There are lots of arguments for, or justifications of, mathematical theorems that make use of principles from physics. Do any of these constitute explanations? On the one hand, physical principles do not seem like they should be explanatorily relevant; on the other, some particular examples of physical justifications do look explanatory. In this article, I defend the idea that (some) physical justifications can and do explain mathematical facts. 1 Physical Arguments for Mathematical Truths2 Preview3 Mathematical Facts4 Purity5 Doubts about Purity: (...) I6 Doubts about Purity: II7 How Physical Arguments Might Explain: I8 How Physical Arguments Might Explain: II9 Conclusion. (shrink)
Philosophers have proposed many alleged examples of non-causal explanations of particular events. I discuss several well-known examples and argue that they fail to be non-causal. 1 Questions2 Preliminaries3 Explanations That Cite Causally Inert Entities4 Explanations That Merely Cite Laws I5 Stellar Collapse6 Explanations That Merely Cite Laws II7 A Final Example8 Conclusion.
?Those ice cubes melted because by melting total entropy increased and entropy increase has a very high objective chance.? What role does the chance in this explanation play? I argue that it contributes to the explanation by entailing that the melting was almost necessary, and defend the claim that the fact that some event was almost necessary can, in the right circumstances, constitute a causal explanation of that event.
A desert-sensitive moral theory says that whether people get what they deserve, whether they are treated as they deserve to be treated, plays a role in determining what we ought to do. Some popular forms of consequentialism are desert-sensitive. But where do facts about what people deserve come from? If someone deserves a raise, or a kiss, in virtue of what does he deserve those things? One plausible answer is that what someone deserves depends, at least in part, on how (...) well he meets his moral requirements. The wicked deserve to suffer and the decent do not. Shelly Kagan (2006) has argued that this plausible answer is wrong. But his argument for that conclusion does not succeed. I will show how to formulate a desert-sensitive moral theory (and also a desert-sensitive version of consequentialism) on which this answer is correct. (shrink)
It is better when people get what they deserve. So we need an axiology according to which the intrinsic value of a possible world is a function of both how well-off and how deserving the people in that world are. But how should these ?desert-adjusted? values of possible worlds be calculated? It is easy to come up with some qualitative ideas. But these qualitative ideas leave us with an embarrassment of riches: too many quantitative functions that implement those qualitative ideas. (...) In this paper I will select one of these quantitative functions and defend its superiority. (shrink)
According to the moving spotlight theory of time, the property of being present moves from earlier times to later times, like a spotlight shone on spacetime by God. In more detail, the theory has three components. First, it is a version of eternalism: all times, past present and future, exist. (Here I use “exist” in its tenseless sense.) Second, it is a version of the A-theory of time: there are nonrelative facts about which times are past, which time is present, (...) and which times are future. That is, it is not just that the year 1066 is past relative to 2007. The year 1066 is also past full-stop, not relative to any other time. (The A-theory is opposed to the B-theory of time, which says that facts about which times are past are relative to other times.) And third, on this view the passage of time is a real phenomenon. Which moment is present keeps changing. As I will sometimes put it, the NOW moves from the past toward the future.1 And this does not mean that relative to different times, different times are present. Even the B-theory can say that 1999 is present relative to 1999 but is not present relative to 2007. No, according to the moving spotlight theory, the claim that which moment is present keeps changing is supposed to be true, even from a perspective outside time. (shrink)
Is there anything more to temperature than the ordering of things from colder to hotter? Are there also facts, for example, about how much hotter (twice as hot, three times as hot...) one thing is than another? There certainly are---but the only strong justification for this claim comes from statistical mechanics. What we knew about temperature before the advent of statistical mechanics (what we knew about it from thermodynamics) provided only weak reasons to believe it.
Some philosophers believe that the passage of time is a real phenomenon. And some of them find a reason to believe this when they attend to features of their conscious experience. In fact this “argument from experience” is supposed to be one of the main arguments for passage. What exactly does this argument look like? Is it any good?
In this paper I distinguish interpretations of the question "How fast does time pass?" that are important for the debate over the reality of objective becoming from interpretations that are not. Then I discuss how one theory that incorporates objective becoming—the moving spotlight theory of time—answers this question. It turns out that there are several ways to formulate the moving spotlight theory of time. One formulation says that time passes but it makes no sense to ask how fast; another formulation (...) says that time passes at one second per supersecond; and a third says that time passes at one second per second. I defend the intelligibility of this final version of the theory. (shrink)
A recent theory of metaphysical indeterminacy says that metaphysical indeterminacy is multiple actuality: there is metaphysical indeterminacy when there are many 'complete precisifications of reality'. But it is possible for there to be metaphysical indeterminacy even when it is impossible to precisify reality completely. The orthodox interpretation of quantum mechanics illustrates this possibility. So this theory of metaphysical indeterminacy is not adequate.
