Supervenience, Logic, and Empirical Content: Commentary on Hans Halvorson, The Logic in Philosophy of Science

Halvorson’s book’s real achievement is that it is both a source and a challenge, and not just for philosophers of science. I will begin with some notes to add to Halvorson’s discussion of supervenience and definability. Then secondly I will engage the book’s way of dealing with empirical content. Extension of formal methods to the relation of theory to world, as mediated by experiment and measurement, seems to me crucial to its value, and I will make three suggestions for this. Then thirdly I will turn to the tantalizing hints Halvorson gives us of an overall view of logic and language, and speculate about how that would answer questions about scientific representation and more specifically about the object language / metalanguage relation

Supervenience, Logic, and Empirical Content: Commentary on Hans Halvorson, The Logic in Philosophy of Science

Halvorson’s book’s real achievement is that it is both a source and a challenge, and not just for philosophers of science. I will begin with some notes to add to Halvorson’s discussion of supervenience and definability. Then secondly I will engage the book’s way of dealing with empirical content. Extension of formal methods to the relation of theory to world, as mediated by experiment and measurement, seems to me crucial to its value, and I will make three suggestions for this. Then thirdly I will turn to the tantalizing hints Halvorson gives us of an overall view of logic and language, and speculate about how that would answer questions about scientific representation and more specifically about the object language / metalanguage relation

Appearance vs. Reality as a Scientific Problem

The history of science is replete with ideals that involve some criterion of completeness. One such criterion requires that physics explain how the appearances are produced in reality. This paper argues that it is scientifically acceptable to reject this criterion, along with all other completeness criteria that have been proposed for modern science

Bohrification of operator algebras and quantum logic

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families of projections indexed by a partially ordered set C(A) of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that C(A) consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Heyting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n-by-n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski-Mulvey) of the "Bohrification" of A, which is a commutative Rickart C*-algebra in the topos of functors from C(A) to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns-Lakser completions. Finally, we establish a connection between probability measure on the lattice of projections on a Hilbert space H and probability valuations on the internal Gelfand spectrum of A for A = B(H).Comment: 31 page

Explanatory pluralism in the medical sciences: theory and practice

Explanatory pluralism is the view that the best form and level of explanation depends on the kind of question one seeks to answer by the explanation, and that in order to answer all questions in the best way possible, we need more than one form and level of explanation. In the first part of this article, we argue that explanatory pluralism holds for the medical sciences, at least in theory. However, in the second part of the article we show that medical research and practice is actually not fully and truly explanatory pluralist yet. Although the literature demonstrates a slowly growing interest in non-reductive explanations in medicine, the dominant approach in medicine is still methodologically reductionist. This implies that non-reductive explanations often do not get the attention they deserve. We argue that the field of medicine could benefit greatly by reconsidering its reductive tendencies and becoming fully and truly explanatory pluralist. Nonetheless, trying to achieve the right balance in the search for and application of reductive and non-reductive explanations will in any case be a difficult exercise

Causation, complexity, and the concert: the pragmatics of causal explanation in international relations

A causal explanation provides information about the causal history of whatever is being explained. However, most causal histories extend back almost infinitely and can be described in almost infinite detail. Causal explanations therefore involve choices about which elements of causal histories to pick out. These choices are pragmatic: they reflect our explanatory interests. When adjudicating between competing causal explanations, we must therefore consider not only questions of epistemic adequacy (whether we have good grounds for identifying certain factors as causes) but also questions of pragmatic adequacy (whether the aspects of the causal history picked out are salient to our explanatory interests). Recognizing that causal explanations differ pragmatically as well as epistemically is crucial for identifying what is at stake in competing explanations of the relative peacefulness of the nineteenth-century Concert system. It is also crucial for understanding how explanations of past events can inform policy prescription