Some statistical questions that arise in studies of Einstein-Podolsky-Rosen correlations are given precise and complete answers for a very simple but artificial set of pair distributions. Some recent results and conjectures about hidden variable representations of the more complex distributions that describe the Einstein-Podolsky-Rosen experiment are examined in the light of the behavior of the simple model.

The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional philosophies of mathematics indicating how each is prepared to deal with the present problem. It is shown that (the standard formulations of) some views seem to deny outright that there is a relationship between mathematics and any non-mathematical reality; such philosophies are clearly unacceptable. Other views leave the relationship rather mysterious and, thus, are incomplete at best. The final, more speculative section provides the direction of a positive account. A structuralist philosophy of mathematics is outlined and it is proposed that mathematics applies to reality though the discovery of mathematical structures underlying the non-mathematical universe.

In his book, The Scientific Image, Bas van Fraassen argues for an anti-realist view of science according to which the sole epistemological aim of science is to “save the phenomena”. As originally conceived, his constructive empiricism is strongly extensional, but in his account of the empirical adequacy of probabilistic theories, van Fraassen reluctantly abandons this extensional position, arguing that modal (intensional) notions are unavoidable in interpreting probability. I argue in this paper that van Fraassen has not presented the strongest possible case for a fully extensional account of empirical adequacy. On the present account, a probabilistic theory is empirically adequate just in case there is no theory that has a higher likelihood relative to all the phenomena in the actual world. I prove that a theory is empirically adequate if and only if the probability attributed to each observable event that occurs in the actual world is its limiting relative frequency. Thus, in so far as one is concerned with the empirical adequacy (rather than with the literal truth) of probabilistic theories, strict relative frequencies provide an adequate basis for “interpreting probability”.

Probabilistic theories are treated in a genuine measurement context. In this connection I distinguish between worlds that are “strongly infinite” and worlds that are only “weakly infinite”. It is characteristic of the former worlds that there is no limit to the precision of actual measurements. I show by example that in some “strongly infinite” worlds, theories will be empirically adequate only if observables are represented by continuous (rather than discrete) random variables. The range of such examples is clarified by a theorem which states necessary and sufficient conditions under which the “phenomena can be saved” without recourse to continuous random variables and real numbers.

The author proposes the thesis that all perception, including observation in natural science, is hermeneutical as well as causal; that is, the perceiver (or observer) learns to ‘read’ instrumental or other perceptual stimuli as one learns to read a text. This hermeneutical aspect at the heart of natural science is located where it might be least expected, within acts of scientific observation. In relation to the history of science, the question is addressed to what extent the hermeneutical component within scientific observation opens natural science to the charge of reflecting merely cultural values, and of providing merely a culturally acceptable reading of the “Book of Nature”, rather than, as the author states, one stating universal antecedent conditions of possibility of cultural activity itself.

It is not easy to assess the extent to which decision theory constitutes a contribution to philosophy. On the one hand, the enthusiasts seem tirelessly to churn out highly technical Bayesian reconstructions of scientific practice. On the other hand, their opponents dismiss the result as a body of theory that is overidealized and falsely precise, bearing no important relation to the actual conduct of inquiry. And most philosophers seem happy to ignore the debate altogether and pursue a theory of inquiry as best they can. I take the opponents’ criticism seriously, but I am still an enthusiast. The aim of this paper is to explain why. The paper consists of an accessible argument for a Bayesian decision theory designed to enable any interested philosopher to see how the insights of decision theory provide, without idealization or false precision, a fundamental (and somewhat revolutionary) contribution to our understanding of the enterprise of rational inquiry.

The system presented by the author in The Logical Foundations of Statistical Inference (Kyburg 1974) suffered from certain technical difficulties, and from a major practical difficulty; it was hard to be sure, in discussing examples and applications, when you had got hold of the right reference class. The present paper, concerned mainly with the characterization of randomness, resolves the technical difficulties and provides a well structured framework for the choice of a reference class. The definition of randomness that leads to this framework is simplified and clarified in a number of respects. It resolves certain puzzles raised by S. Spielman and W. Harper in their contributions to Profiles: Henry E. Kyburg, Jr. and Isaac Levi (R. Bogdan (ed.) 1982).

