Kevin Davey

Is Mathematical Rigor Necessary in Physics

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. 1Introduction 2Rejecting inferential permissiveness 3The agreement problem 4Independent objections to the liberal view

The Justification of Probability Measures in Statistical Mechanics

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.

Inseparability in recursive copies

Abstract 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 L S by a special type of infinitary formula, a ∑rα(p) 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.

Insufficient reason in the ‘new cosmological argument’

In a recent article in this journal, Richard Gale and Alexander Pruss offer a new cosmological proof for the existence of God relying only on the Weak Principle of Sufficient Reason, W-PSR. We argue that their proof relies on applications of W-PSR that cannot be justified, and that our modal intuitions simply do not support W-PSR in the way Gale and Pruss take them to.

Can good science be logically inconsistent

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.

Idealizations and Contextualism in Physics

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.

Thermodynamic Entropy and Its Relation to Probability in Classical Mechanics

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 (in classical mechanics) thermodynamic entropy and probability are connected in a deep and general way.

What Is Gibbs's Canonical Distribution?

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.

Obligation and the Conditional in Stit Theory

In this paper, we consider two different ways in which modus-ponens type reasoning with conditional obligations may be formalized. We develop necessary and sufficient conditions for the validity of each, and make some philosophical observations about the differences between the minor premises that each formalization requires. All this is done within the context of the Belnap-Perloff stit theory.