediction and Free-Will Dilemma,’ 102-9. This sample's members are more likely to recall that math texts endorse taking one box.

5 Stalnaker, Robert ‘Letter to David Lewis’ in Harper, Stalnaker and Pearce, eds., lfs (Dordrecht: D. Reidel 1981), 151-2Google Scholar

6 Dummett, Michael ‘Bringing About the Past,’ The Philosophical Review, 73 (1964) 338–59CrossRefGoogle Scholar

7 J. Howard Sobel's version, published in Jeffrey, Richard The Logic of Decision, 2nd ed. (Chicago: University of Chicago Press 1983) 15.Google Scholar Compare: suppose God had informed Adam, not that he was forbidden the apple, but that God had irrevocably predestined him and all his progeny to heavenly bliss if and only if He has predicted that Adam would reject the yummy apple. Should a perfectly rational Adam reject the apple? Further: should anyone who believes in the predestination of the elect, forgo those pleasures of the flesh with no earthly bad consequences but with bad news value concerning one's otherworldly prospects?

8 Stalnaker, Robert ‘Stalnaker to Van Fraassen’ in Harper, W. and Hooker, C. eds., Foundations of Probability Theory, Statistical inference, and Statistical Theories of Science (Dordrecht: D. Reidel 1976) vol. 1, 302–6Google Scholar

9 Jeffrey, chapter 1.7; also Eells, Ellery Rational Decision and Causality (Cambridge: Cambridge University Press 1982).CrossRefGoogle Scholar They both agree with one-boxers that probabilistic dependencies between acts and conditions are sufficient by themselves to render the dominance argument favored by two-boxers fallacious. But they take two boxes nevertheless because they accept a principle of ‘ratification.’

10 Either that or p(A)=O. But this alternative way of securing independence must be excluded from systems following Popper, Karl R. The Logic of Scientific Discovery (New York: Science Editions 1961)Google Scholar New Appendix *v.

11 Lewis, David ‘Prisoners’ Dilemma is a Newcomb Problem,’ Philosophy & Public Affairs, 8 (1979) 235–40Google Scholar

12 ‘≈1’ means ‘is close enough to 1 to warrant full belief.’ If .9 is close enough, a counter example exists: p(ABC) = .01; p(AB-C) = .05; p(A-BC) = .44; p(A-B-C) =0. For a rigorous exploration of the relation of the two conditionals, see Allan Gibbard, Two Recent Theories of Conditionals,’ in Harper, Stalnaker, and Pearce, 211-47. He also introduced me to Zack and Sly Pete, soon to appear here.

13 Lewis, C.I. An Analysis of Knowledge and Evaluation (La Salle: Open Court 1946)Google Scholar chapter 8, sections 10ff

14 Lewis, David ‘Probabilities of Conditionals and Conditional Probabilities,’ The Philosophical Review, 85 (1976) 297–315.CrossRefGoogle Scholar But see the Van Fraassen-Stalnaker correspondence in Harper and Hooker for an important hiatus in Lewis's proof.

15 Ernest W., Adams ‘Subjunctive and Indicative Conditionals,’ Foundations of Language, 6 (1970) 89–94Google Scholar

16 Stalnaker, Robert ‘Indicative Conditionals,’ Philosophia, 5 (1975) 269–86CrossRefGoogle Scholar

17 Adams, Ernest ‘Prior Probabilities and Counterfactual Conditionals’ in Harper, W. and Hooker, C. eds., vol. 1, 1-21.Google Scholar Also see his The Logic of Conditionals (Dordrecht: D. Reidel 1975). [Adams informs me that I am mistaken about some of his views and that he has revised others, but accepts my not altering my text.]

18 David Lewis, ‘Probabilities of Conditionals and Conditional Probabilities’

19 The problem specifies that the predictor is reliable. But this is ambiguous. Does it mean that I will most likely do what he predicts or that he will most likely predict what I will do? It is traditional to assume the latter as given. As I state the problem, the probability of correct prediction is the same no matter what choice is made: ‘neither choice … is more likely … to have outfoxed him.’

