The principle of indifference is supposed to suffice for the rational assignation of probabilities to possibilities. Bertrand advances a probability problem, now known as his paradox, to which the principle is supposed to apply; yet, just because the problem is ill-posed in a technical sense, applying it leads to a contradiction. Examining an ambiguity in the notion of an ill-posed problem shows that there are precisely two strategies for resolving the paradox: the distinction strategy and the well-posing strategy. The main contenders for resolving the paradox, Marinoff and Jaynes, offer solutions which exemplify these two strategies. I show that Marinoff's attempt at the distinction strategy fails, and I offer a general refutation of this strategy. The situation for the well-posing strategy is more complex. Careful formulation of the paradox within measure theory shows that one of Bertrand's original three options can be ruled out but also shows that piecemeal attempts at the well-posing strategy will not succeed. What is required is an appeal to general principle. I show that Jaynes's use of such a principle, the symmetry requirement, fails to resolve the paradox; that a notion of metaindifference also fails; and that, while the well-posing strategy may not be conclusively refutable, there is no reason to think that it can succeed. So the current situation is this. The failure of Marinoff's and Jaynes's solutions means that the paradox remains unresolved, and of the only two strategies for resolution, one is refuted and we have no reason to think the other will succeed. Consequently, Bertrand's paradox continues to stand in refutation of the principle of indifference.

Homeostatic Property Cluster (HPC) theory suggests that species and other biological taxa consist of organisms that share certain similarities. HPC theory acknowledges the existence of Darwinian variation within biological taxa. The claim is that “homeostatic mechanisms” acting on the members of such taxa nonetheless ensure a significant cluster of similarities. The HPC theorist's focus on individual similarities is inadequate to account for stable polymorphism within taxa, and fails properly to capture their historical nature. A better approach is to treat distributions of traits in species populations as irreducible facts, explained in terms of selection pressures, genealogy, and other evolutionary factors. We call this view Population Structure Theory (PST). PST accommodates the view, implicit in biological systematics, that species are identified by reference to particular historical populations.

The article argues for the epistemic rationale of triangulation, namely, the use of multiple and independent sources of evidence. It claims that triangulation is to be understood as causal reasoning from data to phenomenon, and it rationalizes its epistemic value in terms of controlling for likely errors and biases of particular data-generating procedures. This perspective is employed to address objections against triangulation concerning the fallibility and scope of the inference, as well as problems of independence, incomparability, and discordance of evidence. The debate on the existence of social preferences is used as an illustrative case.

Brandon ([1982] 1984, 1990) has argued that Salmon's (1971) concept of screening-off can be used to characterize (i) the idea that natural selection acts directly on an organism's phenotype, only indirectly on its genotype, and (ii) the biological problem of the levels of selection. Brandon also suggests (iii) that screening-off events in a causal chain are better explanations than the events they screen off. This paper critically evaluates Brandon's proposals.

Today's most sophisticated simulation studies of future climate employ not just one climate model but a number of models. I explain why this “ensemble” approach has been adopted—namely, as a means of taking account of uncertainty—and why a comprehensive investigation of uncertainty remains elusive. I then defend a middle ground between two camps in an ongoing debate over the transformation of ensemble results into probabilistic predictions of climate change, highlighting requirements that I refer to as ownership, justification, and robustness.

The biological sciences have become increasingly reliant on so-called ‘model organisms’. I argue that in this domain, the concept of a descriptive model is essential for understanding scientific practice. Using a case study, I show how such a model was formulated in a preexplanatory context for subsequent use as a prototype from which explanations ultimately may be generated both within the immediate domain of the original model and in additional, related domains. To develop this concept of a descriptive model, I focus on use of the nematode worm Caenorhabditis elegans and the wiring diagrams that were developed as models of its neural structure. In addition, implications of the concept of a descriptive model, particularly its relevance for the data-phenomena distinction as well as its relation to long-standing debates on realism, are briefly examined.

For many years—and with some energy since Laudan’s “Confutation of Convergent Realism” (1981)—the scientific realist has sought to accommodate examples of false-yet-successful theories in the history of science. One of the most prominent strategies is to identify ‘success fueling’ components of false theories that themselves are at least approximately true (judging by our current understanding). In this article I develop both sides of the debate, introducing new challenges from the history of science as well as suggesting adjustments to the divide et impera realist strategy. A new ‘recipe’ for the prospective identification of (at least some) working/idle posits is considered.

Recently something close to a consensus about the best way to naturalize the notion of biological function appears to be emerging. Nonetheless, teleological notions in biology remain controversial. In this paper we provide a naturalistic analysis for the notion of natural design. Many authors assume that natural design should be assimilated directly to function. Others find the notion problematic because it suggests that evolution is a directed process. We argue that both of these views are mistaken. Our naturalistic account does not simply equate design with function. We argue that the distinction between function and design is important for understanding the evolution of the physical and behavioral traits of organisms.

The aim of this paper is to describe a methodology for revising logical principles in the light of empirical psychological findings. Historical philosophy of science and wide reflective equilibrium in ethics are considered as providing possible models for arguing from the descriptive to the normative. Neither is adequate for the psychology/logic case, and a new model is constructed, employing criteria for evaluating inferential systems. Once we have such criteria, the notion of reflective equilibrium becomes redundant.