After clarifying the probabilistic conception of causality suggested by Good (1961–2), Suppes (1970), Cartwright (1979), and Skyrms (1980), we prove a sufficient condition for transitivity of causal chains. The bearing of these considerations on the units of selection problem in evolutionary theory and on the Newcomb paradox in decision theory is then discussed.

We here present explicit relational theories of a class of geometrical systems (namely, inner product spaces) which includes Euclidean space and Minkowski spacetime. Using an embedding approach suggested by the theory of measurement, we prove formally that our theories express the entire empirical content of the corresponding geometric theory in terms of empirical relations among a finite set of elements (idealized point-particles or events) thought of as embedded in the space. This result is of interest within the general phenomenalist tradition as well as the theory of space and time, since it seems to be the first example of an explicit phenomenalist reconstruction of a realist theory which is provably equivalent to it in observational consequences.

The interesting paper “On the Space-Time Ontology of Physical Theories” by Ken Manders, Philosophy of Science, vol. 49, number 4, December 1982, p. 575–590, has significant affinities to this one. We both, in a sense, try to formally vindicate Leibniz's notion of a relational theory of space, by constructing theories of spatial relations among physical objects which are provably equivalent to the standard absolutist theories. The essential difference between our approaches is that Manders retains Leibniz's explicitly modal framework, whereas I do not. Manders constructs a spacetime theory which explicitly characterizes the totality of possible configurations of physical objects, using a modal language in which the notion of a possible configuration occurs as a primitive. There is no doubt that this is a more accurate realization of Leibniz's own conception of space than the embedding-based approach developed here. However, it also remains open to objections (such as those cited here from Sklar) on account of the special appeal to modal notions.

Our approach here, by contrast, aims to avoid the special appeal to modal notions by giving directly a set of laws which are satisfied by a configuration individually, if and only if it is one of the allowable ones. One thus avoids the need for reference to possible but not actual configurations or objects, in the statement of the spacetime laws. We may then take this alternative set of laws as the actual geometric theory, and do away with the hypothetical entity called ‘space'. Yet at the same time there is no invocation of modality, except in the ordinary sense in which every physical theory constrains what is possible. So that a relationalist is not forced to utilize a modal language (though Leibniz certainly does.)

One of the most interesting programs in the foundations of quantum mechanics is the realist quantum logic approach associated with Putnam, Bub, Demopoulos and Friedman (and which is the focus of my own research.) I believe that realist quantum logic is our best hope for making sense of quantum mechanics, but I have come to suspect that the usual version may not be the correct one. In this paper, I would like to say why and to propose an alternative.

We list, with discussions, various principles of scientific realism, in order to exhibit their diversity and to emphasize certain serious problems of formulation. Ontological and epistemological principles are distinguished. Within the former category, some framed in semantic terms (truth, reference) serve their purpose vis-à-vis instrumentalism (Part 1). They fail, however, to distinguish the realist from a wide variety of (constructional) empiricists. Part 2 seeks purely ontological formulations, so devised that the empiricist cannot reconstruct them from within. The main task here is to characterize “independence of mind”. A pair of notions, “physical invariance” and “anti-determination”, seem to work. They enable us to assess anew “the problem of constructing the physical out of the phenomenal” (yielding certain clarifications demanded by Goodman). Modern cosmology, especially, is seen to present insuperable obstacles to such empiricist approaches to science. The final section on epistemological principles reveals a morass better avoided in favor of an elementary claim about perception, together with a rejection of any absolute observation/theory dichotomy. Finally, a positive, realist notion of “observable-in-principle” is sketched, and it is suggested that, from the perspective of relativistic cosmology, even this defines no boundary to potential knowledge.

This paper makes explicit and takes issue with the bizarre view, which is unfortunately prevalent among social scientists, that causal relations are features of models only. There are some good reasons to represent causal factors with independent variables. But the association between causes and independent variables is only a desideratum in model construction. It is not a criterion for judging which things are causes and which are effects.

For Savage (1954) as for de Finetti (1974), the existence of subjective (personal) probability is a consequence of the normative theory of preference. (De Finetti achieves the reduction of belief to desire with his generalized Dutch-Book argument for previsions.) Both Savage and de Finetti rebel against legislating countable additivity for subjective probability. They require merely that probability be finitely additive. Simultaneously, they insist that their theories of preference are weak, accommodating all but self-defeating desires. In this paper we dispute these claims by showing that the following three cannot simultaneously hold:

(i) Coherent belief is reducible to rational preference, i.e. the generalized Dutch-Book argument fixes standards of coherence.

