That quantum mechanical measurement processes are indeterministic is widely known. The time evolution governed by the differential Schrödinger equation can also be indeterministic under the extreme conditions of a quantum supertask, the quantum analogue of a classical supertask. Determinism can be restored by requiring normalizability of the supertask state vector, but it must be imposed as an additional constraint on the differential Schrödinger equation.

Modern readers turning to Einstein’s famous 1905 paper on special relativity may not find what they expect. Its title, “On the electrodynamics of moving bodies,” gives no inkling that it will develop an account of space and time that will topple Newton’s system. Even its first paragraph just calls to mind an elementary experimental result due to Faraday concerning the interaction of a magnet and conductor. Only then does Einstein get down to the business of space and time and lay (...) out a new theory in which rapidly moving rods shrink and clocks slow and the speed of light becomes an impassable barrier. This special theory of relativity has a central place in modern physics. As the first of the modern theories, it provides the foundation for particle physics and for Einstein’s general theory of relativity; and it is the last point of agreement between them. It has also received considerable attention outside physics. It is the first port of call for philosophers and other thinkers, seeking to understand what Einstein did and why it changed everything. It is often also their last port. The theory is arresting enough to demand serious reflection and, unlike quantum theory and general relativity, its essential content can be grasped fully by someone merely with a command of simple algebra. It contains Einstein’s analysis of simultaneity, probably the most celebrated conceptual analysis of the century. (shrink)

I deny that the world is fundamentally causal, deriving the skepticism on non-Humean grounds from our enduring failures to find a contingent, universal principle of causality that holds true of our science. I explain the prevalence and fertility of causal notions in science by arguing that a causal character for many sciences can be recovered, when they are restricted to appropriately hospitable domains. There they conform to a loose collection of causal notions that form a folk science of causation. This (...) recovery of causation exploits the same generative power of reduction relations that allows us to recover gravity as a force from Einstein's general relativity and heat as a conserved fluid, the caloric, from modern thermal physics, when each theory is restricted to appropriate domains. Causes are real in science to the same degree as caloric and gravitational forces. (shrink)

Contrary to formal theories of induction, I argue that there are no universal inductive inference schemas. The inductive inferences of science are grounded in matters of fact that hold only in particular domains, so that all inductive inference is local. Some are so localized as to defy familiar characterization. Since inductive inference schemas are underwritten by facts, we can assess and control the inductive risk taken in an induction by investigating the warrant for its underwriting facts. In learning more facts, (...) we extend our inductive reach by supplying more localized inductive inference schemes. Since a material theory no longer separates the factual and schematic parts of an induction, it proves not to be vulnerable to Hume's problem of the justification of induction. (shrink)

Eliminative induction is a method for finding the truth by using evidence to eliminate false competitors. It is often characterized as "induction by means of deduction"; the accumulating evidence eliminates false hypotheses by logically contradicting them, while the true hypothesis logically entails the evidence, or at least remains logically consistent with it. If enough evidence is available to eliminate all but the most implausible competitors of a hypothesis, then (and only then) will the hypothesis become highly confirmed. I will argue (...) that, with regard to the evaluation of hypotheses, Bayesian inductive inference is essentially a probabilistic form of induction by elimination. Bayesian induction is an extension of eliminativism to cases where, rather than contradict the evidence, false hypotheses imply that the evidence is very unlikely, much less likely than the evidence would be if some competing hypothesis were true. This is not, I think, how Bayesian induction is usually understood. The recent book by Howson and Urbach, for example, provides an excellent, comprehensive explanation and defense of the Bayesian approach; but this book scarcely remarks on Bayesian induction's eliminative nature. Nevertheless, the very essence of Bayesian induction is the refutation of false competitors of a true hypothesis, or so I will argue. (shrink)

Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

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)

The epistemic state of complete ignorance is not a probability distribution. In it, we assign the same, unique, ignorance degree of belief to any contingent outcome and each of its contingent, disjunctive parts. That this is the appropriate way to represent complete ignorance is established by two instruments, each individually strong enough to identify this state. They are the principle of indifference (PI) and the notion that ignorance is invariant under certain redescriptions of the outcome space, here developed into the (...) ‘principle of invariance of ignorance' (PII). Both instruments are so innocuous as almost to be platitudes. Yet the literature in probabilistic epistemology has misdiagnosed them as paradoxical or defective since they generate inconsistencies when conjoined with the assumption that an epistemic state must be a probability distribution. To underscore the need to drop this assumption, I express PII in its most defensible form as relating symmetric descriptions and show that paradoxes still arise if we assume the ignorance state to be a probability distribution. *Received February 2007; revised July 2007. †To contact the author, please write to: Department of History and Philosophy of Science, University of Pittsburgh, Pittsburgh, PA 15260; e-mail: [email protected]. (shrink)

I deny that the world is fundamentally causal, deriving the skepticism on non-Humean grounds from our enduring failures to find a contingent, universal principle of causality that holds true of our science. I explain the prevalence and fertility of causal notions in science by arguing that a causal character for many sciences can be recovered, when they are restricted to appropriately hospitable domains. There they conform to loose and varying collections of causal notions that form folk sciences of causation. This (...) recovery of causation exploits the same generative power of reduction relations that allows us to recover gravity as a force from Einstein's general relativity and heat as a conserved fluid, the caloric, from modern thermal physics, when each theory is restricted to appropriate domains. Causes are real in science to the same degree as caloric and gravitational forces. (shrink)

Supertasks recently discussed in the literature purport to display a failure ofenergy conservation and determinism in Newtonian mechanics. We debatewhether these supertasks are admissible as Newtonian systems, with Earmanand Norton defending the affirmative and Alper and Bridger the negative.