We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as 'Trumped' (Arntzenius and McCarthy 1997), 'Rouble trouble' (Arntzenius and Barrett 1999), 'The airtight Dutch book' (McGee 1999), and 'The two envelopes puzzle' (Broome 1995). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably (...) additive. The resolution also shows that when infinitely many decisions are involved, the difference between making the decisions simultaneously and making them sequentially can be the difference between riches and ruin. Finally, the resolution reveals a new way in which the ability to make binding commitments can save perfectly rational agents from sure losses. (shrink)
I argue that standard decision theories, namely causal decision theory and evidential decision theory, both are unsatisfactory. I devise a new decision theory, from which, under certain conditions, standard game theory can be derived.
We develop a Bayesian framework for thinking about the way evidence about the here and now can bear on hypotheses about the qualitative character of the world as a whole, including hypotheses according to which the total population of the world is infinite. We show how this framework makes sense of the practice cosmologists have recently adopted in their reasoning about such hypotheses.
Frank Arntzenius presents a series of radical new ideas about the structure of space and time. Space, Time, and Stuff is an attempt to show that physics is geometry: that the fundamental structure of the physical world is purely geometrical structure. Along the way, he examines some non-standard views about the structure of spacetime and its inhabitants, including the idea that space and time are pointless, the idea that quantum mechanics is a completely local theory, the idea that antiparticles are (...) just particles travelling back in time, and the idea that time has no structure whatsoever. The main thrust of the book, however, is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, and metaphysics in particular, plays an important role here: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal. Without this assumption one gets nowhere. That is to say, when trying to extract the fundamental structure of the world from theories of physics one ignores philosophy at one's peril! (shrink)
Time travel has been a staple of science fiction. With the advent of general relativity it has been entertained by serious physicists. But, especially in the philosophy literature, there have been arguments that time travel is inherently paradoxical. The most famous paradox is the grandfather paradox: you travel back in time and kill your grandfather, thereby preventing your own existence. To avoid inconsistency some circumstance will have to occur which makes you fail in this attempt to kill your grandfather. Doesn't (...) this require some implausible constraint on otherwise unrelated circumstances? We examine such worries in the context of modern physics. (shrink)
Zeno argued that since at any instant an arrow does not change its location, the arrow does not move at any time, and hence motion is impossible. I discuss the following three views that one could take in view of Zeno's argument:(i) the "at-at" theory, according to which there is no such thing as instantaneous velocity, while motion in the sense of the occupation of different locations at different times is possible,(ii) the "impetus" theory, according to which instantaneous velocities do (...) exist but these are only contingently and causally related to the temporal developments of positions,(iii) the "no instants" theory, according to which instants in time do not exist, and hence instantaneous velocities do not exist, while motion, in the sense of different areas occupied during different time intervals, is possible.I argue that, despite the fact that there have been interesting and relevant developments in mathematics and physics since the time of Zeno, each of these views still has serious drawbacks. (shrink)
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. Feynman's view is interesting because, in particular, it suggests a nonstandard, and possibly illuminating, interpretation of the CPT theorem. In this paper, we explore a classical analog of Feynman's view, in the context of (...) the recent debate between David Albert and David Malament over time reversal in classical electromagnetism. (shrink)
The ‘Principal Principle’ states, roughly, that one's subjective probability for a proposition should conform to one's beliefs about that proposition's 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. 1 Introduction 2 Preliminaries 3 Undermining futures and the New Principle 4 The Old Principle rescued? 5 The New Bug 6 Conclusion. (shrink)
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 Quinn's argument goes wrong, and (...) apply this to the moral puzzles. (shrink)
I argue that it may well be the case that space and time do not consist of points, indeed that they have no smallest parts. I examine two different approaches to such pointless spaces : a topological approach and a measure theoretic approach. I argue in favor of the measure theoretic approach.
Suppose that two geysers, about one mile apart, erupt at irregular intervals, but usually erupt almost exactly at the same time. One would suspect that they come from a common source, or at least that there is a common cause of their eruptions. And this common cause surely acts before both eruptions take place. This idea, that simultaneous correlated events must have prior common causes, was first made precise by Hans Reichenbach (Reichenbach 1956). It can be used to infer the (...) existence of unobserved and unobservable events, and to infer causal relations from statistical relations. Unfortunately it does not appear to be universally valid, nor is there agreement as to the circumstances in which it is valid. (shrink)
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.
We tell a story where an agent who chooses in such a way as to make the greatest possible profit on each of an infinite series of transactions ends up worse off than an agent who chooses in such a way as to make the least possible profit on each transaction. That is, contrary to what one might suppose, it is not necessarily rational always to choose the option that yields the greatest possible profit on each transaction.