When distinguishing absolute, true, and mathematical time from relative, apparent, and common time, Newton wrote: “absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, ﬂows uniformly” [Newton 2004b: 64]. Newton thought that the temporal metric is intrinsic. Many philosophers have argued—for empiricist reasons or otherwise—that Newton was wrong about the nature of time. They think that the ﬂow of time does involve “reference to something external.” They think that the temporal (...) metric is extrinsic. Among others, Mach, Poincaré, and Grünbaum seem to accept this view.1 And these are not the only two views available. Perhaps both Newton and his opponents are wrong and there is no temporal metric at all. (shrink)
Bohmian mechanics faces an underdetermination problem: when it comes to solving the measurement problem, alternatives to the Bohmian guidance equation work just as well as the official guidance equation. One way to argue that the guidance equation is superior to its rivals is to use a symmetry argument: of the candidate guidance equations, the official guidance equation is the simplest Galilean-invariant candidate. This symmetry argument---if it worked---would solve the underdetermination problem. But the argument does not work. It fails because it (...) rests on assumptions about how Galilean transformations (especially boosts) act on the wavefunction that are (in this context) unwarranted. My discussion has larger morals about the physical significance of certain mathematical results (like, for example, Wigner's theorem) in non-orthodox interpretations of quantum mechanics. (shrink)
Maybe there is something rather than nothing because the nothingness force acted on itself, and when the nothing nothings itself it produces something. Robert Nozick suggested this as a candidate explanation of the fact that there is something rather than nothing. If he is right that it is a candidate explanation, we should pay attention: there are not many candidates out there. But his "explanation" looks, instead, like a paradigm case of philosophical nonsense. In this paper I describe a "metaphysical (...) dynamics" that makes sense out of Nozick's apparent nonsense. (shrink)
The paradox of desire is an objection to desire-satisfaction, or preferentist, theories of welfare. In a nutshell, the objection goes like this. I can certainly desire that I be badly oﬀ. But if a desire-satisfaction theory of welfare is true, then—under certain assumptions—the hypothesis that I desire that I be badly oﬀ entails a contradiction. So much the worse for desire-satisfaction theories of welfare.
A standard objection to the moving spotlight theory of time is that it is incompatible with special relativity. I show how to formulate the moving spotlight theory so that it is perfectly compatible with special relativity. There is no need to re-interpret the physics or add to it a notion of absolute simultaneity.
Possible-worlds talk obscures the debate about haecceitism, rather than clarifying it. I distinguish haecceitism and anti-haeccatismfrom other doctrìnes which sometimes go under those names. Then defend the claim that any definition of 'haecceitism' using possible-worlds talk depends for its conectness on a substantive theory of the nature of possible worlds. This explains why using possible-worlds talk when discussing haecceitism causes confusion: the term will mean different things to parties who depend on different presuppositions about possible worlds.
Local versions of the (special) principle of relativity say that if the same type of experiment is conducted in two isolated, unaccelerated laboratories, then the outcomes of those experiments must be the same. Global versions of the principle say that if you take a physically possible world and boost the entire material content of that world, you get another physically possible world. Some authors say that the local and the global principles are logically independent, and that the local version is (...) more important. These authors are wrong. I argue that the global version entails the local version, and discuss why a counterexample to this entailment offered by Tim Budden fails. (shrink)
It is widely believed that shapes are intrinsic properties. But this claim is hard to defend. I survey all known theories of shape properties, and argue that each theory is either incompatible with the claim that shapes are intrinsic, or can be shown to be false.
Earman and Roberts (2005) argue that a standard deﬁnition of “empiricism about laws of nature” is inadequate, and propose an alternative deﬁnition they think is better. But their argument against the standard deﬁnition fails, and their alternative is defective.
Sklar () claimed that relationalism about ontology-the doctrine that space and time do not exist-is compatible with Newtonian mechanics. To defend this claim he sketched a relationalist interpretation of Newtonian mechanics. In his interpretation, absolute acceleration is a fundamental, intrinsic property of material bodies; that a body undergoes absolute acceleration does not entail that space and time exist. But Sklar left his proposal as just a sketch; his defense of relationalism succeeds only if the sketch can be filled in. I (...) argue that this cannot be done. There can be no (relationalist) dynamical laws of motion based on Sklar's proposal that capture the content of Newton's theory. So relationalists must look elsewhere for a relationalist interpretation of Newtonian mechanics. (shrink)
No one denies that time and space are diﬀerent; and it is easy to catalog diﬀerences between them. I can point my ﬁnger toward the west, but I can’t point my ﬁnger toward the future. If I choose, I can now move to the left, but I cannot now choose to move toward the past. And (as D. C. Williams points out) for many of us, our attitudes toward time diﬀer from our attitudes toward space. We want to maximize our (...) temporal extent and minimize our spatial extent: we want to live as long as possible but we want to be thin.1 But these diﬀerences are not very deep, and don’t get at the essence of the diﬀerence between time and space. That’s what I want to understand: I want to know what makes time diﬀerent from space. I want to know which diﬀerence is the fundamental diﬀerence between them. (shrink)