Bas C. Van Fraassen

This chapter concentrates on isolating criteria of adequacy for any philosophical account of what laws of nature are. Sources include David Hume, Charles Sanders Peirce, Hans Reichenbach, Donald Davidson, David Armstrong, and David Lewis. Criteria examined pertain to universality, necessity, intensionality, explanation, prediction, confirmation, counter‐factuals, objectivity, and inference to the best explanation. Two main problems are presented: the problem of inference (that it is a law that A should imply that A is the case) and the problem of identification (there should be some identifiable aspect of nature that makes for laws). These two problems together constitute a dilemma, since a solution to one tends to pre‐empt any solution to the other.

Basic to the idea of logical probability is the principle of indifference: equal possibilities are to be assigned equal probabilities. This principle appeared on the one hand to yield surprisingly fruitful results and on the other hand to engender paradoxes—the first, for example, in eighteenth‐ century empirical examples (Buffon's needle problem) and cosmological explanations (data concerning planets and comets), and the second, richly displayed by Joseph Bertrand. It is argued here, with reference to work by Henri Poincaré, Edwin Jaynes, Roger Rosencrantz, and others, that though refinable and restrictable in various useful ways, the principle of indifference cannot be salvaged so as to yield a foundation for probability judgements.

Universals accounts of laws of nature begin with a robust anti‐nominalism: there are real properties and relations that are to be distinguished from sets or arbitrary classifications. Those real entities are then drawn on to provide a concept of laws operative in nature. Accounts of this sort here critically examined include those of Fred Dretske, Michael Tooley, and David Armstrong. These accounts display most saliently the impossibility of a simultaneous metaphysical solution to the joint problems of inference and of identification. Special attention is given to the failures of David Armstrong's account of probabilistic laws and of Michael Tooley's concept of probability inspired by Rudolf Carnap's views.

While it was argued earlier in the book that no rule‐governed notion of rational opinion change could be adequate, there are certainly patterns of normal opinion change (updating in response to new data or new constraints accepted in response to experience), which have a rule‐following form. The basic example is Simple Conditionalization (often characterized as the application of Bayes's rule or Bayes's theorem, sometimes called Bayesian Conditionalization, and sometimes accepted as the sole admissible form of opinion change), but more advanced patterns (beginning with Jeffrey Conditionalization) have been described in the literature, as well as challenged there, e.g. by Isaac Levi. The question of what can justify such rules is addressed using symmetry arguments, and the (hidden or explicit) premises of such arguments analysed. Probability kinematics, as formulated initially by Richard Jeffrey, is the general theory of rules for changing a (‘prior’) probability function, subject to given or imposed constraints, into a new (‘updated’, ‘posterior’) function. Such constraints can take various forms, and the rules offered for them can be limited by symmetry considerations but may not be uniquely determined.

According to Lewis's original account, the laws of nature in a given possible world are the principles of the best scientific theory of that world, where ‘best’ denotes an optimal combination of strength and simplicity. This serves to provide content to a notion of physical necessity, but needed to be qualified with a restriction of such possible descriptions to languages whose predicates have a special status (in the simplest case, that of standing for ‘natural’ classes of entities in that world). Lewis provides an anti‐nominalist metaphysics, while staying as close as possible to the nominalist preferences that had characterized e.g. Quine's philosophical work. This Chapter argues that his account is at best deceptively successful, and solves the problem of inference at the cost of an inability to address the problem of identification.

The underground river of probabilism, slowly growing in force over three centuries, burst forth above ground in the twentieth century and brought new hope for epistemology. Probabilism sees its historical origin in the work of Blaise Pascal in the seventeenth century, but has for the main part been developed in the last 100 years, notably by Leonard Savage, Rudolf Carnap, Bruno De Finetti, Isaac Levi, Richard Jeffrey, and many other writers on the interface of statistics, probability theory, and epistemology. This chapter provides a liberal version of probabilism, as basic framework for descriptive epistemology. Benefits include proofs of the incoherence of Inference to the Best Explanation and related ideas pertaining to Induction or, in general, to rule‐governed notions of rational opinion change. It is argued that this is not a form of scepticism and does provide a basis for an empiricist epistemology adequate for philosophy of science.

This chapter concentrates on philosophical theories of laws of nature that take for granted certain concepts of possibility, possible worlds, necessity, or physical probability. The accounts of Wilfrid Sellars, Storrs McCall, Peter Vallentyne, and Robert Pargetter are criticized. Crucial to any such account that draws on a notion of objective chance or probability is the ’horizontal‐vertical problem’ (of accounting for statistical predictions based on assumptions about chance). It is argued that if the metaphysical point of view is maintained, then this problem is unsolvable.

An initial introduction to the semantic approach to science, this chapter provides a view of scientific theories in terms of classes of models and their relation to the phenomena. The main tasks of philosophy of science can be carried out within the framework of this approach without drawing on any metaphysical notions or principles. A specific problem examined here (which introduces a change from the author's previous book _The Scientific Image_) is how to characterize acceptance of a probabilistic theory. Probabilities in certain contemporary physical theories are irreducible and thus purport to stand for physical aspects of nature. But on and empiricist view, acceptance of such a theory does not need to involve belief in the reality of such objective chances. This problem is solved in an extension of the probabilist epistemology of the previous chapter.

This approach, developed (under various names) in the twentieth century provides a model‐oriented view, identifying scientific theories in terms of classes of models and their relation to both nature and to the observable phenomena. Originally, it was offered in reaction to the syntactic, axiomatic view of theories that dominated logical positivist discussions of science; it has the merit of being equally hospitable to scientific realist and empiricist views. This chapter discusses specifically, theory structure, the relation between theoretical models and data models, interpretations of theories, and the many‐faceted character of experimentation.

