We take it that what is intended by “laws” in the title of this session—“Confirming Ceteris Paribus Laws in the Social Sciences”—is reliable rather than fortuitous relations, that is, Millian “tendencies,” with “forcing” properties. These refer to causes which do their work whether or not interfered with, or even counteracted by, other causes. Early econometricians had this in mind when they referred to “autonomous” relations (or behavioral relations). We entirely beg the question of how we know when we are dealing with genuine causes and with the related question how we come by autonomous relations. Instead, we concentrate upon some implications of our supposing that we can identify the experimental conditions necessary to confirm the operation of whatever tendency is in question.

Another expression for these experimental conditions is the steps necessary in order to transform a theoretical model into an estimable one.

Although generally informed by an intimate knowledge of evolutionary biology and taxonomy, the controversy over the nature of species is clearly philosophical; it consists almost entirely of the clarification of old, and the invention of new arguments for or against calling the species category a class, The debate seems firmly divided between those, like Kitts and Bernier, who see homo sapiens as a class, and those, like Hull and Ghiselin, who see it as an individual. In the first case, particular human beings are members; in the second case, parts. To the champions of class, the essentialists, each species can be defined by means of a unique set of necessary and sufficient conditions, and every organism can be placed without equivocation into a particular species. To the individualists, nothing could be further from the truth. As a contingent, product of evolution, each species shares that crucial characteristic of an individual, spacio-temporal identity; each is a chunk of genealogical nexus.

Game theory studies the behavior of rational players in interactive situations and its possible outcomes. For such an investigation, the notion of players’ rationality is crucial. While notions of rationality have been extensively discussed in game theory, the epistemic conditions under which a game is played — though implicitly presumed — have seldom been explicitly analyzed and formalized. These conditions involve the players’ reasoning processes and capabilities, as well as their knowledge of the game situation. Game theory treats some aspects of information about chance moves and other players’ moves by means of information partitions in extensive form games. But a player's knowledge of the structure, for example, of information partitions themselves is different from his information about chance moves and other players’ moves. The informational aspects captured by the extensive form games have nothing to do with a player's knowledge of the structure of the game.

In earlier publications Jaakko Hintikka has introduced the interrogative model of inquiry and studied some of its applications.1 At its simplest, the interrogative model takes the form of a game between a player known as the Inquirer and a source of information we call Nature. The inquirer is trying to derive a conclusion C from a given set of premises T by standard deductive means augmented by additional information gained from Nature. (We can think of C as a set of formulas related disjunctively to each other.) The inquirer may obtain this additional information by means of questions put to Nature. The answers to these questions, when available, are then added to the premise set T. When a question is answerable but no true answer is available, Nature may respond with a false answer.

The deductive steps employed are subject to certain limitations. For instance, if the derivation is being carried out in a Beth-style tableau system, we require that the deductive steps obey the subformula principle.2

Logical analyses of scientific representations of the world have usually focused on axiomatized or axiomatizable theories. As practiced, science seldom employs such theories. Rather, we find aggregations of claims, the logical relations of which are not as neat as philosophers of science might like them to be. Indeed, a common feature of such aggregations is the presence of certain “theoretical anomalies,” statements that are in some way incompatible with the remainder of the corpus. Huygens’ description of light as exhibiting an asymmetry with respect to its direction of propagation in polarization phenomena was such an anomaly because of its inconsistency with his account of light as longitudinal waves in a medium. (See Sabra 1981, pp. 226-227.) Although the occurrence of these anomalies is indicative of a problem that must be dealt with, inconsistent representations of the world are not without significant heuristic value.

Von Neumann and Morgenstern based their theory of games on the representation of individual preferences for outcomes by utilities generated by preferences for gambles over these outcomes. A utility function (an assignment of numbers to outcomes) represents an agent's preferences just in case the agent's preference relation between any two gambles agrees with the numerical relation between their expected utilities (where these expectations are calculated using the objective probabilities specified in the gambles). This representation constrains the utility assignments up to scale transformations (multiplying each value by the same positive number) and adjustments of the zero point (adding the same positive or negative number to each value). This fixes the ratios of differences between utilities of outcomes.

Von Neumann and Morgenstem proposed qualitative constraints on the agent's preferences among these gambles which are equivalent to the assertion that such a utility representation exists. Here is an equivalent formulation of such rationality postulates.

It is by now rather well understood that the notion of common knowledge (first introduced by Lewis (1969) and later formalized by Aumann (1976)) plays a central role in the theory of games. (An event E is common knowledge between two individuals, if each knows E, each knows the other knows E, etc…). Indeed, most justifications of Nash's (1951) equilibrium concept usually include (perhaps only implicitly) the assumption that it is common knowledge among the players that both the Nash equilibrium in question will be played by all and that all players are expected utility maximizers. (We shall henceforth call expected utility maximizers, “rational”.) We hope to illustrate in an informal manner that there is in fact a large class of extensive form games, in which each of which it is not possible for rationality to be common knowledge throughout the game.

