This volume recreates the received notion of reflective equilibrium. It reconfigures reflective equilibrium as both a cognitive ideal and a method for approximating this ideal. The ideal of reflective equilibrium is restructured using the concept of discursive strata, which are formed by sentences and differentiated by function. Sentences that perform the same kind of linguistic function constitute a stratum. The book shows how moral discourse can be analyzed into phenomenal, instrumental, and teleological strata, and the ideal of reflective equilibrium reworked (...) in these terms. In addition, the work strengthens the method of reflective equilibrium by harnessing the resources of decision theory and inductive logic. It launches a comparative version of decision theory and employs this framework as a guide to moral theory choice. It also recruits quantitative inductive logic to inform a standard of inductive cogency. When used in tandem with comparative decision theory, this standard can aid in the effort to turn the undesirable condition of reflective disequilibrium into reflective equilibrium. (shrink)

Ockham’s razor is the characteristic scientific penchant for simpler, more testable, and more unified theories. Glymour’s early work on confirmation theory eloquently stressed the rhetorical plausibility of Ockham’s razor in scientific arguments. His subsequent, seminal research on causal discovery still concerns methods with a strong bias toward simpler causal models, and it also comes with a story about reliability—the methods are guaranteed to converge to true causal structure in the limit. However, there is a familiar gap between convergent reliability and (...) scientific rhetoric: convergence in the long run is compatible with any conclusion in the short run. For that reason, Carnap suggested that the proper sense of reliability for scientific inference should lie somewhere between short-run reliability and mere convergence in the limit. One natural such concept is straightest possible convergence to the truth, where straightness is explicated in terms of minimizing reversals of opinion and cycles of opinion prior to convergence. We close the gap between scientific rhetoric and scientific reliability by showing that Ockham’s razor is necessary for cycle-optimal convergence to the truth, and that patiently waiting for information to resolve conflicts among simplest hypotheses is necessary for reversal-optimal convergence to the truth. (shrink)

Most handbooks on statistics and the theory of probability leave the reader in a mysterious tangle of mathematical rules for computing apparently arbitrarily chosen numerical functions. At first sight, then, a treatise on the Logical Foundations of Probability raises hopes that it will be a guide to clarity in these matters. These hopes are strengthened if the reader remembers that the author, Professor Rudolph Carnap of the University of Chicago, is noted for his thesis that philosophy is the study of (...) the logic of science. On the other hand, a first glance into this book may discourage a reader who, though familiar with statistics, is not familiar with modern logic and its notation. For this reason particularly I shall try to give an account of this book that will enable the interested student to form some opinion of its usefulness to him. (shrink)

Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning, we explicate inductive truth conduciveness in terms of optimally direct (...) convergence to the truth, where optimal directness is explicated in terms of reversals and cycles of opinion prior to convergence. Concerning, we explicate Ockham’s razor and related principles of choice in terms of the information topology of the empirical problem context and show that the principles are necessary for reversal or cycle optimal convergence to the truth. Concerning, we weaken the standard principles of agm belief revision theory in intuitive ways that are also necessary for reversal or cycle optimal convergence. Then we show that some of our weakened principles of change entail corresponding principles of choice, completing the triangle of relations between,, and. (shrink)

Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning, we explicate inductive truth conduciveness in terms of optimally direct (...) convergence to the truth, where optimal directness is explicated in terms of reversals and cycles of opinion prior to convergence. Concerning, we explicate Ockham’s razor and related principles of choice in terms of the information topology of the empirical problem context and show that the principles are necessary for reversal or cycle optimal convergence to the truth. Concerning, we weaken the standard principles of agm belief revision theory in intuitive ways that are also necessary for reversal or cycle optimal convergence. Then we show that some of our weakened principles of change entail corresponding principles of choice, completing the triangle of relations between,, and. (shrink)

With the ascent of modern epidemiology in the Twentieth Century came a new standard model of prediction in public health and clinical medicine. In this article, we describe the structure of the model. The standard model uses epidemiological measures-most commonly, risk measures-to predict outcomes (prognosis) and effect sizes (treatment) in a patient population that can then be transformed into probabilities for individual patients. In the first step, a risk measure in a study population is generalized or extrapolated to a target (...) population. In the second step, the risk measure is particularized or transformed to yield probabilistic information relevant to a patient from the target population. Hence, we call the approach the Risk Generalization-Particularization (Risk GP) Model. There are serious problems at both stages, especially with the extent to which the required assumptions will hold and the extent to which we have evidence for the assumptions. Given that there are other models of prediction that use different assumptions, we should not inflexibly commit ourselves to one standard model. Instead, model pluralism should be standard in medical prediction. (shrink)

