An adequate account of laws should satisfy at least five desiderata: it should provide a unified account of laws and chances, it should yield plausible relations between laws and chances, it should vindicate numerical chance assignments, it should accommodate dynamical and non-dynamical chances, and it should accommodate a plausible range of nomic possibilities. No extant account of laws satisfies these desiderata. This paper presents a non-Humean account of laws, the Nomic Likelihood Account, that does.

This chapter focuses on the relations between objective probabilities in physical theories at different levels. In general philosophy of probability, it is frequently assumed that a fundamental deterministic theory cannot support probabilistic phenomena at any higher level, or more generally that there cannot be non-trivial probabilities in higher-level theories that are not encoded in probabilities at the lower level. These assumptions face significant challenges from some well-understood physical theories – I focus on statistical mechanics and Bohmian mechanics – where a (...) deterministic description at some lower level gives rise to an effectively probabilistic theory at some higher level; in each case, constraints arising from an objective physical limitation on the acquisition of evidence concerning the lower level plays a crucial role in supporting the higher-level probabilities. (shrink)

In previous work I’ve defended an interest-relative theory of belief. This paper continues the defence. It has four aims. -/- 1. To offer a new kind of reason for being unsatis ed with the simple Lockean reduction of belief to credence. 2. To defend the legitimacy of appealing to credences in a theory of belief. 3. To illustrate the importance of theoretical, as well as practical, interests in an interest-relative account of belief. 4. To revise my account to cover propositions (...) that are practically and theoretically irrelevant to the agent. (shrink)

A proposal for an objective interpretation of probability is introduced and discussed: probabilities as deriving from ranges in suitably structured initial-state spaces. Roughly, the probability of an event on a chance trial is the proportion of initial states that lead to the event in question within the space of all possible initial states associated with this type of experiment, provided that the proportion is approximately the same in any not too small subregion of the space. This I would like to (...) call the “natural-range conception” of probability. Providing a substantial alternative to frequency or propensity accounts of probability in a deterministic setting, it is closely related to the so-called “method of arbitrary functions”. It is explicated, confronted with certain problems, and some ideas how these might be overcome are sketched and discussed. (shrink)

This paper examines the debate between permissive and impermissive forms of Bayesianism. It briefly discusses some considerations that might be offered by both sides of the debate, and then replies to some new arguments in favor of impermissivism offered by Roger White. First, it argues that White’s (Oxford studies in epistemology, vol 3. Oxford University Press, Oxford, pp 161–186, 2010) defense of Indifference Principles is unsuccessful. Second, it contends that White’s (Philos Perspect 19:445–459, 2005) arguments against permissive views do not (...) succeed. (shrink)

This pair of articles provides a critical commentary on contemporary approaches to statistical mechanical probabilities. These articles focus on the two ways of understanding these probabilities that have received the most attention in the recent literature: the epistemic indifference approach, and the Lewis-style regularity approach. These articles describe these approaches, highlight the main points of contention, and make some attempts to advance the discussion. The first of these articles provides a brief sketch of statistical mechanics, and discusses the indifference approach (...) to statistical mechanical probabilities. (shrink)

I discuss the formal implementation, interpretation, and justification of likelihood attributions in cosmology. I show that likelihood arguments in cosmology suffer from significant conceptual and formal problems that undermine their applicability in this context.

In this paper I propose an interpretation of classical statistical mechanics that centers on taking seriously the idea that probability measures represent complete states of statistical mechanical systems. I show how this leads naturally to the idea that the stochasticity of statistical mechanics is associated directly with the observables of the theory rather than with the microstates (as traditional accounts would have it). The usual assumption that microstates are representationally significant in the theory is therefore dispensable, a consequence which suggests (...) interesting possibilities for developing non-equilibrium statistical mechanics and investigating inter-theoretic answers to the foundational questions of statistical mechanics. (shrink)

The present paper draws on climate science and the philosophy of science in order to evaluate climate-model-based approaches to assessing climate projections. We analyze the difficulties that arise in such assessment and outline criteria of adequacy for approaches to it. In addition, we offer a critical overview of the approaches used in the IPCC working group one fourth report, including the confidence building, Bayesian and likelihood approaches. Finally, we consider approaches that do not feature in the IPCC reports, including three (...) approaches drawn from the philosophy of science. We find that all available approaches face substantial challenges, with IPCC approaches having as a primary source of difficulty their goal of providing probabilistic assessments. (shrink)

Decisions, whether moral or prudential, should be guided at least in part by considerations of the consequences that would result from the various available actions. For any given action, however, the majority of its consequences are unpredictable at the time of decision. Many have worried that this leaves us, in some important sense, clueless. In this paper, I distinguish between ‘simple’ and ‘complex’ possible sources of cluelessness. In terms of this taxonomy, the majority of the existing literature on cluelessness focusses (...) on the simple sources. I argue, contra James Lenman in particular, that these would-be sources of cluelessness are unproblematic, on the grounds that indifference-based reasoning is far less problematic than Lenman (along with many others) supposes. However, there does seem to be a genuine phenomenon of cluelessness associated with the ‘complex’ sources; here, indifference-based reasoning is inapplicable by anyone’s lights. This ‘complex problem of cluelessness’ is vivid and pressing, in particular, in the context of Effective Altruism. This motivates a more thorough examination of the precise nature of cluelessness, and the precise source of the associated phenomenology of discomfort in forced-choice situations. The latter parts of the paper make some initial explorations in those directions. (shrink)

