In their contributions to this volume, Bruce Buchanan (1983) and Lindley Darden (1983) have provided compelling reasons why philosophers of science concerned with the nature of scientific discovery should be aware of current work in artificial intelligence. Buchanan presents abundant examples of the mechanization of generation of empirical hypotheses in current AI programs, while Darden, at a more speculative level, discusses the use of analogy in theoretical discovery. The implication of both these studies is that the philosophy of discovery can profitably borrow notions from work in artificial intelligence, since useful analogies can be found between problems in that field and the problems facing philosophers studying scientific discovery.

I have no quarrel with this claim, except that it is too weak. I shall argue that work in AI is not only useful but essential for investigations in philosophy of science concerning discovery. The connecting link between the two fields is empirical cognitive psychology.

Scientific Realism, as I shall understand it, holds that (a) the purportedly referential terms of current theory are genuinely referential, and (b) the theoretical, lawlike statements of current theory are at least approximately or partly true. Realism recommends itself as an explanation of the success of current science at the level of explanations and predictions of experientially accessible phenomena. That is, the case for realism assumes:

• (1) Current theory in fact achieves such success, and achieves it on balance, i.e., is free of serious disconfirmations.

• (2) Realism explains such success; i.e., the truth of (a) and (b) would justify us in expecting current theory to be successful.

• (3) There is no viable nonrealist explanation of the success of current theory.

• (4) No features of current theory independent of predictive failure discredit (a) or (b).

I shall comment briefly on each of these assumptions.

The year 1982 marks the twentieth anniversary of Carl G. Hempel's “Deductive-Nomological vs. Statistical Explanation,” published in Minnesota Studies in the Philosophy of Science, volume III. This work constitutes, to the best of my knowledge, the first extended and systematic philosophical treatment of statistical or probabilistic explanation, and the first serious attempt to articulate explicitly a precise model for such explanations. Because of this fact, it seems to me, we may take 1962 as the year in which the philosophical theory of scientific explanation first entered the twentieth century. By that time, virtually every branch of empirical science made indispensable use of statistical methods and most of them counted statistical generalizations among their important results.

Scientific realism is the doctrine that our theories are intended to literal descriptions of the world. It is the claim that there is a realm of non-observable entities and processes, and that science legitimately appeals to this realm in its explanations of the observable world. This is a sketchy characterization, and with it go some sketchy arguments. These are the miracle arguments for scientific realism. Here is the way J.J.C. Smart puts his version:

Philosophers tend to view the relationship between a particular scientific theory and its data as representable by means of a single logical structure. The relationship is not ordinarily viewed as requiring a hierarchy of structures of different logical type. Two recent and excellent books illustrate this tendency. Glymour in Theory and Evidence (1980) continues the positivist tradition of viewing theories as axiomatic systems which connect with their evidence by means of ordinary quantification and truth functional connectives. Theory testing can be understood in terms of the syntactic properties of a single logical system. In The Scientific Image (1980), van Fraassen adopts a version of what is sometimes called the “semantic view”: a theory is a set of models of some purely formal system. Evidence constitutes (if confirmatory) a sub-model imbedded in a model of the equivalence class that is the theory.

The subject of this panel discussion is probabilistic explanation. However, I would like to broaden the scope of my remarks to include the subject of probabilistic causality as well. For, I will argue in this paper that recent attempts to develop a theory of objective probabilistic causality are vulnerable to the same criticisms that in a previous paper I have advanced against the theories of objective probabilistic explanation proposed by Salmon and Fetzer.

During the past decade or so, both Salmon and Fetzer have written widely on the subject of probabilistic explanation, - and the Statistical-Relevance and Causal-Relevance models for which they are, respectively, well known have been extensively discussed in the literature. During this same period, Patrick Suppes' (1970) monograph has been a common reference point for discussions of probabilistic causality (though as Salmon points out in a recent article , Suppea' account shares many features with earlier accounts of causality proposed by Good and Reichenbach).

