Abstract
X says ‘It is probable that h’ and Y says ‘It is improbable that h’. No doubt X and Y disagree in some ways. In particular, they disagree in the way they evaluate h with respect to credal (or personal) probability to be used in practical deliberation and scientific inquiry in computing expectations.
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Bibliography
Hacking, I., 1965, The Logic of Statistical Inference.
Kyburg, H., 1961, Probability and the Logic of Rational Belief.
Kyburg, H., 1974, ‘Propensities and Probabilities’, British Journal for the Philosophy of Science 25, 358 – 375.
Levi, I., 1967a, Gambling with Truth.
Levi, I., 1967b, ‘Information and Inference’, Synthese 17, 369 – 391.
Levi, I., 1969, ‘Are Statistical Hypotheses Covering Laws’, Synthese 20, 297 – 307.
Levi, I., 1973, Review of Mellor (1971), Phil. Review 82, 524 – 530.
Levi, I., 1974, ‘On Indeterminate Probabilities’, Journal of Philosophy 71, 391 – 418.
Levi, I., 1977a, ‘Truth, Fallibility and the Growth of Knowledge’, forthcoming in R. S. Cohen and M. W. Wartofsky (eds.), Boston Studies in the Philosophy of Science, vol. xxxi, Reidel, Dordrecht and Boston.
Levi, I., 19776, ‘Direct Inference’, to be published in the Journal of Philosophy 74.
Levi, I. and Morgenbesser, S., 1964, ‘Belief and Disposition’, American Philosophical Quarterly 1, 221 – 232.
Lewis, D., 1973, Counterfactuals.
Mackie, J. L., 1962, ‘Counterfactuals and Causal Laws’ in Analytical Philosophy (ed. by R. J. Butler ), pp. 66 – 80.
Mellor, D. H., 1971, The Matter of Chance.
The criterion for determining the appropriate ‘credal state’ for each potential corpus of knowledge corresponds approximately to what Carnap has called ‘credibility’. I call such a criterion or rule a ‘confirmational commitment’. For further discussion of confirmational commitments, see Levi (1974).
See Levi (1977a).
ibid.
ibid.
ibid.
ibid. See also Levi (1967a) and Levi (1967b).
Of the many authors who have advanced views resembling the proposal advanced here, the positions most similar to mine seem to be found in Kyburg (1961), p. 239 and Mackie (1962).
This is the main difference between my account of counterfactuals and the view contained in J. L. Mackie’s excellent discussion in Mackie (1962). If X’s full beliefs of the moment constitute his evidence or knowledge, he cannot discriminate between causal laws and accidental generalizations in his corpus with respect to the evidence supporting them. Hence, he cannot account for the relative vulnerability of accidental generalizations to removal in terms of deficiency in evidential support. Mackie appears to think otherwise. Apparently, X’s full beliefs at the moment do not serve as his standard for serious possibility and, hence, as his evidence according to Mackie’s view. Because I differ from Mackie on this point, I have modified his account of counterfactuals in the manner indicated.
In Lewis (1973), David Lewis offers what he takes to be a decisive counterinstance to Mackie’s view. Lewis considers a ‘moderate Warrenite’ who suspends judgement as to whether Oswald killed Kennedy, somebody else did or no one did. (See Lewis, 1973, pp. 70-72.) He is, nonetheless, a Warrenite because he assigns high credal probability to the first alternative. According to Lewis, he assigns low probability to the remaining two alternatives but more to someone else’s killing Kennedy than to the hypothesis that no one else does.
No doubt some moderate Warrenites might assign credal probabilities in the manner described by Lewis. But I could equally well imagine probabilistically moderate Warrenites assigning higher credal probability to the hypothesis that no one killed Kennedy than to the hypothesis that somebody else did.
Lewis invites us to consider the result of adding the statement ‘Oswald did not kill Kennedy’ to the moderate Warrenite’s corpus of full beliefs. When the moderate Warrenite has views such as those attributed to him by Lewis, he should, according to conditionalization, assign high probability to ‘somebody other than Oswald killed Kennedy’ and very low probability to ‘No one killed Kennedy’. (‘Oswald killed Kennedy’, of course, receives probability 0.) Lewis argues that Mackie’s analysis recommends that the following counterfactual be legitimately assertible by the moderate Warrenite: ‘If Oswald had not killed Kennedy, somebody else would have’. Lewis goes on to claim that this is ‘just backward from the truth’ and that Mackie’s analysis leads to untenable results.
There are three glaring defects in Lewis’ argument: (1) Lewis distorts Mackie’s analysis of counterfactuals and constructs his criticism by appealing to the distorted analysis rather than to the view Mackie actually endorses. Mackie quite clearly indicates that when someone legitimately asserts a counterfactual, he believes the truth of the negation of the indicative version of the antecedent. When the agent does not assume this but is in a state of suspense regarding the antecedent, he may assert an ‘open conditional’ but not a counterfactual. Mackie explicitly recognizes important differences between the two (e.g., with respect to what conditionals accidental generalizations support). Lewis has elected to ignore Mackie’s clear statements on this score. Had he attended to Mackie’s view, he would have appreciated the fact that, for Mackie, the probabilistically moderate Warrenite is not in a position to affirm a counterfactual at all. Rather an open conditional would be appropriate. Perhaps, the moderate Warrenite might say, ‘Should it turn out that Oswald did not kill Kennedy, then someone else must have done so’ or ‘If Oswald did not kill Kennedy, somebody else did’. Lewis (1973), p. 3 seems to endorse this result.