A Bayesian account of independent evidential support is outlined. This account is partly inspired by the work of C. S. Peirce. I show that a large class of quantitative Bayesian measures of confirmation satisfy some basic desiderata suggested by Peirce for adequate accounts of independent evidence. I argue that, by considering further natural constraints on a probabilistic account of independent evidence, all but a very small class of Bayesian measures of confirmation can be ruled out. In closing, another application of (...) my account to the problem of evidential diversity is also discussed. (shrink)

Confirmation theorists seek to define a function that will take into account the various factors relevant in determining the degree to which an hypothesis is confirmed by its evidence. Among confirmation theorists, only Rudolf Carnap has constructed a system which purports to consider factors in addition to the number of instances, viz. the variety manifested by the instances and the amount of analogy between the instances. It is the purpose of this paper to examine the problem which these additional factors (...) raise for confirmation theory, and to prove that, despite Carnap's claim, no confirmation function satisfying the requirements he has specified can take account of variety and analogy. This result is first proved for a special case, and then, in a subsequent section, is generalized through the introduction of a theorem (the proof of which is given in Appendix I). In the final section of the paper it is shown that, contrary to a claim which Carnap has made, not even the concept of the "logical width" of a predicate will enable confirmation functions satisfying his requirements to take adequate account of analogies between instances. (shrink)

I propose a framework for pragmatic reliability in-the-limit criteria, extending the epistemic reliability framework. I identify some common scientific contexts that complicate the application or i...

1. Deductive and Inductive Inference. Within the traditional treatments of scientific method, e.g., in and, it was customary to divide scientific inference into two parts: deductive and inductive. Deductive inference was taken to mean the activity of deducing theorems from postulates and definitions, whereas inductive inference represented the activity of constructing a general statement from a set of particular “facts.” Deductive inference was relegated to the mathematical sciences, and inductive inference to the empirical sciences. As a consequence, the whole of (...) science was split into two quite distinct parts: deductive science was conceived to start with precise axioms, postulates, and definitions, and its method consisted in drawing inferences from these “givens” in such a way that if the original assumptions are taken as true, then the theorems must be taken as true also. The obligation behind this “must” of the mathematical sciences was an obligation based on strict rules of deductive inference; in the earlier analyses, it was supposed that these rules were all aspects of the general theory of the syllogism, as it was described in an almost complete form in but in later work the rules have been formalized in more general terms. Inductive inference, on the other hand, was supposed to start with observed facts; these facts, or “data,” were presumably given by the senses, and described particular aspects of the external world. If the facts were given in a certain way, then the empirical scientist could “infer” a generalized description; this generalization had the characteristic that if it were granted as true, then all the facts could be deduced as consequences. The inductive process admittedly does not lead to unique generalizations, and the philosopher of science searched for other defining characteristics of good inference, such as “simplicity” and “convenience.” These empirical generalizations were taken to be “descriptions of the phenomenal world of the scientist”; a further inductive step might be taken by constructing a set of very general principles out of the more specialized generalizations within specific research problems. These “higher” inductive inferences were regarded as “theories,” which could be studied by themselves within the method of deductive inference. The scientist was then described as “checking” theory by determining whether or not the predicted consequences deduced from theory actually hold in the phenomenal world. (shrink)

Peter Achinstein gives in his papers [1] and [2] interesting analyses of some problems of inductive logic and of some approaches I have proposed. I shall discuss here some of these problems in order to clarify my present position. My comments will mainly concern the variety of instances, and only briefly the analogy influence, and the inductive methods for a coordinate language.

My goal, in this paper, is to critically assess the categorization of “interpretations of probability” as it appears in the literature. In some sources only Carnap’s treatment of probability is understood to be the best example of “logical” probability. This is surprisingly narrow and I will here suggest otherwise. In fact, I believe that certain forms of Baysianism should also be included in the logical camp.

Consider a group of people whose preferences satisfy the axioms of one of the current versions of utility theory, such as von Neumann-Morgenstern (1944), Savage (1954), or Bolker-Jeffrey (1965). There are political and economic contexts in which it is of interest to find ways of aggregating these individual preferences into a group preference ranking. The question then arises of whether methods of aggregation exist in which the group’s preferences also satisfy the axioms of the chosen utility theory, and in which (...) at the same time the aggregation process satisfies certain plausible conditions (e.g., the Pareto conditions below). (shrink)