The two envelope paradox can be dissolved by looking closely at the connection between conditional and unconditional expectation and by being careful when summing an infinite series of positive and negative terms. The two envelope paradox is not another St. Petersburg paradox and that one does not need to ban talk of infinite expectation values in order to dissolve it. The article ends by posing a new puzzle to do with infinite expectations.
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.
A theory is usually said to be time reversible if whenever a sequence of states S 1 , S 2 , S 3 is possible according to that theory, then the reverse sequence of time reversed states S 3 T , S 2 T , S 1 T is also possible according to that theory; i.e., one normally not only inverts the sequence of states, but also operates on the states with a time reversal operator T . David Albert and (...) Paul Horwich have suggested that one should not allow such time reversal operations T on states. I will argue that time reversal operations on fundamental states should be allowed. I will furthermore argue that the form that time reversal operations take is determined by the type of fundamental geometric quantities that occur in nature and that we have good reason to believe that the fundamental geometric quantities that occur in nature correspond to irreducible representations of the Lorentz transformations. Finally, I will argue that we have good reason to believe that space-time has a temporal orientation. (shrink)
Pulier (2000, Theory and Decision 49: 291) and Machina (2000, Theory and Decision 49: 293) seek to dissolve the BarrettâArntzenius infinite decision puzzle (1999, Theory and Decision 46: 101). The proposed dissolutions, however, are based on misunderstandings concerning how the puzzle works and the nature of supertasks more generally. We will describe the puzzle in a simplified form, address the recent misunderstandings, and describe possible morals for decision theory.
Many phenomena in the world display a striking time-asymmetry: the forwards transition frequencies are approximately invariant while the backwards ones are not. I argue in this paper that theories of such phenomena will entail that time has a direction, and that quantum mechanics in particular entails that the future is objectively different from the past.
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. *I am most grateful for helpful comments made by John Earman, and especially John Norton, who is responsible for anything that makes sense in this paper. I am also grateful for the reception of a Mellon postdoctoral fellowship, which supported me whilst doing the research for this paper. (shrink)
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.
I show that for any quantum dynamics and any choice of observables as hidden variables an adequate hidden variable theory always exists. I argue that hidden variable theories have no more problems in reconciling non-locality with relativity than no-hidden-variable theories.
The frequencies with which photons pass through half-silvered mirrors in the forward direction of time is always approximately 1/2, whereas the frequencies with which photons pass through mirrors in the backward direction in time can be highly time-dependent. I argue that whether one should infer from this time-asymmetric phenomenon that time has an objective direction will depend on one's interpretation of quantum mechanics.
The general claims of this paper are as follows. As a result of chaotic dynamics we can usually not know what the deterministic causes of events are. There will, however, be invariant forwards transition chances from earlier types of events, which we typically call the causes, to later types of events, which we typically call the effects. There will be no invariant backwards transition chances between these types of events. This asymmetry has the same origin and explanation as the arrow (...) of time of thermodynamics. (shrink)
It has often been suggested that the meaning of terms is theory dependent. Bas van Fraassen has proposed a particular way of inferring which sentences are true in virtue of meaning, given a theory in so-called state-space format. I examine his claims by means of simple examples.
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. (shrink)
The measurement problem in quantum mechanics is presented in a completely non-technical way by means of the results of some very simple experiments. These experimental results themselves, rather than the formalism of quantum theory, are shown to be extremely hard to incorporate in a sensible state-space picture of the world. A novel twist is then added which makes the problem even harder than it appears to be in other presentations of the measurement problem.
One of our more fundamental beliefs is that causal chains are continuous in time: we believe that every influence from the past upon the future runs through the present. I argue that this tenet, given certain data, can force conceptual changes upon us. I attempt to formulate a heuristic for discovery, based as explicitly as possible upon this tenet, and illustrate it by means of several examples, one of which is Mendel's discovery of genes.
A theory is usually said to be time reversible if whenever a sequence of states S 1, S 2, S 3 is possible according to that theory, then the reverse sequence of time reversed states S 3 T, S 2 T, S 1 T is also possible according to that theory; i.e., one normally not only inverts the sequence of states, but also operates on the states with a time reversal operator T. David Albert and Paul Horwich have suggested that (...) one should not allow such time reversal operations T on states. I will argue that time reversal operations on fundamental states should be allowed. I will furthermore argue that the form that time reversal operations take is determined by the type of fundamental geometric quantities that occur in nature and that we have good reason to believe that the fundamental geometric quantities that occur in nature correspond to irreducible representations of the Lorentz transformations. Finally, I will argue that we have good reason to believe that space-time has a temporal orientation. (shrink)