Suppose you attend a seminar where a mathematician presents a proof to some of his colleagues. Suppose further that what he is proving is an important mathematical statement Now the following happens: as the mathematician proceeds, his audience is amazed at first, then becomes angry and finally ends up disturbing the lecture (some walk out, some laugh, …). If in addition, you see that the proof he is presenting is formally speaking (nearly) correct, would you say you are witnessing an extraordinary event in urgent need of explanation? Surely, your answer would be yes. But do events of this type actually occur? The matter of the fact is, yes, they do. This paper presents the details of such an event, suggests a possible explanation and examines its implications for our understanding of mathematical practice.

One of the most obvious features of empirical science is that scientists attempt to relate their theories to data, that is to the results of observation and experiment. In so doing, they will find it necessary to use the term ‘confirms’ or ‘confirmation’ or at least terms with more or less the same meaning. Thus scientists may think that a theory is well- confirmed by a considerable body of observational evidence. In this case they will regard it as rational to have a high degree of confidence in the theory, and, in particular, to use it in practical applications. Alternatively a theory T may be seen as badly confirmed by the evidence. In this case it would be thought undesirable to use T in practice, and the problem would become that of modifying or replacing T so as to obtain a new theory T’ which is better confirmed than T.

Although statistical techniques like regression analysis and path analysis are widely used in the biomedical, behavioral and social sciences to make causal inferences there has been surprisingly little philosophical discussion of the details of such techniques and of the conceptions of causation and explanation implicit in them. There also has been relatively little attempt to compare such techniques with various probabilistic models of causation and explanation in the philosophical literature.

In this paper I explore, for reasons of space in a very sketchy and schematic way, some issues in philosophy of science raised by regression analysis. One general conclusion I reach is that it is considerably less obvious than one might suppose that the philosophical theories alluded to above are plausibly viewed as reconstructions of regression techniques.

It is widely believed that if a piece of evidence for a theory was known at the time the theory was proposed, then it does not confirm the theory as strongly as it would if the evidence had been discovered after the theory was proposed. I shall call this view the predictivist thesis. Those who have endorsed it include Leibniz (1678), Huygens (1690, preface), Whewell (1847 vol. 2, p. 64f.), Peirce (1883), Duhem (1914, ch. II, §5), Popper (1965, p. 241f.), Lakatos (1970, p. 123), and Kuhn (1977, p. 322). On the other hand, the thesis has been rejected by a number of philosophers, including Mill (1872 bk. III, ch. 14, §6), Keynes (1921, p. 305), Rosenkrantz (1977, p. 169f.), Horwich (1982, pp. 108-117) and Schlesinger (1987). Others, while not rejecting the predictivist thesis, nevertheless regard the justification of the thesis as problematic; these include Hempel (1966, p. 38) and Gardner (1982).

‘A hypothesis can only be received upon the ground of its having been verified by successful prediction’, C.S. Peirce, Collected Papers, Vol. II, p.466.

Hempel, in his classic [1966], raised a problem which already had a long pedigree. Balmer, having examined measurements of the wavelengths of lines in the emission spectrum of hydrogen, constructed a now well-known formula for generating these, and also other lines at that time unknown to him. Hempel asked whether Balmer's formula would have been as strongly confirmed by the new lines had they too formed part of Balmer's database. Hempel's question poses the famous and ancient accommodation-versus-prediction problem: is a hypothesis h, designed among other things to account for data e, confirmed by e as much as h would have been, had it been found to explain e without, however, having been constructed to do so? An unconditionally negative answer has been given by a numerous and influential body of scientists and philosophers; this unconditional view of the matter I shall call predictionism.

For the past century the Central Dogma of confirmation theory has been:

All empirical support (of a theoretical claim) = empirical evidence = empirical data = successful test results = successful predictions or postdictions = true empirical consequences (of the claim plus auxiliary assumptions).

According to the Dogma, all empirical support derives from empirical testing of predicted consequences. I shall attack this pure consequentialism and defend the importance of generative justification in science.

One question which has been widely debated through the years is whether “postdicting” or explaining already known phenomena provides as much epistemic support for an hypothesis as predicting new phenomena or, indeed, whether explanation provides any support at all. I believe that explanation is on a par with prediction, but I want to address a different question here. Both explanation and prediction (as usually construed) involve consequential reasoning.

In his recent book Foundations of Space-Time Theories Michael Friedman argues for a realism about theoretical structure based on specific methodological practices concerning theory unification. Theoretical structures that are essential to the unifying process are to be given a literal realistic interpretation while the remaining ones can be considered as having merely representational status. Friedman’s account of unification involves the notion of a literal reduction or identification of observational properties of entities or objects with their theoretical counterparts. The relationship between these two levels of theory can be construed as that of submodel to model. Once the appropriate reductions are achieved we are then free to conjoin certain theoretical structures with others thereby enabling us, over time, to produce a unified theory encompassing a variety of domains.