(ii) Finitely additive probability is coherent.

(iii) Admissible preference structures may be free of consequences, i.e. they may lack prizes whose values are robust against all contingencies.

If we take the state function of quantum mechanics to describe belief states, arguments by Stairs and Friedman-Putnam show that the projection postulate may be justified as a kind of minimal change. But if the state function takes on a physical interpretation, it provides no more than what I call a fortuitous approximation of physical measurement processes, that is, an unsystematic form of approximation which should not be taken to correspond to some one univocal “measurement process” in nature. This fact suggests that the projection postulate does not provide a proper locus for interpretive investigation. Readers will also find section 3's analysis of fortuitous approximations of independent interest and presented without the perils of quantum mechanics.

The conditional probability of h given e is commonly claimed to be equal to the probability that h would have if e were learned. Here I contend that this general claim about conditional probabilities is false. I present a counter-example that involves probabilities of probabilities, a second that involves probabilities of possible future actions, and a third that involves probabilities of indicative conditionals. In addition, I briefly defend these counter-examples against charges that the probabilities they involve are illegitimate.

Criteria are given to characterize mature theories in contradistinction to developing theories. We lean heavily on the physical sciences. An established theory is defined as a mature one with known validity limits. The approximate truth of such theories is thereby given a quantitative character. Superseding theories do not falsify established theories because the latter are protected by their validity limits. This view of scientific realism leads to ontological levels and cumulativity of knowledge. It is applied to a defense of realism against recent attacks by Laudan.

Quine and others have recommended principles of charity which discourage judgments of irrationality. Such principles have been proposed to govern translation, psychology, and economics. After comparing principles of charity of different degrees of severity, we argue that the stronger principles are likely to block understanding of human behavior and impede progress toward improving it. We support a moderate principle of charity which leaves room for empirically justified judgments of irrationality.

Ronald Giere's analysis of causal effectiveness in populations involves the comparison of two hypothetical populations, one in which every individual has the suspected causal factor, and the other in which none do. Elliott Sober has argued that in cases where causal effectiveness depends on relative population sizes, Giere's analysis breaks down. I take issue with this claim, and argue to the contrary that Giere's analysis can help provide insight into these cases.

E. C. Tolman's ‘purposive behaviorism’ is commonly interpreted as an attempt to operationalize a cognitivist theory of learning by the use of the ‘Intervening Variable’ (IV). Tolman would thus be a counterinstance to an otherwise reliable correlation of cognitivism with realism, and S-R behaviorism with operationalism. A study of Tolman's epistemological background, with a careful reading of his methodological writings, shows the common interpretation to be false. Tolman was a cognitivist and a realist. His ‘IV’ has been systematically misinterpreted by both behaviorists and antibehaviorists. For this reason, Tolman's alliance with modern cognitivism and his influence on its development have been underestimated.

Several paleontologists have recently challenged the explanatory adequacy of the modern synthetic theory of evolution. Their position is that, contrary to the prevailing view that evolutionary change is gradual, the fossil record manifests long periods of species stasis (equilibrium) punctuated by periods of rapid species formation. And, they argue, this punctuated equilibria pattern challenges the gradualist, adaptationist and extrapolationist assumptions of the modern synthetic theory of evolution and supports a hierarchical, non-extrapolationist (non-reductionist) view of evolution. In this paper I argue that the challenge rests on an inadequate characterization of the modern synthetic theory and that, even accepting punctuated equilibria and an irreducible evolutionary hierarchy, the modern synthetic theory is adequate to explain evolutionary change at all levels of the hierarchy.

The background hypothesis of this essay is that psychological phenomena are typically explained, not by subsuming them under psychological laws, but by functional analysis. Causal subsumption is an appropriate strategy for explaining changes of state, but not for explaining capacities, and it is capacities that are the central explananda of psychology. The contrast between functional analysis and causal subsumption is illustrated, and the background hypothesis supported, by a critical reassessment of the motivational psychology of Clark Hull. I argue that Hull's work makes little sense construed along the subsumptivist lines he advocated himself, but emerges as both interersting and methodologically sound when construed as an exercise in the sort of functional analysis featured in contemporary cognitive science.