A fundamental tenet of Paul Feyerabend’s pluralistic view of science has it that theory proliferation, that is, the availability of theoretical alternatives, is of crucial importance for the detection of anomalies in established theories. Paul Hoyningen-Huene calls this the Anomaly Importation Thesis, according to which anomalies are imported, as it were, into well-established theories from competing alternatives. This article pursues two major objectives: (a) to work out the systematic details of Feyerabend’s ideas on theory proliferation and anomaly import as they (...) are presented in his early publications and his Against Method and (b) to compare Feyerabend’s ideas on theory proliferation and anomaly import with corresponding features in Popper’s critical rationalist philosophy of science. As it turns out, neither the Principle of Proliferation nor the Anomaly Importation Thesis are necessarily incompatible with critical rationalism. In spite of Feyerabend’s general anti-Popperian attitude, I argue that theoretical pluralism can be seen as an advancement of the critical rationalist philosophy and that critical rationalism provides good arguments for pluralism. (shrink)

1.1 Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Tangent Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (...) . . . . . . . . . . . 7 1.3 Vector Fields, Integral Curves, and Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Tensors and Tensor Fields on Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.5 The Action of Smooth Maps on Tensor Fields . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.6 Lie Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.7 Derivative Operators and Geodesics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 1.8 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 1.9 Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 1.10 Hypersurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 1.11 Volume Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96.. (shrink)

An energy condition, in the context of a wide class of spacetime theories, is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be positive". The remarkable fact I will discuss in this paper is that such simple, general, almost trivial seeming propositions have profound and far-reaching import for our understanding of the structure of relativistic spacetimes. It is therefore especially surprising when one also learns that (...) we have no clear understanding of the nature of these conditions, what theoretical status they have with respect to fundamental physics, what epistemic status they may have, when we should and should not expect them to be satisfied, and even in many cases how they and their consequences should be interpreted physically. Or so I shall argue, by a detailed analysis of the technical and conceptual character of all the standard conditions used in physics today, including examination of their consequences and the circumstances in which they are believed to be violated. (shrink)

This paper investigates the historical origins of the notion of incommensurability in contemporary philosophy of science. The aim is not to establish claims of priority, but to enhance our understanding of the notion by illuminating the various issues that contributed to its development. Kuhn developed his notion of incommensurability primarily under the influence of Fleck, Polanyi, and Köhler. Feyerabend, who had developed his notion more than a decade earlier, drew directly from Duhem, who had developed a notion of incommensurability in (...) 1906. The idea is that in the course of scientific advance, when fundamental theories change, meanings change, which can result in a new conception of the nature of reality. Feyerabend repeatedly used this notion of incommensurability to attack various forms of conceptual conservativism. These include the logical positivists’ foundational use of protocol statements, Heisenberg’s methodological principle that established results must be presupposed by all further research, attempts to separate philosophical accounts of ontology from physics, Bohr’s principle of complementarity, and logical empiricist accounts of reduction and explanation. Focusing on the function of the notion of incommensurability common to Feyerabend’s various critiques explicates Feyerabend’s early philosophy as a series of challenges to forms of conceptual conservativism.Keywords: Incommensurability ; Paul Feyerabend; Thomas Kuhn; Pierre Duhem; Wolfgang Köhler; Ludwik Fleck. (shrink)

This paper investigates the historical origins of the notion of incommensurability in contemporary philosophy of science. The aim is not to establish claims of priority, but to enhance our understanding of the notion by illuminating the various issues that contributed to its development. Kuhn developed his notion of incommensurability primarily under the influence of Fleck, Polanyi, and Köhler. Feyerabend, who had developed his notion more than a decade earlier, drew directly from Duhem, who had developed a notion of incommensurability in (...) 1906. The idea is that in the course of scientific advance, when fundamental theories change, meanings change, which can result in a new conception of the nature of reality. Feyerabend repeatedly used this notion of incommensurability to attack various forms of conceptual conservativism. These include the logical positivists’ foundational use of protocol statements, Heisenberg’s methodological principle that established results must be presupposed by all further research, attempts to separate philosophical accounts of ontology from physics, Bohr’s principle of complementarity, and logical empiricist accounts of reduction and explanation. Focusing on the function of the notion of incommensurability common to Feyerabend’s various critiques explicates Feyerabend’s early philosophy as a series of challenges to forms of conceptual conservativism.Keywords: Incommensurability; Paul Feyerabend; Thomas Kuhn; Pierre Duhem; Wolfgang Köhler; Ludwik Fleck. (shrink)

Cosmologists often use certain global properties to exclude "physically unreasonable" cosmological models from serious consideration. But, on what grounds should these properties be regarded as "physically unreasonable" if we cannot rule out, even with a robust type of inductive reasoning, the possibility of the properties obtaining in our own universe?

It has been argued that spacetime must be inextendible – that it must be “as large as it can be” in some sense. Here, we register some skepticism with respect to this position.

In this note, we cast doubt on the requirement of spacetime inextendibility; it is not at all clear that our universe is “as large as it can be.”.

Here, we briefly review the notion of observational indistinguishability within the context of classical general relativity. We settle a conjecture given by Malament (1977) concerning the subject and then strengthen the result considerably. The upshot is this: There seems to be a robust sense in which the global structure of every cosmological model is underdetermined.

I suggest following Paul Feyerabend's own advice, and interpreting Feyerabend's work in light of the principles laid out by John Stuart Mill. A review of Mill's essay, On Liberty, emphasizes the importance Mill placed on open and critical discussion for the vitality and progress of various aspects of human life, including the pursuit of scientific knowledge. Many of Feyerabend's more unusual stances, I suggest, are best interpreted as attempts to play certain roles--especially the role of "defender of unpopular minority opinion"--that (...) are necessary to fulfilling Mill's conditions for rational exchange and optimal human development. (shrink)

This exploration of the global structure of spacetime within the context of general relativity examines the causal and singular structures of spacetime, revealing some of the curious possibilities that are compatible with the theory, such as `time travel' and `holes' of various types. Investigations into the epistemic and modal structures of spacetime highlight the difficulties in ruling out such possibilities, unlikely as they may seem at first. The upshot seems to be that what counts as a `physically reasonable' spacetime structure (...) in modern physics is far from clear. (shrink)