Given the central importance of the Copernican theory to the birth of modern science, it is somewhat surprising to learn that there were remarkably few committed Copernicans prior to 1600. In a recent study, Westman (1980) finds only ten, of whom fewer than five were major scientific figures. The vast majority of scientists in this period continued to accept the Earth-centered astronomy of Ptolemy or later switched to the geoheliocentric system of Tychp Brahe. This widespread reluctance to adopt the heliocentric theory suggests the following questions about the Copernican Revolution: When and why did it become rational to reject the Ptolemaic theory as false? When and why did it become rational to accept the Copernican theory as true? Or, to put these questions in the more familiar language of the epistemologist: When and why did the beliefs that the Ptolemaic theory is false and that the Copernican theory is true become justified beliefs?

The history of science provides two prima facie reasons for believing that there is a “logic” to scientific discovery. The first is the phenomenon of multiple or simultaneous discoveries. The second is the fact that internalist historians of science (who eschew non-cognitive explanations) routinely explain how a discovery was made and why scientist X took an important step which scientist Y did not!

However, some philosophers have argued that purported historical explanations of discovery are all sleight-of-hand tricks—what we really have is a confused mixture of rational reconstructions of the justification steps in the process combined with a description, not an explanation, of the creative leaps. Others would claim that historians do indeed help us to understand scientific discoveries, but the mode of understanding involved is not that provided by the Hempelian covering law model. Rather we empathize with the creative leaps of past geniuses.

Though Imre Lakatos's ideas have been of first importance to recent History and Philosophy of Science, one of his central theses has been ill-received by philosophers and historians alike. I refer to his thesis that historiography of science is (and should be) so laden with normative philosophical doctrines about scientific rationality that “history of science without philosophy of science is blind.” (1971, p.91). In defending this ‘norm-ladenness thesis’ (as I shall call it), Lakatos employs a notion of “rational reconstruction” and “internal history” that has been indicted by Thomas Kuhn as “not history at all but philosophy fabricating examples.” (1971, p. 143). Kuhn's charge, echoed in varying degrees by Holton (1974, p. 68), Laudan (1977, p. 170), McMullin (1970, p.33), Suppe (1977, p. 669), and others, has such wide currency that I shall call it ‘the Received Critique’ of Lakatos's norm-ladenness thesis.

Explanations sometimes involve a certain asymmetry. For example, given Ohm's Law and the voltage of a battery, one can calculate the current in an electric circuit if one knows the resistance, or one can calculate the resistance if one knows the current. Both of these calculations are (roughly) deductive-nomological arguments, but only the calculation of the current from the resistance is an explanation. Why should only one of these calculations be an explanation?

One plausible diagnosis of such explanatory asymmetries is that they arise from the asymmetry of causal relations (see, for example, Salmon 1978 or Beauchamp and Rosenberg 1981, p. 313). The direction of explanation is the direction of causation. The resistance of the wire is a causal condition influencing the amount of the current, while the amount of current does not (as a first approximation) influence the resistance.

In The Cement of the Universe J. L. Mackie offered—with supplementation—a necessary-condition analysis of singular causal claims: “It seems that if any X is both necessary in the circumstances for and causally prior to Y, we shall say that X caused Y; also, wherever we are prepared to say that X caused Y we are prepared to say that X was necessary in the circumstances for and causally prior to Y” (p. 51). As Mackie interprets ‘necessary’, this is a counter-factual analysis.

Although there are difficulties with treating necessity (supplemented with the indicated qualifications) as sufficient for our being justified in saying that X caused Y (argued by Berofsky 1977 and Earman 1976, among others), I want to challenge the second half of the analysis, because refuting it seems to shake more deeply my sympathies for necessary-condition analyses.

There is an ancient principle for which a number of writers on time and causation feel a certain allegiance. Bertrand Russell puts the idea with his characteristic flare for style: “… it seems strange—too strange to be accepted, in spite of bare logical possibility—that the cause, after existing placidly for some time, should suddenly explode into the effect, when it might just as well have done so at an earlier time, or have gone unchanged without producing its effect.” (Russell 1912, pp. 178-179). The maxim has a habit in the history of thought of lying unnoticed but once spotted leading its viewer to less than cautious theses. With maxim in hand, David Hume (1739, p. 76) concludes that simultaneous causation is impossible, Myles Brand (1980) concludes that every causal relation is one of simultaneity, Russell.(1912) declares that the very notion of causation is incoherent.

This paper will summarize positions explained and defended more fully in my book, Space-Perception and The Philosophy of Science (Heelan 1982). The philosophical genre of this paper is that of a hermeneutical phenomenology, it addresses questions from the point of view of such writers as, E. Husserl, M. Heidegger, M. Merleau-Ponty, P. Ricoeur, and H-G. Gadamer (see references). Those who are not familiar with this kind of writing may well find the exposition too brief to be persuasive; those who are, may wonder at the audacity of applying such methods of analysis to the natural sciences. It is unlikely that either group will be entirely pleased with the content of what I have to say.

My principal theses are the following: (1) reality is the content of World, and this comprises whatever is or can be given directly in a public way within perception;

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.

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.

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.

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.

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.

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.

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.