I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects living in infinite-dimensional spaces, working through many examples from cosmology. I focus on the relation of topological to measure-theoretic notions of and relating to probability, how they diverge in unpleasant ways in the infinite-dimensional case, and are even difficult to work with on their own. Even in cases where an appropriate family of spacetimes (...) is finite-dimensional, and so admits a measure of the relevant sort, however, it is always the case that the family is not a compact topological space, and so does not admit a physically significant, well behaved probability measure. Problems of a different but still deeply troubling sort plague arguments about likelihood in that context, which I also discuss. I conclude that most standard forms of argument used in cosmology to estimate the likelihood of the occurrence of various properties or behaviors of spacetimes have serious mathematical, physical and conceptual problems. (shrink)

One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question of whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is yes: (...) I state and sketch proofs of two technical results—inspired by simple physical arguments about the generic properties of classical systems—to the effect that, in a precise sense, classical systems evince exactly the geometric structure Lagrangian mechanics provides for the representation of systems, and none provided by Hamiltonian. The argument not only clarifies the conceptual structure of the two systems of mechanics, but also their relations to each other and their respective mechanisms for representing physical systems. It also shows why naïvely structural approaches to the representational content of physical theories cannot work. [Lagrange] grasped that he had gained a method of stating dynamical truths in a way, which is perfectly indifferent to the particular methods of measurement employed in fixing the positions of the various parts of the system. Accordingly, he went on to deduce equations of motion, which are equally applicable whatever quantitative measurements have been made, provided that they are adequate to fix positions. The beauty and almost divine simplicity of these equations is such that these formulae are worthy to rank with those mysterious symbols which in ancient times were held directly to indicate the Supreme Reason at the base of all things. (Whitehead [1948], p. 63)1. Introduction2.Classical Systems3. The Possible Interactions of a Classical System and the Structure of Its Space of States4. Classical Systems Are Lagrangian5. Classical Systems Are Not Hamiltonian6. How Lagrangian and Hamiltonian Mechanics Represent Classical Systems7. The Conceptual Structure of Classical Mechanics. (shrink)

The incredible achievements of modern scientific theories lead most of us to embrace scientific realism: the view that our best theories offer us at least roughly accurate descriptions of otherwise inaccessible parts of the world like genes, atoms, and the big bang. In Exceeding Our Grasp, Stanford argues that careful attention to the history of scientific investigation invites a challenge to this view that is not well represented in contemporary debates about the nature of the scientific enterprise. The historical record (...) of scientific inquiry, Stanford suggests, is characterized by what he calls the problem of unconceived alternatives. Past scientists have routinely failed even to conceive of alternatives to their own theories and lines of theoretical investigation, alternatives that were both well-confirmed by the evidence available at the time and sufficiently serious as to be ultimately accepted by later scientific communities. Stanford supports this claim with a detailed investigation of the mid-to-late 19th century theories of inheritance and generation proposed in turn by Charles Darwin, Francis Galton, and August Weismann. He goes on to argue that this historical pattern strongly suggests that there are equally well-confirmed and scientifically serious alternatives to our own best theories that remain currently unconceived. Moreover, this challenge is more serious than those rooted in either the so-called pessimistic induction or the underdetermination of theories by evidence, in part because existing realist responses to these latter challenges offer no relief from the problem of unconceived alternatives itself. Stanford concludes by investigating what positive account of the spectacularly successful edifice of modern theoretical science remains open to us if we accept that our best scientific theories are powerful conceptual tools for accomplishing our practical goals, but abandon the view that the descriptions of the world around us that they offer are therefore even probably or approximately true. (shrink)

Thomas S. Kuhn's classic book is now available with a new index.

We propose an "explanation scheme" for why the Gibbs phase average technique in classical equilibrium statistical mechanics works. Our account emphasizes the importance of the Khinchin-Lanford dispersion theorems. We suggest that ergodicity does play a role, but not the one usually assigned to it.

Two chief problems of the theory of knowledge are the question of meaning and the question of verification. The first question asks under what conditions a sentence has meaning, in the sense of cognitive, factual meaning. The second one asks how we get to know something, how we can find out whether a given sentence is true or false. The second question presupposes the first one. Obviously we must understand a sentence, i.e. we must know its meaning, before we can (...) try to find out whether it is true or not. But, from the point of view of empiricism, there is a still closer connection between the two problems. In a certain sense, there is only one answer to the two questions. If we knew what it would be for a given sentence to be found true then we would know what its meaning is. And if for two sentences the conditions under which we would have to take them as true are the same, then they have the same meaning. Thus the meaning of a sentence is in a certain sense identical with the way we determine its truth or falsehood; and a sentence has meaning only if such a determination is possible. (shrink)

Hierarchical Bayesian models (HBMs) provide an account of Bayesian inference in a hierarchically structured hypothesis space. Scientific theories are plausibly regarded as organized into hierarchies in many cases, with higher levels sometimes called ‘paradigms’ and lower levels encoding more specific or concrete hypotheses. Therefore, HBMs provide a useful model for scientific theory change, showing how higher‐level theory change may be driven by the impact of evidence on lower levels. HBMs capture features described in the Kuhnian tradition, particularly the idea that (...) higher‐level theories guide learning at lower levels. In addition, they help resolve certain issues for Bayesians, such as scientific preference for simplicity and the problem of new theories. *Received July 2009; revised October 2009. †To contact the authors, please write to: Leah Henderson, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 32D‐808, Cambridge, MA 02139; e‐mail: [email protected]. (shrink)