20 See footnote 9 for those who charge incompleteness. For those who charge irrationality see Gibbard, Allan and Harper, William L. ‘Counterfactuals and Two Kinds of Expected Utility’ in Hooker, C. Leach, J. and McClennan, E. eds., Foundations and Applications of Decision Theory (Dordrecht: D. Reidel 1978) vol. I, 125–62.Google Scholar For a discussion of recent developments within the camp of the two boxers who charge one-boxers with irrational procedures, see Lewis, David ‘Causal Decision Theory,’ Australasian Journal of Philosophy, 59 (1981) 5–30.CrossRefGoogle Scholar According to David Lewis, ‘“Why Ain'cha Rich?”,’ Nous, 15 (1981) 377-80, the debate with us one-boxers is at a standoof for lack of sufficient common ground to resolve issues.

21 Peirce, Charles Sanders Collected Papers. Hartshorne, Charles and Weiss, Paul eds. (Cambridge, MA: Harvard University Press 1931)Google Scholar vol. 2, nos. 269 and 757, fn.

22 Teller, Paul ‘Conditionalization and Observation,’ Synthese, 26 (1973) 218–58CrossRefGoogle Scholar

23 A bridge has fallen, and I am an engineer trying to determine what caused it to. Among the causal variables I am looking at is x. I want to find its strength, measured numerically. Given all that I know, that x = 7 is equiprobable with x = 6. Let us say that all worlds in which x = 6 are closer to the worlds in which x<S than any world in which x = 7 is. Now I discover that indeed x>5. Does my discovery that x>8 give me reason to be more dubious about x = 6 than about x = 7 Or do they remain equiprobable?

24 Jeffrey, chapter 11

25 Lewis, Counterfactuals, 71f; also Lewis, ‘Probabilities of Conditionals and Conditional Probabilities’

26 Bennett, Jonathan ‘Counterfactuals and Possible Worlds,’ Canadian Journal of Philosophy, 4 (1974) 381–402,CrossRefGoogle Scholar section 7; and Lewis, David ‘Counterfactual Dependence and Time's Arrow’ Nous 13 (1979), 455–476.CrossRefGoogle Scholar

27 Adams, ‘Prior Probabilities and Counterfactual Conditionals,’ also his The Logic of Conditionals, ch. 4Google Scholar

28 Disputed by Wolfgang Spohn, ‘Where Luce and Krantz Do Really Generalize Savage's Decision Model,’ Erkenntnis 11 (1977) 113-34. Jeffrey's system, sections 10.4f., permits probabilities of one's up-coming decisions without having to envision them as one's propensities to gamble on the outcomes of one's current deliberations.

29 Jeffrey, 168f.

30 Adams, The Logic of Conditionals, ch. 4,Google Scholar section 8; Brian Skyrms, ‘The Prior Propensity Account of Subjunctive Conditionals,’ in Harper, Stalnaker, and Pearce, 259-65

31 Robert Stalnaker, ‘Stalnaker to Van Fraassen’

32 For two other unacceptable consequences of causal decision theory, see Gibbard and Harper, section 11, the case of ‘Death in Damascus,’ an interminable deliberation, and Hunter, Daniel and Richter, Reed ‘Counterfactuals and Newcomb's Paradox,’ Synthese 39 (1978) 249–61CrossRefGoogle Scholar, see 257 for the case of ‘Push a Button to Win’ which a two-boxer refuses to do. Gibbard and Harper reply that the former case is unparadoxical; D. Lewis in ‘Causal Decision Theory,’ 29f., replies that the latter case is misanalyzed. Both replies perplex me.

33 For this version, see Factor, R. Lance ‘Newcomb's Paradox and Omniscience,’ International Journal for Philosophy of Religion, 9 (1978) 30–40;CrossRefGoogle Scholar also Daniel Hunter and Reed Richter, 253.

34 David Lewis, ‘Counterfactual Dependence and Time's Arrow’

35 Falk, Arthur ‘New Wrinkles on Old Fatalisms,’ forthcoming in Jadavpur Studies in Philosophy, Vol. 7,Google Scholar edited by Pranab Kumar Sen.