The alternative to this view Friedman describes as the representationalist approach. Instead of characterizing the relationship between observational and theoretical structures as that of submodel to model the observational properties are simply correlated by way of an embedding (as opposed to an identity) map with their appropriate theoretical counterparts.

Imagine a scientist who examines an unending sequence of data about an unknown reality and responds to each datum by announcing a first-order theory in a fixed language L. The scientist hopes to determine the truth or falsity of every sentence of L, but he does not feel obliged to reach a stage in his investigation when all such questions will have been resolved. One way to represent the scientist's project is as follows. Let the unknown reality correspond to the L-structure S. Then the scientist hopes that for every sentence ϕ ∊ L, if S ╞ ϕ, then all but finitely many of the theories he emits, imply ϕ and do not imply - ϕ Following Kelly & Glymour (1987), we say in this case that the scientist “AE-identifies” S. The AE prefix signifies that for all ϕ ∊ L, there is a stage beginning at which the scientist's theories correctly decide ϕ.

In several recent papers, Arthur Fine has developed a far-reaching attack upon both the standard realist interpretations of science and their most prominent anti-realist alternatives (1986a, 1986b, 1986c). In their place, Fine proposes not another position on the realist/anti-realist axis, but an attitude toward science, the “natural ontological attitude” (NOA), which is supposed to remove any felt need for a philosophical interpretation of science.

In this paper I will be concerned with Fine’s reasons for adopting NOA rather than his arguments against realism and anti-realism. Unless these reasons are adequate, Fine’s papers are likely to set off a scramble for new and better arguments concerning realism, rather than the reorientation of the philosophy of science which his polemics are clearly intended to provoke. Thus for my purposes, we can presume that Fine’s criticisms of standard positions are generally sound. The question is whether Fine’s proposed alternative attitude can then satisfy the same argumentative standards.

Ludwik Fleck’s Genesis and Development of a Scientific Fact is an extended argument for the inclusion of social factors in the history and philosophy of science. Fleck uses the history of syphilis as his case study, which falls into two parts. In the first two chapters of his book, Fleck presents a history of the change of the concept of syphilis as a “carnal scourge with strong moralistic connotations” in the middle ages to the modern concept of syphilis as an infectious disease (1979, 77). In the second part of the book, he presents a detailed account of the development of a serum test for syphilis, the Wasserman reaction. Fleck also argues that perception is theory-laden, for example, in his comparative study of anatomical drawings, and for the importance of social pressures on the development of science, for example, in his discussion of the rivalry between nations to first develop a cure for syphilis, as demanded by politicians (1979, 133 ff. and 68).

Consider the following collection of familiar questions in the philosophy of science.

Underdetermination: What collections of theories can be reliably distinguished from one another on a given sort of evidence presentation? How do differences in evidence presentation, background knowledge, and hypothesis vocabulary affect underdetermination?

Realism: How plausible is it that the methods employed by science are capable of arriving at the truth in a given domain of inquiry? If not, is it plausible that there exist such methods? How does the answer differ from domain to domain?

Scientific progress: Is it possible that scientific knowledge could be continually improved, even if it is never perfectly correct? Is there any sense to be made of the increasing verisimilitude of inquiry?

Methodology: How do standard methodological directives interact? Do different directives interfere with one another or do our favorite ideas about method complement one another? Is experiment really more powerful than passive observation?

Philosophers of science, e.g. Cartwright (1979) and Skyrms (1980), have given accounts of general causation in probabilistic terms; not surprising since we often accept general causal sentences as true despite being aware of apparent counterinstances. Consider:

(E1) Smoking is a cause of heart attacks.

We accept (E1) as true though aware of smokers who never have a heart attack. Here I quickly review familiar problems in two existing probabilistic accounts, offer a new objection, and suggest the beginnings of an alternative account.

The traditional model of general causation maintains that causes, and only causes, raise the probability of the effect That is:

(TM) F is a cause of G if and only if .

Despite some intuitive appeal, the traditional model faces at least three basic objections. First, consider cases of epiphenomena in which there are properties F, G, and H such that F is a cause of G, F is a cause of H, but G is not a cause of H and H is not a cause of G.

The performance of a connectionist learning system on a simple problem has been described by Hinton and is briefly reviewed here: a finite function is learned, and the system generalizes correctly from partial information by finding simple “features” of the environment. For comparison, a very similar problem is formulated in the Gold paradigm of discrete learning functions. Identification in the limit from positive text of a large class of functions including Hinton's is achievable with a trivial, conservative learning strategy. Using Valiant's approach, we place an arbitrary finite bound on function complexity and then we can guarantee text and resource efficiency relative to a probabilistic criterion of success. But the connectionist system generalizes. That is, it uses a non-conservative learning strategy. We define a simple, non-conservative strategy that also generalizes like the connectionist system, finding simple “features” of the environment.