Two of the most influential theories about scientific inference are inference to the best explanation and Bayesianism. How are they related? Bas van Fraassen has claimed that IBE and Bayesianism are incompatible rival theories, as any probabilistic version of IBE would violate Bayesian conditionalization. In response, several authors have defended the view that IBE is compatible with Bayesian updating. They claim that the explanatory considerations in IBE are taken into account by the Bayesian because the Bayesian either does or should (...) make use of them in assigning probabilities to hypotheses. I argue that van Fraassen has not succeeded in establishing that IBE and Bayesianism are incompatible, but that the existing compatibilist response is also not satisfactory. I suggest that a more promising approach to the problem is to investigate whether explanatory considerations are taken into account by a Bayesian who assigns priors and likelihoods on his or her own terms. In this case, IBE would emerge from the Bayesian account, rather than being used to constrain priors and likelihoods. I provide a detailed discussion of the case of how the Copernican and Ptolemaic theories explain retrograde motion, and suggest that one of the key explanatory considerations is the extent to which the explanation a theory provides depends on its core elements rather than on auxiliary hypotheses. I then suggest that this type of consideration is reflected in the Bayesian likelihood, given priors that a Bayesian might be inclined to adopt even without explicit guidance by IBE. The aim is to show that IBE and Bayesianism may be compatible, not because they can be amalgamated, but rather because they capture substantially similar epistemic considerations. 1 Introduction2 Preliminaries3 Inference to the Best Explanation4 Bayesianism5 The Incompatibilist View : Inference to the Best Explanation Contradicts Bayesianism5. 1 Criticism of the incompatibilist view6 Constraint - Based Compatibilism6. 1 Criticism of constraint - based compatibilism7 Emergent Compatibilism7. 1 Analysis of inference to the best explanation7. 1. 1 Inference to the best explanation on specific hypotheses7. 1. 2 Inference to the best explanation on general theories7. 1. 3 Copernicus versus Ptolemy7. 1. 4 Explanatory virtues7. 1. 5 Summary7. 2 Bayesian account8 Conclusion. (shrink)

My purpose in this chapter is to survey some of the principal approaches to inductive inference in the philosophy of science literature. My first concern will be the general principles that underlie the many accounts of induction in this literature. When these accounts are considered in isolation, as is more commonly the case, it is easy to overlook that virtually all accounts depend on one of very few basic principles and that the proliferation of accounts can be understood as efforts (...) to ameliorate the weaknesses of those few principles. In the earlier sections, I will lay out three inductive principles and the families of accounts of induction they engender. In later sections I will review standard problems in the philosophical literature that have supported some pessimism about induction and suggest that their import has been greatly overrated. In the final sections I will return to the proliferation of accounts of induction that frustrates efforts at a final codification. I will suggest that this proliferation appears troublesome only as long as we expect inductive inference to be subsumed under a single formal theory. If we adopt a material theory of induction in which individual inductions are licensed by particular facts that prevail only in local domains, then the proliferation is expected and not problematic. (shrink)

Every physical theory has two different forms of mathematical equations to represent its target systems: the dynamical and the kinematical. Kinematical constraints are differentiated from equations of motion by the fact that their particular form is fixed once and for all, irrespective of the interactions the system enters into. By contrast, the particular form of a system's equations of motion depends essentially on the particular interaction the system enters into. All contemporary accounts of the structure and semantics of physical theory (...) treat dynamics, i.e., the equations of motion, as the most important feature of a theory for the purposes of its philosophical analysis. I argue to the contrary that it is the kinematical constraints that determine the structure and empirical content of a physical theory in the most important ways: they function as necessary preconditions for the appropriate application of the theory; they differentiate types of physical systems; they are necessary for the equations of motion to be well posed or even just cogent; and they guide the experimentalist in the design of tools for measurement and observation. It is thus satisfaction of the kinematical constraints that renders meaning to those terms representing a system's physical quantities in the first place, even before one can ask whether or not the system satisfies the theory's equations of motion. (shrink)

I argue that an adequate semantics for physical theories must be grounded on an account of the way that a theory provides formal and conceptual resources appropriate for---that have propriety in---the construction of representations of the physical systems the theory purports to treat. I sketch a precise, rigorous definition of the required forms of propriety, and argue that semantic content accrues to scientific representations of physical systems primarily in virtue of the propriety of its resources. In particular, neither the adequacy (...) of those representations nor any referential relations their terms may enter into play any fundamental role in the determination of the representation's semantic content. One consequence is that anything like traditional Tarskian semantics is inadequate for the task. (shrink)

This paper examines Newton's argument from the phenomena to the law of universal gravitation-especially the question how such a result could have been obtained from the evidential base on which that argument rests. Its thesis is that the crucial step was a certain application of the third law of motion-one that could only be justified by appeal to the consequences of the resulting theory; and that the general concept of interaction embodied in Newton's use of the third law most probably (...) evolved in the course of the very investigation that led to this theory. (shrink)

The philosophy of science has lost its self-confidence, witness the lack of advanced textbooks in contrast to the abundance of elementary textbooks. Structures in Science is an advanced textbook that explicates, updates, accommodates, and integrates the best insights of logical-empiricism and its main critics. This `neo-classical approach' aims at providing heuristic patterns for research. The book introduces four ideal types of research programs and reanimates the distinction between observational laws and proper theories. It explicates various patterns of explanation by subsumption (...) and specification as well as structures in reductive and other types of interlevel research. Its analysis of theory evaluation leads to new characterizations of confirmation, empirical progress, and pseudoscience. Partial analogies between progress in nomological research and progress in explicative and design research emerge. Finally, special chapters are devoted to design research programs, computational philosophy of science, the structuralist approach to theories, and research ethics. (shrink)