Even if we overlook Lewis’ distortion, he seems to think that when the antecedent is added to the stock of beliefs, the conditional is assertible if the probability of the consequence relative to the new stock of beliefs is sufficiently high. The naivete of this view is well documented in the literature and deserves no further comment. Even if high probability were necessary, it can scarcely be sufficient.
Finally, even if we ignore the second point along with the first, it remains the case that Lewis obtains his allegedly objectionable consequence from a characterization of a probabilistically moderate Warrenite which is by no means the only one envisageable. I have identified above a sort of probabilistically moderate Warrenite whose beliefs are such that, on Lewis interpretation of Mackie, that individual would be justified in asserting the counterfactual Lewis thinks appropriate. Of course, the other sort of Warrenite would be entitled to assert the counterfactual Lewis thinks backward from the truth. What does this prove except that Lewis is one sort of probabilistically moderate Warrenite and not another?
I suspect that lurking behind Lewis’ discussion of Mackie is the following worry: Consider the convinced Warrenite. Should he assert ‘If Oswald had not killed Kennedy, somebody else would have?’ In the text, I described a scenario where the committed Warrenite should do so. I suspect that it is a scenario that most committed Warrenites should fit. Yet, those same Warrenites should be prepared to assert ‘If Oswald had not killed Kennedy, Kennedy would have been reelected for a second term’. This may seem incoherent. Surely those who lust after a logic of counterfactuals and who wish to use modal semantics will wish to regard the legitimate assertibility of these two counterfactuals by convinced Warrenites as untenable. But, as I explained in the text, there is no incoherence, once obvious considerations of context are taken into account. Perhaps, we should keep our lust for a logic of counterfactuals in check.
Levi and Morgenbesser (1964). See also Levi (1967a), ch. Xiv.
Levi (1969).
Hacking (1965), p. 135.
This view is expressed in Levi (1967a), p. 200 and Levi (1969)
I mean to exclude Hacking (1965) from the blizzard of propensity theories as I mean to exclude myself. Mellor’s discussion of propensities, displays and chances is developed in chapter 4 of Mellor (1971). The criticisms I offer here are elaborations on criticisms already advanced in Levi (1973).
Mellor (1971), pp. 68–70 rejects the tendency analysis on the grounds that the concept of tendency needs as much analysis as the concept of chance itself. Mellor is, no doubt, right. What I find puzzling is the notion that clarity is advanced by introducing the notion of a display. But be that as it may, disputes between those favoring tendencies and those favoring displays are precisely the sorts of diversionary controversies which give propensity interpretations a bad name.
Kyburg (1974), pp. 374–375. Kyburg and others have also classified Hacking as a ‘long run relative frequency disposition’ advocate apparently on the grounds that Hacking has used the terms ‘chance’ and ‘frequency in the long run’ interchangeably and when emphasizing the misleading character of the latter term points to the fact that chance concerns what the long run relative frequency would be were a sequence of trials conducted (Hacking (1965), p. 10.) But if I understand Hacking correctly, he maintains that if X knows that the chance of heads on a toss of a is 0.999999, he should endorse the claim that were a tossed once and only once it would land heads. I shall let Hacking speak for himself, but in my view the controversy over whether chances are long run dispositions or single case dispositions is another example of a dispute which gives propensity interpretations a bad name. I might add that I do not recognize the positions attributed to me by Kyburg on pp. 374-375 under the categories ‘Nature of Disposition’ and ‘Semantics’ and would qualify his attribution of views to me under ‘Empirical meaningfulness’ and ‘application problem’ by noting that I have always thought that the problem of direct inference involved both a principle for assigning credal probabilities to hypotheses about test behavior on the basis of knowledge of chances and a rule for inductive acceptance like rule A and that a rule of the latter sort requires a rule of the former type. I have, however, often called the latter sort of rule a rule of direct inference rather than applying that description to the former sort of rule as I do here. I trust that this lack of consistency in terminology is not taken to reflect an inconsistency in viewpoint. See Levi (1967a) ch. XV. In spite of these inaccuracies of attribution, Kyburg’s discussion ends with a critique of other propensity views in agreement with the one I am advancing here and advanced in Levi (1973).
Levi (1967a), pp. 219–225.
Levi (1969).
Kyburg (1961), pp. 248–253 contains a discussion of five probability statements which I favor construing as objective nonepistemological statements of chance. Insofar as Kyburg and I disagree over the interpretation of ‘probability’, a major difference concerns whether contexts illustrated by these five examples are to be analysed epistemologically or as statements of objective chance. However, a close examination of Kyburg’s epistemological analysis reveals that-its adequacy does, indeed, depend upon whether his effort to legitimize direct inference from knowledge of frequencies in lieu of knowledge of chances can succeed. Hence, the central dispute between us concerns direct inference.
Levi (1977b).
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Levi, I. (1978). Subjunctives, Dispositions and Chances. In: Tuomela, R. (eds) Dispositions. Synthese Library, vol 113. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1282-8_18
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