Hanna (l981) and Humphreys (1981) have offered criticisms which tend to undermine the plausibility of the single-case propensity account of probabilistic explanation advanced in Fetzer (1974) and (1981a). Hanna contends that, on single-case criteria, there typically are no unique single-case propensity values to assign to the occurrence of particular explanandum-events because the propensities for these outcomes to occur are continuously evolving over time (yielding “the temporal relativity of probabilistic explanations”), while Humphreys suggests that, whether or not unique single-case probability values happen to be available at all, they are nevertheless incidental and dispensable elements of otherwise potentially acceptable explanatory accounts. Indeed, Humphreys and Railton (1978) and (l981) appear to converge in common agreement on the inessential function of single-case probability assignments within the context of probabilistic explanations.

It is widely assumed that disposition predicates do not designate events, processes, or states of affairs which could be causal factors in the production of natural phenomena, yet the fact that an object has a given dispositional property is frequently taken to help explain the behavior exhibited by the object to which the disposition can be ascribed. Considerable philosophical effort has been devoted to the task of explaining how this could be so. The results run the gamut from Hume's (1739, p. 224) view that faculties and occult qualities have absolutely no explanatory import to Armstrong's (1968, p. 88) recent conclusion that dispositions are causes. Most proposals, however, lie between these extremes. Most contemporary philosophers take it for granted that disposition ascriptions have some explanatory import even though disposition predicates do not designate causes.

In my paper “Aleatory Explanations” (Humphreys 1981a) I presented the rudiments of a theory of explanation which had the following features:

1. 1) Explanations of indeterministic phenomena are given by means of a specification of the contributing and counteracting causes involved;

2. 2) Probability values are not themselves explanatory and explanations need not specify probability values;

3. 3) Maximal specificity criteria are not part of the logical criteria of adequacy for explanations;

4. 4) Partial explanations which are nevertheless true can thus be given;

5. 5) Explanations of this kind show that the traditional ‘X because Y’ pattern of explanation is inadequate for indeterministic causal explanations and must be replaced by ‘X because Y, despite Z’.

In that paper, I restricted myself to explanations of events and their complements, involving only direct causes in two-state Markov chains.

According to de Finetti's representation theorem, probabilities of exchangeable sequences of events are unique mixtures of Bernoullian probabilities. The exchangeable probability P(E) of the sequence E equals an integral of the form , where Px(E) is for each x (0≦x≦1) a Bernoullian measure with the probability x for ‘success’ and independence between consecutive events, and F a uniquely determined distribution of the parameter x. P(E) equals the expected value of Px(E). If F has a derivative f, Probabilities can be calculated under the integral sign as if events were independent and had a constant success probability. Therefore there cannot be anything one can do with Bernoullian probabilities, but could not do with the exchangeable ones, de Finetti thinks that he has, because of the unique correspondence between exchangeable measures and distributions over a parameter each value of which gives a Bernoullian probability, shown the unnecessity of the latter.

Whether it is due to the incompleteness of information, inaccuracies of measurement, or stochastic nature of phenomena, a great deal of scientific inference requires probabilistic considerations. In carrying out such inferences, the statistical methods predominantly used are from the Neyman-Pearson Theory of statistics (NPT). Nevertheless, NPT has been the target of such severe criticisms that nearly all philosophers of induction and statistics have rejected it as inadequate for statistical inference in science. If these criticisms do in fact demonstrate the inadequacy of NPT, then a good portion of statistical inference in science will lack justification. Because of the seriousness of such a conclusion, it is important to carefully consider whether critics of NPT have succeeded in demonstrating its inadequacy.

The Emperor Vespasian, presented with an invention to enable columns to be transported cheaply, praised the inventor but declined to make use of the innovation, apparently fearing the risk of upheaval from the displaced workers (Gimpel 1976, p. 9). Imbued as they are with the notions of progress and efficiency, few leaders in the modern world seem to have followed Vespasian's precedent and rejected the promise of technological innovations. Yet the sheer magnitude of the possible consequences of some technologies, and the multiplicity of choices made possible by competing technological solutions to this or that problem have fostered techniques for the appraisal of benefits and costs (including risks) in proposed courses of action. What information do these techniques give us, and what are the grounds for using them to guide decision making?

Randomization is a generally accepted principle of sound experimental design and common practice among working scientists. But many philosophers and some theoretical statisticians have rejected it. Bayesians have most often stated their opposition to randomization in terms of a decision theoretic argument. Not all Bayesians, however, could go along with that argument, as the above quotation by Leonard Savage testifies.