A four dimensional approach to Newtonian physics is used to distinguish between a number of different structures for Newtonian space-time and a number of different formulations of Newtonian gravitational theory. This in turn makes possible an in-depth study of the meaning and status of Newton's Law of Inertia and a detailed comparison of the Newtonian and Einsteinian versions of the Law of Inertia and the Newtonian and Einsteinian treatments of gravitational forces. Various claims about the status of Newton's Law of Inertia are critically examined including these: the Law of Inertia is not an empirical law but a definition; it is not a law simpliciter but a family of schemata; it is a convention and gravitational forces exist only by convention; it is (or is not) redundant; the concepts it embodies can be dispensed with in favor of operationally defined entities; it is unique for a given theory. More generally, the paper demonstrates the importance of space-time structure for the philosophy of space and time and provides support for a realist interpretation of space-time theories.

Current debates about the replication crisis in psychology take it for granted that direct replication is valuable, largely focusing on its role in uncovering questionable statistical practices. This article takes a broader look at the notion of replication in psychological experiments. It is argued that all experimentation/replication involves individuation judgments and that research in experimental psychology frequently turns on probing the adequacy of such judgments. In this vein, I highlight the ubiquity of conceptual and material questions in research, arguing that replication has its place but is not as central to psychological research as it is sometimes taken to be.

According to Marr, a computational-level theory consists of two elements, the what and the why. This article highlights the distinct role of the Why element in the computational analysis of vision. Three theses are advanced: (a) that the Why element plays an explanatory role in computational-level theories, (b) that its goal is to explain why the computed function (specified by the What element) is appropriate for a given visual task, and (c) that the explanation consists in showing that the functional relations between the representing cells are similar to the “external” mathematical relations between the entities that these cells represent.

Formal implication is usually represented by symbolization such as ‘(x) φx ⊃ Ψx,’ which may be read, “for all values of ‘x’, φx (materially) implies Ψx.” If the values of the variable ‘x’, in ‘φx’ and ‘Ψx’ be ‘x1’ ‘x2’ ‘x3’, etc., then … ‘φx’ formally implies ‘Ψx’ if and only if, whatever values of ‘x’, ‘xn’, be chosen, ‘φxn’ materially implies ‘Ψxn’ …

However, this still leaves it doubtful which of two possible interpretations of expressions having the form ‘(x) φx ⊃ Ψx’ is to be taken as correct. … It means one thing to say, “Every existent having the property φ … has also the property Ψ,” and it means quite a different thing to say, “Every thinkable thing which should have the property φ must also have the property Ψ.” The second of these holds only when having the properly φ logically entails having the property Ψ; when ‘Ψx’ is deductible from ‘φx’. … The first of them, however, holds not only in such cases … but also in every case where among existent things, one property is universally accompanied by another. (C. I. Lewis, An Analysis of Knowledge and Evaluation, pp. 217–8. I am responsible for the italicizing of the sentence, otherwise the italics follow Lewis.)

In evolutionary biology changes in population structure are explained by citing trait fitness distribution. I distinguish three interpretations of fitness explanations—the Two-Factor Model, the Single-Factor Model, and the Statistical Interpretation—and argue for the last of these. These interpretations differ in their degrees of causal commitment. The first two hold that trait fitness distribution causes population change. Trait fitness explanations, according to these interpretations, are causal explanations. The last maintains that trait fitness distribution correlates with population change but does not cause it. My defense of the Statistical Interpretation relies on a distinctive feature of causation. Causes conform to the Sure Thing Principle. Trait fitness distributions, I argue, do not.

Since Ramsey, much discussion of the relation between probability and belief has taken for granted that there are degrees of belief, i.e., that there is a real-valued function, B, that characterizes the degree of belief that an agent has in each statement of his language. It is then supposed that B is a probability. It is then often supposed that as the agent accumulates evidence, this function should be updated by conditioning:$B^{E}(\cdot) $ should be$B(\cdot \wedge E) / B(E) $ . Probability is also important in classical statistics, where it is generally supposed that probabilities are frequencies, and that inference proceeds by controlling error and not by conditioning. I will focus on the tension between these two approaches to probability, and in the main part of the paper show where and when Bayesian conditioning conflicts with error based statistics and how to resolve these conflicts.

This is an essay in the Bayesian theory of how opinions should be revised over time. It begins with a discussion of the principle that van Fraassen has dubbed “Reflection”. This principle is not a requirement of rationality; a diachronic Dutch argument, that purports to show the contrary, is fallacious. But under suitable conditions, it is irrational to actually implement shifts in probability that violate Reflection. Conditionalization and probability kinematics are special cases of the principle not to implement shifts that violate Reflection; hence these principles are also requirements of rationality under suitable conditions, though not universal requirements of rationality.

Our aim in this paper is to bring the woefully neglected literature on predictive modeling to bear on some central questions in the philosophy of science. The lesson of this literature is straightforward: For a very wide range of prediction problems, statistical prediction rules (SPRs), often rules that are very easy to implement, make predictions than are as reliable as, and typically more reliable than, human experts. We will argue that the success of SPRs forces us to reconsider our views about what is involved in understanding, explanation, good reasoning, and about how we ought to do philosophy of science.

Halvorson argues that the semantic view of theories leads to absurdities. Glymour shows how to inoculate the semantic view against Halvorson’s criticisms, namely, by making it into a syntactic view of theories. I argue that this modified semantic-syntactic view cannot do the philosophical work that the original “language-free” semantic view was supposed to do.

I maintain that quantum mechanics is fundamentally about a system of N particles evolving in three-dimensional space, not the wave function evolving in 3N-dimensional space.