Kevin Davey

Examples involving infinite suspended chains or infinite trains are sometimes used to defend perceived weaknesses in traditional cosmological arguments. In this article, we distinguish two versions of the cosmological argument, suggest that such examples can only be relevant if it is one specific type of cosmological argument that is being considered, and then criticize the use of such examples in this particular type of cosmological argument. Our criticism revolves around a discussion of what it means to call a system closed, and what it means to call an explanation complete. Our analysis makes no suppositions about the nature of the infinite, and is therefore independent of many of the issues around which contemporary discussions of the cosmological argument have tended to revolve.

Some philosophers have recently argued that contrary to the traditional view, good scientific theories can in fact be logically inconsistent. The literature is now full of case-studies that are taken to support this claim. I will argue however that as of yet no-one has managed to articulate a philosophically interesting view about the role of logically inconsistent theories in science that genuinely goes against tradition, is plausibly true, and is supported by any of the case studies usually given

According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low entropy macrostates are less probable than high entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law of thermodynamics is fundamentally flawed, and will show that some puzzles sometimes associated with the second law are merely artifacts of this incorrect justification.

Many arguments found in the physics literature involve concepts that are not well-defined by the usual standards of mathematics. I argue that physicists are entitled to employ such concepts without rigorously defining them so long as they restrict the sorts of mathematical arguments in which these concepts are involved. Restrictions of this sort allow the physicist to ignore calculations involving these concepts that might lead to contradictory results. I argue that such restrictions need not be ad hoc, but can sometimes be justified by considering some of the metaphysical issues surrounding the question of the applicability of mathematics to physical reality. 1 Introduction 2 Rejecting inferential permissiveness 3 The agreement problem 4 Independent objections to the liberal view.

According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low-entropy macrostates are less probable than high-entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law is unhelpful at best and wrong at worst, and will argue that certain puzzles sometimes associated with the second law are merely artifacts of this questionable justification. *Received October 2006; revised October 2007. †To contact the author, please write to: Department of Philosophy, University of Chicago, 1115 E. 58th St., Chicago, IL 60637; e-mail: [email protected].

Although the canonical distribution is one of the central tools of statistical mechanics, the reason for its effectiveness is poorly understood. This is due in part to the fact that there is no clear consensus on what it means to use the canonical distribution to describe a system in equilibrium with a heat bath. I examine some traditional views as to what sort of thing we should take the canonical distribution to represent. I argue that a less explored alternative, according to which the canonical distribution represents a time ensemble of sorts, has a number of advantages that rival interpretations lack. †To contact the author, please write to: Department of Philosophy, University of Chicago, 1115 E. 58th St., Chicago, IL 60637; e‐mail: [email protected].

Describing a physical system in idealized terms involves making claims about the system that we know to be literally false. Because of this, it is not clear how calculations involving idealizations can generate justified belief and explain facts about the world. I argue that this puzzling aspect of idealizations cannot be explained away by talking about approximations, as is often supposed. I develop a different account of how justified beliefs and explanations can be generated from idealized descriptions of physical systems. My account involves a type of contextualism about the truth of mathematical descriptions of physical systems.

A gas relaxing into equilibrium is often taken to be a process in which a system moves from an “improbable” to a “probable” state. Given that the thermodynamic entropy increases during such a process, it is natural to conjecture that the thermodynamic entropy is a measure of the probability of a macrostate. For nonideal classical gases, however, I claim that there is no clear sense in which the thermodynamic entropy of a macrostate measures its probability. We must therefore reject the idea that thermodynamic entropy and probability are connected in a deep and general way.

Why is it that even strong formal theories of truth fail to prove their own consistency? Although Field has addressed this question for many theories of truth, I argue that there is an important and attractive class of theories of truth that he omitted in his analysis. Such theories cannot prove that all their axioms are true, though unlike many of the cases Field considers, they do not prove that any of their axioms are false or that any of their rules of inference are not truth preserving. I argue that it is the fact that such theories are not finitely axiomatizable that stops them from proving their own consistency.

Although the inferring of explanations plays an important role in both our everyday lives and in the workings of science, I argue that inference to the best explanation as it is commonly conceived is often not the best way to capture this sort of reasoning. I suggest that a different form of reasoning – so-called immediate explanatory inference – is instead often much better suited to this task. This is a form of inference in which we are justified in believing explanations for the evidence before us purely in virtue of this evidence, and not in virtue of the evidence plus some general principle or rule of non-deductive reasoning. I defend the idea of such a notion of inference, and argue that it plays a central role in both ordinary life and science.

In [7] and [8], it is established that given any abstract countable structure S and a relation R on S, then as long as S has a recursive copy satisfying extra decidability conditions, R will be ∑0α on every recursive copy of S iff R is definable in S by a special type of infinitary formula, a ∑rα() formula. We generalize the typ e of constructions of these papers to produce conditions under which, given two disjoint relations R1 and R2 on S, there is a recursive copy of S in which R1 and R2 are 0α inseparable. We then apply these theorems to specific everyday structures such as linear orderings, boolean algebras andvector spaces

Inspired by the work of Kuhn, we might want to develop an account of science that explains how it is that while much of science involves the investigation of a world as articulated by a paradigm, the scientist is nevertheless an observer and rational interpreter of a mind-independent world that does not change its character over time. Kuhn himself recognizes that there is a challenge here that he does not know how to meet. I argue that progress can be made on this challenge by carefully examining and criticizing Kuhn’s account of deliberation in science. Inspired by certain views about Gestalt psychology and examples such as the duck/rabbit picture, Kuhn takes deliberation in science to be a consequence of seeing things a certain way, rather than rational deliberation in science making new ways of seeing things possible. I argue that the most serious problems of Kuhn’s view of science stem from this fact, and that we can free ourselves from these problems by not following Kuhn here. In particular, I argue using material from Hanson and Peirce that we should think of the revolutionary scientist as being revolutionary not merely in virtue of seeing things in a new way, but rather for showing – typically through painstaking deliberation – that certain conjectures connected with new ways of seeing the world are reasonable This makes coming to see the world differently a deliberative process that is importantly unlike seeing a rabbit/duck picture differently. Such a way of thinking allows us to view the articulation of a new paradigm as a deliberative process that does not take some paradigm or other for granted, but rather as a deliberative process that interrogates existing orthodoxy for its suitability to survive into the next paradigm. The result is a view of science that maintains much of what is important to Kuhn, but departs from him where his view is least convincing.

It is often supposed that we can use mathematics to capture the time evolution of any physical system. By this, I mean that we can capture the basic truths about the time evolution of a physical system with a set of mathematical assertions, which can then be used as premises in arbitrary mathematical arguments to deduce more complex properties of the system. ;I would like to argue that this picture of the role of mathematics in physics is incorrect. Specifically, I shall assert: ;The Deduction Failure Thesis: Bodies of knowledge in physics are generally not closed under otherwise valid mathematical argument forms. ;The Representation Failure Thesis: We cannot assume that the state of any system, together with its fundamental laws, can be captured by some set of mathematical assertions or equations. In fact, it is more likely that the world is not representable by a set of mathematical assertions or equations than that it is. ;The dissertation largely consists of arguments for these two theses