In this paper I will examine the Bayesian decision theoretic argument against randomization and show why it fails. By means of an example I will then give a partial justification of randomization in Bayesian terms.

One of the roles of government is to regulate new technologies and control the risks to life and health that they impose. This will be true according to any plausible theory of government or politics. There are many reasons for centralizing the control of technological risk. First, the problem can elude individual or decentralized solutions because the transaction costs for bargaining to take place are too high, either because many different actors each impose slight risks which are intolerable only in their aggregate, or else because one actor imposes significant risks which are distributed thinly over very many individuals. A second reason is that technological risks are often invisible, delayed, and exceptionally complex, so the costs of gathering enough information to make reasonable decisions can be so prohibitively high that they are incapable of being borne except at the most centralized levels of government where resources can be pooled.

The gambler's fallacy runs like this: We know

• 1) the bias for heads of a certain coin and flipping device is 1/2, and

• 2) flips of the coin with the flipping device are independent.

Given these facts we can easily compute the probability of 4 heads or fewer turning up in 20 flips, P(h≤4), to be

Suppose we flip the coin 15 times and get—improbably enough—all tails. If the coin lands tails up once more in the next 5 flips the improbable event of 4 or fewer heads in 20 flips, h≤4, will have occurred. Since P(h≤4) is so small we might be tempted to infer that all of the next five flips will be heads.

We shall not belabor the importance of having a clear idea of the difference between classificatory, comparative, and quantitative terms. Even though some of the goals that were set for theories of measurement of empirical attributes no longer seem viable, and some do not seem generally applicable, there is every reason to believe that suitable general goals for such theories will rely upon a distinction between quantitative and qualitative terms. The distinction seems also to have an intrinsic interest, even though some of the claims originally made for it, no longer seem historically accurate, or philosophically defensible. The subject, then, is quantitative terms in theories of the measurement of empirical attributes like length, mass, charge, and utility. We shall consider two problems.

The current theory of biological evolution (the “Synthetic Theory” or “Modern Synthesis”) may be traced to Theodosius Dobzhansky's Genetics and the Origin of Species, published in 1937: a synthesis of genetic knowledge and Darwin's theory of evolution by natural selection. The excitement provoked by Dobzhansky's book soon became reflected in many important contributions which incorporated into the Modern Synthesis relevant fields of biological knowledge. Notable landmarks are Ernst Mayr's Systematics and the Origin of Species (1942), Julian S. Huxley's Evolution: The Modern Synthesis (1942), George Gaylord Simpson's Tempo and Mode in Evolution (1944), and G. Ledyard Stebbins’ Variation and Evolution in Plants (1950). It seemed to many scientists that the theory of evolution was essentially complete and that all that was left was to fill in the details.

Deeply held scientific beliefs, like metaphysical presumptions, color the world in their own hues, leaving in shadow questions which might be both posable and answerable under a different light. Contemporary evolutionary theory, derived from the intellectual marriage of Darwin and Mendel, is such a world view. Whatever conceptual order this intellectual union has brought, it remains true that heritable mutations and Natural Selection are processes exploring and pruning a complex tree of possibilities. The central epistemological failure of contemporary evolutionary theory, I shall argue, is that it has supplied little insight into the expected character of the possibilities which are explored. Prune though it may, selection itself cannot generate biological order, and variation can only explore. Hidden in the shadows of current theory lies the concept that the ultimate sources of order in the living world must derive from basic properties of structural or dynamical self-organization in complex molecular systems; further that an appropriate understanding of such self-organizing properties would help limit and explain the possibilities explored in evolution.

This paper describes recent work on a theory of approximate generalizations which, following J.S. Mill (1895, Book III Chapter XXIII), are propositions often expressed in the form Most A's are B's, and whose degrees of truth (“probabilities’ in Mill's terms) are the proportions of A's that are B's. Earlier work by Ian Carlstrom and myself studied the logic of approximate generalizations — the theory of necessary connections among their degrees of truth — and basic ideas and results of that work will be briefly summarized here, along with a related extension of this study. However our present concern is primarily with two matters having to do with the effects of small changes in the extensions of predicates on degrees of truth. One is the question of which generalizations are continuous in that small changes in the extensions of “empirical” predicates would not entail large changes in the degrees of truth of the generalizations.