Online research in philosophy

In his famous 1979 article 'A Puzzle About Belief' Saul Kripke presents two puzzles regarding belief attribution, and he uses them to cast doubt on classical substitution arguments against the Millian view that a proper name has a 'denotation' (or reference) but no 'connotation' (or sense). In this article, I present Kripke's puzzles in what I take to be their most revealing form, discuss their relevance to the abovementioned arguments, briefly survey the ways in which philosophers have responded to these puzzles, and call attention to some issues related to the puzzles that have yet to receive the consideration they deserve.

Late in the nineteenth century, physics noticed a puzzling conflict between the laws of physics and what actually happens. The laws make no distinction between past and future—if they allow a process to happen one way, they allow it in reverse.1 But many familiar processes are in practice ‘irreversible’, common in one orientation but unknown ‘backwards’. Air leaks out of a punctured tyre, for example, but never leaks back in. Hot drinks cool down to room temperature, but never spontaneously heat up. Once we start looking, these examples are all around us—that’s why films shown in reverse often look odd. Hence the puzzle: What could be the source of this widespread temporal bias in the world, if the underlying laws are so even-handed? Call this the Puzzle of Temporal Bias, or PTB for short. It’s an oft-told tale how other puzzles of the late nineteenth century soon led to the two most famous achievements of twentieth century physics, relativity and quantum mechanics. Progress on PTB was much slower, but late in the twentieth century cosmology provided a spectacular answer, or partial answer, to this deep puzzle. Because the phenomena at the heart of PTB are so familiar, so ubiquitous, and so crucial to our own existence, the achievement is one of the most important in the entire history of physics. Yet it is littleknown and underrated, at least compared to the other twentieth century solutions to nineteenth century puzzles. Why is it underrated? Partly because people underestimate the original puzzle, or misunderstand it, and so don’t see what a big part of it is addressed by the new cosmology. And partly for a deeper, more philosophical reason, connected with the view that we don’t need to explain initial conditions. This has two effects. First, people undervalue the job done so far by cosmology, in telling us something very surprising..

In many physical systems, coupling forces provide a way of carrying the energy stored in adjacent harmonic oscillators from place to place, in the form of waves. The wave equations governing such phenomena are time-symmetric: they permit the opposite processes, in which energy arrives at a point in the form of incoming concentric waves, to be lost to some external system. But these processes seem rare in nature. What explains this temporal asymmetry, and how is it related to the thermodynamic asymmetry? This paper attempts to clarify these old issues, in the light of recent contributions. After brief introductory remarks (§1), the paper is in three main parts. §2 examines the so-called ‘Sommerfeld Radiation Condition’, arguing that its link to the observed asymmetry is much less direct than commonly supposed. §3 begins with Zeh's proposal to make the Sommerfeld condition an ingredient in an explanation of the observed asymmetry, and makes explicit a useful distinction between two ways in which the thermodynamic asymmetry might connect to the radiation asymmetry. §4 reviews a proposal I have defended in earlier work about the relation of the radiative asymmetry to that of thermodynamics, and defends it against recent objections by Zeh and Frisch. I also distinguish it from a recent proposal due to North. I agree with North that the observed asymmetry of radiation stems from the low entropy history, but argue that she mis-characterises the asymmetry, and hence misses a crucial element in a proper account of the role of the low entropy past.

Thermodynamics is the science that describes much of the time asymmetric behavior found in the world. This entry's first task, consequently, is to show how thermodynamics treats temporally ‘directed’ behavior. It then concentrates on the following two questions. (1) What is the origin of the thermodynamic asymmetry in time? In a world possibly governed by time symmetric laws, how should we understand the time asymmetric laws of thermodynamics? (2) Does the thermodynamic time asymmetry explain the other temporal asymmetries? Does it account, for instance, for the fact that we know more about the past than the future? The discussion thus divides between thermodynamics being an explanandum or explanans. In the former case the answer will be found in philosophy of physics; in the latter case it will be found in metaphysics, epistemology, and other fields, though in each case there will be blurring between the disciplines.

Iteration presents opposing puzzles for a theory of the imagination. The first puzzle, noted by David Lewis, is that when a person pretends to pretend, the iteration is often preserved. Let’s call this the puzzle of ‘pre- served iteration’. At the other pole, Gregory Currie has noted that very often when we pretend to pretend, the iteration does collapse. We might call this the puzzle of ‘collapsed iteration’. Somehow a theory of the imagination must be able to address these two puzzles. I argue that an empirically inspired cognitive theory of the imagination (Nichols & Stich 2000) can accommodate both puzzles.

I criticize two accounts of the temporal asymmetry of electromagnetic radiation - that of Huw Price, whose account centrally involves a reinterpretation of Wheeler and Feynman's infinite absorber theory, and that of Dieter Zeh. I then offer some reasons for thinking that the purported puzzle of the arrow of radiation does not present a genuine puzzle in need of a solution.

Summary: Contemporary writers often claim that chaos theory explains the thermodynamic arrow of time. This paper argues that such claims are mistaken, on two levels. First, they underestimate the difficulty of extracting asymmetric conclusions from symmetric theories. More important, however, they misunderstand the nature of the puzzle about the temporal asymmetry of thermodynamics, and simply address the wrong issue. Both of these are old mistakes, but mistakes which are poorly recognised, even today. This paper aims to lay bare the mistakes in their classical (pre-chaos theory) manifestations, in order to make it clear that chaos theory cannot possibly do better.

In [Sch05a], it is argued that Boltzmann's intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. [Haw94] presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will be shown to fail. It will be shown that any computational process that can take place in an entropy increasing universe, can equally take place in an entropy decreasing universe. This conclusion does not automatically imply a psychological arrow can run counter to the thermodynamic arrow. Some alternative possible explanations for the alignment of the two arrows will be briefly discussed.

Since the late nineteenth century, physics has been puzzled by the time-asymmetry of thermodynamic phenomena in the light of the apparent T-symmetry of the underlying laws of mechanics. However, a compelling solution to this puzzle has proved elusive. In part, I argue, this can be attributed to a failure to distinguish two conceptions of the problem. According to one, the main focus of our attention is a time-asymmetric lawlike generalisation. According to the other, it is a particular fact about the early universe. This paper aims (i) to distinguish these two different conceptions of the time-asymmetric explanandum in thermodynamics; (ii) to argue in favour of the latter; and (iii) to show that whichever we choose, our rational expectations about the thermodynamic behaviour of the future must depend on what we know about the past: contrary to the common view, statistical arguments alone do not give us good reason to expect that entropy will always continue to increase.

Scientific cosmology is an empirical discipline whose objects of study are the large-scale properties of the universe. In this context, it is usual to call the direction of the expansion of the universe the "cosmological arrow of time". However, there is no reason for privileging the ‘radius’ of the universe for defining the arrow of time over other geometrical properties of the space-time. Traditional discussions about the arrow of time in general involve the concept of entropy. In the cosmological context, the direction past-to-future is usually related to the direction of the gradient of the entropy function of the universe. But entropy is a thermodynamic magnitude that is typically associated with subsystems of the universe: the entropy of the universe as a whole is a very controversial matter. Moreover, thermodynamics is a phenomenological theory. Geometrical properties of space-time provide a more fundamental and less controversial way of defining an arrow of time for the universe as a whole. We will call the arrow defined only on the basis of the geometrical properties of space-time, independently of any entropic considerations, the "cosmological arrow of time". In this paper we will argue that: (i) it is possible to define a cosmological arrow of time for the universe as a whole, if certain conditions are satisfied, and (ii) the standard models of contemporary cosmology satisfy these conditions.