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

Many worlds and modality in the interpretation of quantum mechanics: an algebraic approach

Many worlds interpretations (MWI) of quantum mechanics avoid the measurement problem by considering every term in the quantum superposition as actual. A seemingly opposed solution is proposed by modal interpretations (MI) which state that quantum mechanics does not provide an account of what `actually is the case', but rather deals with what `might be the case', i.e. with possibilities. In this paper we provide an algebraic framework which allows us to analyze in depth the modal aspects of MWI. Within our general formal scheme we also provide a formal comparison between MWI and MI, in particular, we provide a formal understanding of why --even though both interpretations share the same formal structure-- MI fall pray of Kochen-Specker (KS) type contradictions while MWI escape them.Comment: submitted to the Journal of Mathematical Physic

Correlations, deviations and expectations: the Extended Principle of the Common Cause

The Principle of the Common Cause is usually understood to provide causal explanations for probabilistic correlations obtaining between causally unrelated events. In this study, an extended interpretation of the principle is proposed, according to which common causes should be invoked to explain positive correlations whose values depart from the ones that one would expect to obtain in accordance to her probabilistic expectations. In addition, a probabilistic model for common causes is tailored which satisfies the generalized version of the principle, at the same time including the standard conjunctive-fork model as a special case

A Topological Study of Contextuality and Modality in Quantum Mechanics

Kochen-Specker theorem rules out the non-contextual assignment of values to physical magnitudes. Here we enrich the usual orthomodular structure of quantum mechanical propositions with modal operators. This enlargement allows to refer consistently to actual and possible properties of the system. By means of a topological argument, more precisely in terms of the existence of sections of sheaves, we give an extended version of Kochen-Specker theorem over this new structure. This allows us to prove that contextuality remains a central feature even in the enriched propositional system.Comment: 10 pages, no figures, submitted to I. J. Th. Phy

Bayesian Conditioning, the Reflection Principle, and Quantum Decoherence

The probabilities a Bayesian agent assigns to a set of events typically change with time, for instance when the agent updates them in the light of new data. In this paper we address the question of how an agent's probabilities at different times are constrained by Dutch-book coherence. We review and attempt to clarify the argument that, although an agent is not forced by coherence to use the usual Bayesian conditioning rule to update his probabilities, coherence does require the agent's probabilities to satisfy van Fraassen's [1984] reflection principle (which entails a related constraint pointed out by Goldstein [1983]). We then exhibit the specialized assumption needed to recover Bayesian conditioning from an analogous reflection-style consideration. Bringing the argument to the context of quantum measurement theory, we show that "quantum decoherence" can be understood in purely personalist terms---quantum decoherence (as supposed in a von Neumann chain) is not a physical process at all, but an application of the reflection principle. From this point of view, the decoherence theory of Zeh, Zurek, and others as a story of quantum measurement has the plot turned exactly backward.Comment: 14 pages, written in memory of Itamar Pitowsk

A geometric proof of the Kochen-Specker no-go theorem

We give a short geometric proof of the Kochen-Specker no-go theorem for non-contextual hidden variables models. Note added to this version: I understand from Jan-Aake Larsson that the construction we give here actually contains the original Kochen-Specker construction as well as many others (Bell, Conway and Kochen, Schuette, perhaps also Peres).Comment: This paper appeared some years ago, before the author was aware of quant-ph. It is relevant to recent developments concerning Kochen-Specker theorem

Jump-like unravelings for non-Markovian open quantum systems

Non-Markovian evolution of an open quantum system can be `unraveled' into pure state trajectories generated by a non-Markovian stochastic (diffusive) Schr\"odinger equation, as introduced by Di\'osi, Gisin, and Strunz. Recently we have shown that such equations can be derived using the modal (hidden variable) interpretation of quantum mechanics. In this paper we generalize this theory to treat jump-like unravelings. To illustrate the jump-like behavior we consider a simple system: A classically driven (at Rabi frequency $\Omega$) two-level atom coupled linearly to a three mode optical bath, with a central frequency equal to the frequency of the atom, $\omega_0$, and the two side bands have frequencies $\omega_0\pm\Omega$. In the large $\Omega$ limit we observed that the jump-like behavior is similar to that observed in this system with a Markovian (broad band) bath. This is expected as in the Markovian limit the fluorescence spectrum for a strongly driven two level atom takes the form of a Mollow triplet. However the length of time for which the Markovian-like behaviour persists depends upon {\em which} jump-like unraveling is used.Comment: 11 pages, 5 figure