Von Neumann's unification of Schroedinger's and Heisenberg's formalisms came with an interpretation of quantum theory involving two principles. The first is that assertions about the values of observables are equivalent to assertions about the quantum‐mechanical state of the system. This is sometimes known as the ’eigenvalue–eigenstate link’, since it equates an observable having a value with the system being in an eigenstate of that observable. The second is his Projection Postulate—i.e. the postulate that during measurement there is a ’collapse of the wave packet’. It is argued that the theory does not force these principles on us, and that there are severe difficulties in this interpretation, despite also its more recent defences.

The world of quantum theory is not deterministic; however, the quantum theory of an isolated system describes its state as evolving deterministically.How can these two points be reconciled? The modal interpretation (of which a number of variants have been developed) answers this as follows. An observable may have a value even if the system is not in the corresponding eigenstate of that observable. The state of the system only constrains the possible values the observable can have, and (at least under certain conditions) the probabilities that it has those values. Hence, the eigenvalue–eigenstate link is violated. There is no collapse; the state of an isolated system always evolves in accordance with the Schroedinger equation. Hence the values of observables can change indeterministically, though this stochastic process is constrained by the deterministically evolving quantum state. Terminology varies but in this book the quantum state is then called the dynamical state, and a summary of the values of the observables pertaining to the system is called the value state. Since not all observables are mutually compatible, they will not all have simultaneous sharp values, but for each there is a minimum Borel set of values as its current range. The specific modal interpretation developed here is the Copenhagen Variant of the Modal Interpretation, which places holistic constraints on values of observables pertaining to parts of composite systems.

Do the properties of a compound or aggregate supervene on the properties of its parts? Theories that imply a negative answer (or the states they attribute) are called ’holistic’. Besides the EPR paradox, Pauli's Exclusion Principle and quantum statistics (for aggregates of identical bosons or fermions) are all generally cited as establishing the holism of quantum theory. It has been conjectured both that the principle of Permutation Invariance accounts for the departures from classical statistics, and that if ’identical’ in ’aggregate of identical particles’ is properly understood, then it entails Permutation Invariance tautologically. It has also been thought that there can be a proof within elementary (non‐relativistic) quantum mechanics of the principle of Dichotomy, i.e. that only Bose and Fermi statistics, and not intermediate non‐classical ’para‐statistics’ can apply. All three conjectures are contested in this chapter and the next. This chapter is devoted to an exposition of the quantum theoretical foundations for this subject, with implications for limits to interpretation of the theory.

No common cause model can fit the phenomena that violate Bell's Inequalities; what sorts of probability models could do so? To answer this, we need to broaden our concept of statistical or probability models, while not broadening it so much as to trivialize it. Introduced here are the distinctions between a surface (phenomenal) model and a theoretical model, and between the general class of geometric probability models and their subclass of quantum theoretical models, together with some elements of quantum logic, and the basic use of probability models to represent measurement situations.

This chapter aims to place the discussion of holism in quantum theory generally and of the problem of identical particles and quantum statistics specifically in the context of general philosophy. Various debates in metaphysics, both historical and current, broach related subjects and involve analyses of concepts currently used in the philosophy of quantum mechanics. These include concepts of identity, individuation, essence, form, necessity, possibility, modality, contingency, and universality. But this chapter also extends the previous one by introducing Fock space and the transition from elementary quantum mechanics to quantum field theory via 'second quantization’. For this formalism relates clearly to certain ’anti‐essentialist’ approaches in the metaphysics of modality. Finally, in keeping with the empiricism pursued in this book, the general enterprise of metaphysics pertaining to those topics is viewed here within an anti‐metaphysical stance, as having as its value the display of a plurality of interpretations whose very diversity enhances our understanding of the theory.

If the world is not deterministic, then at the very least, some individual events just happen ’by chance’. But the frequency of such events and correlations between them could be subject to constraints, whether local or non‐local. Hans Reichenbach introduced a principle weaker than determinism but non‐trivial: that every positive correlation should be traceable to a common cause (defined in terms of temporal precedence plus certain probabilistic relations). This principle turns out to imply the Bell Inequalities, which quantum theory violates. This chapter discusses the logical relations between indeterminism, common cause models, the Bell Inequalities, non‐contextual hidden variable models, and various concepts of locality and non‐locality, as well as the experiments designed to reveal the predicted violations.

Pure indeterminism is simply the denial of determinism; a theory may augment this with models in which the uncertain events have definite probabilities. De Finetti's representation theorem, which pertains to permutation symmetry, and ergodic theory (for abstract dynamical systems) provide illustrations of classical probabilistic theories. A number of features generally discussed in connection with quantum mechanics are already found in classical probability models. These include symmetry constraints and a general form for dynamical equations (analogous to Schroedinger's equation) as well as the sort of holism involved in ’non‐local’ correlations.

The Einstein–Podolsky–Rosen argument against the completeness of quantum mechanics (‘EPR paradox’) is intimately related to no‐hidden‐variable theorems and to the limited options for interpretation with respect to incompatible observables. The argument is analysed, and its connection to John Bell's derivation of the Bell Inequalities examined. The predictions of statistical correlation are subject to empirical tests; once confirmed, the question of interpretation pertains to the possibility of correlations between spatially separated events in the absence of deterministic ’preprogramming’ or common causes. Topics include Schroedinger's 'spooky action at a distance’ and the supposition that there can be a ’Bell telephone’ to exploit those predicted correlations for instantaneous communication.

The controversy between scientific realism and empiricism can be set aside during the common task of interpreting the theories of modern science. But this book is written within the semantic approach to science, which identifies theories in terms of classes of models and their relation to the phenomena. While this provides the two main ingredients for any view of science, these do not determine but only constrain the interpretation of those theories (‘science as open text’, admitting a plurality of interpretations).