Frank Arntzenius

Some Problems for Conditionalization and Reflection

I will present five puzzles which show that rational people can update their degrees of belief in manners that violate Bayesian Conditionalization and van Fraassen’s Reflection Principle. I will then argue that these violations of Conditionalization and Reflection are due to the fact that there are two, as yet unrecognized, ways in which the degrees of belief of rational people can develop.

The Common Cause Principle

The common cause principle states that correlations have prior common causes which screen off those correlations. I argue that the common cause principle is false in many circumstances, some of which are very general. I then suggest that more restricted versions of the common cause principle might hold, and I prove such a restricted version.

On What We Know About Chance

The ‘Principal Principle’ states, roughly, that ones subjective probability for a proposition should conform to ones beliefs about that propositions objective chance of coming true. David Lewis has argued (i) that this principle provides the defining role for chance; (ii) that it conflicts with his reductionist thesis of Humean supervenience, and so must be replaced by an amended version that avoids the conflict; hence (iii) that nothing perfectly deserves the name ‘chance’, although something can come close enough by playing the role picked out by the amended principle. We show that in fact there must be ‘chances’ that perfectly play what Lewis takes to be the defining role. But this is not the happy conclusion it might seem, since these ‘chances’ behave too strangely to deserve the name. The lesson is simple: much more than the Principal Principle—more to the point, much more than the connection between chance and credence—informs our understanding of objective chance. 1Introduction 2Preliminaries 3Undermining futures and the New Principle 4The Old Principle rescued? 5The New Bug 6Conclusion

Time reversal in classical electromagnetism

Richard Feynman has claimed that anti-particles are nothing but particles ‘propagating backwards in time’; that time reversing a particle state always turns it into the corresponding anti-particle state. According to standard quantum field theory textbooks this is not so: time reversal does not turn particles into anti-particles. Feynmans view is interesting because, in particular, it suggests a non-standard, and possibly illuminating, interpretation of the CPT theorem. This paper explores a classical analog of Feynmans view, in the context of the recent debate between David Albert and David Malament over time reversal in classical electromagnetism. 1. Introduction2. Time Reversal and the Direction of Time3. Classical Electromagnetism: The Story So Far 3.1. The standard textbook view3.2. Alberts proposal3.3. Malaments proposal3.4. Albert revisited4. The ‘Feynman’ Proposal5. Structuralism: A Third Way? 5.1. Structures: the debate recast5.2. Relational structures5.3. Malament and Feynman structures as conventional representors of a relational reality6. Conclusions and Open Questions Introduction Time Reversal and the Direction of Time Classical Electromagnetism: The Story So Far 3.1. The standard textbook view3.2. Alberts proposal3.3. Malaments proposal3.4. Albert revisited The standard textbook view Alberts proposal Malaments proposal Albert revisited The ‘Feynman’ Proposal Structuralism: A Third Way? 5.1. Structures: the debate recast5.2. Relational structures5.3. Malament and Feynman structures as conventional representors of a relational reality Structures: the debate recast Relational structures Malament and Feynman structures as conventional representors of a relational reality Conclusions and Open Questions

Gunk, Topology and Measure

It is standardly assumed that space and time consist of extensionless points. It is also a fairly standard assumption that all matter in the universe has point-sized parts. We are not often explicitly reminded of these very basic assumptions. But they are there. For instance, one standardly assumes that one can represent the states of material objects, and of fields, by functions from points in space and time to the relevant point values. Electric fields, mass densities, gravitational potentials, etc. … are standardly represented as functions from points in space and time to point values. This practice would seem to make no sense if time and space did not have points as parts.

Is Quantum Mechanics Pointless

There exist well‐known conundrums, such as measure‐theoretic paradoxes and problems of contact, which, within the context of classical physics, can be used to argue against the existence of points in space and space‐time. I examine whether quantum mechanics provides additional reasons for supposing that there are no points in space and space‐time.

Self torture and group beneficence

Moral puzzles about actions which bring about very small or what are said to be imperceptible harms or benefits for each of a large number of people are well known. Less well known is an argument by Warren Quinn that standard theories of rationality can lead an agent to end up torturing himself or herself in a completely foreseeable way, and that this shows that standard theories of rationality need to be revised. We show where Quinns argument goes wrong, and apply this to the moral puzzles.

Causal Paradoxes in Special Relativity

It has been argued that the existence of faster than light particles in the context of special relativity would imply the possibility to influence the past, and that this would lead to paradox. In this paper I argue that such conclusions cannot safely be drawn without consideration of the equations of motion of such particles. I show that such equations must be non-local, that they can be deterministic, and that they can avoid the suggested paradoxes. I also discuss conservation of energymomentum, and how instantaneous action at a distance can avoid similar paradoxes.

Physics and common causes

The common cause principle states that common causes produce correlations amongst their effects, but that common effects do not produce correlations amongst their causes. I claim that this principle, as explicated in terms of probabilistic relations, is false in classical statistical mechanics. Indeterminism in the form of stationary Markov processes rather than quantum mechanics is found to be a possible saviour of the principle. In addition I argue that if causation is to be explicated in terms of probabilities, then it should be done in terms of probabilistic relations which are invariant under changes of initial distributions. Such relations can also give rise to an asymmetric cause-effect relationship which always runs forwards in time.

Kochen's Interpretation of Quantum Mechanics

Kochen has suggested an interpretation of quantum mechanics in which he denies that wavepackets ever collapse, while affirming that measurements have definite results. In this paper I attempt to show that his interpretation is untenable. I then suggest ways in which to construct similar, but more satisfactory, hidden variable interpretations.