Can stable regularities be explained without appealing to governing laws or any other modal notion? In this paper, I consider what I will call a ‘Humean system’—a generic dynamical system without guiding laws—and assess whether it could display stable regularities. First, I present what can be interpreted as an account of the rise of stable regularities, following from Strevens [2003], which has been applied to explain the patterns of complex systems (such as those from meteorology and statistical mechanics). Second, since (...) this account presupposes that the underlying dynamics displays deterministic chaos, I assess whether it can be adapted to cases where the underlying dynamics is not chaotic but truly random—that is, cases where there is no dynamics guiding the time evolution of the system. If this is so, the resulting stable, apparently non-accidental regularities are the fruit of what can be called statistical necessity rather than of a primitive physical necessity. (shrink)

One of the most difficult problems in the foundations of physics is what gives rise to the arrow of time. Since the fundamental dynamical laws of physics are (essentially) symmetric in time, the explanation for time's arrow must come from elsewhere. A promising explanation introduces a special cosmological initial condition, now called the Past Hypothesis: the universe started in a low-entropy state. Unfortunately, in a universe where there are many copies of us (in the distant ''past'' or the distant ''future''), (...) the Past Hypothesis is not enough; we also need to postulate self-locating (de se) probabilities. However, I show that we can similarly use self-locating probabilities to strengthen its rival---the Fluctuation Hypothesis, leading to in-principle empirical underdetermination and radical epistemological skepticism. The underdetermination is robust in the sense that it is not resolved by the usual appeal to 'empirical coherence' or 'simplicity.' That is a serious problem for the vision of providing a completely scientific explanation of time's arrow. (shrink)

The foundations of probability are viewed through the lens of the subjectivist interpretation. This article surveys conditional probability, arguments for probabilism, probability dynamics, and the evidential and subjective interpretations of probability.

The most promising accounts of ontic probability include the Spielraum conception of probabilities, which can be traced back to J. von Kries and H. Poincaré, and the best system account by D. Lewis. This paper aims at comparing both accounts and at combining them to obtain the best of both worlds. The extensions of both Spielraum and best system probabilities do not coincide because the former only apply to systems with a special dynamics. Conversely, Spielraum probabilities may not be part (...) of the best system, e.g. if a broad class of random devices is not often used. Spielraum probabilities have the potential to provide illuminating explanations of frequencies with which outcomes of trials on gambling devices arise. They ultimately fail to account for such frequencies though because they are compatible with frequencies that grossly differ from the values of the respective probabilities. I thus follow recent proposals by M. Strevens and M. Abrams and strengthen the definition of Spielraum probabilities by adding a further condition that restricts some actual frequencies. The resulting account remains limited in scope, but stands objections raised against it in the recent literature: it is neither circular nor based upon arbitrary choices of a measure or of physical variables. Nor does it lack any explanatory power. (shrink)

Over the years I’ve written many papers defending an idiosyncratic version of interest-relative epistemology. This book collects and updates the views I’ve expressed over those papers. -/- Interest-relative epistemologies all start in roughly the same way. A big part of what makes knowledge important is that it rationalises action. But for almost anything we purportedly know, there is some action that it wouldn’t rationalise. I know what I had for breakfast, but I wouldn’t take a bet at billion to one (...) odds about it. Knowledge has practical limits. The first idiosyncratic feature of my version of interest-relative epistemology is how those limits are identified. Other interest-relative philosophers typically say that the limits have to do with stakes; in high stakes situations knowledge goes away. That’s no part of my view. I think knowledge goes away in long odds situations. High stakes situations are almost always are long odds situations, for reasons to do with the declining marginal utility of money. But the converse isn’t true. On my view, knowledge often goes away in cases where it is trivial to check before action. This idea, that interests matter in long odds cases, and not just in high stakes cases, is the main constant in what I’ve written on interest-relativity over the years. -/- But there are three other respects in which the view I’m going to set out and defend in this book is very different from the view I set out in older papers. -/- I used to identify the practical limits on knowledge with cases where relying on the purported knowledge would get the wrong answer. I focused, that is, on the outputs of inquiry. Knowledge goes away if relying on it would lead one to make a mistake. I now think I was looking at the wrong end of inquiry. Knowledge goes away if the thinker starts conducting an inquiry where the purported knowledge is an inappropriate starting point, and inappropriate for the special reason that it might be false. Now one way we can tell that something is a bad starting point is that starting there will mean we end up at the wrong place. But it’s not the only way. Sometimes a bad starting point will lead to the right conclusion for the wrong reasons. As the Nyāya philosophers argued, rational inquiry starts with knowledge. If it would be irrational to start this inquiry with a particular belief, that belief isn’t knowledge. -/- Not all inquiries are practical inquiries, but many are. And practical inquiries are usually going to be at the center of attention in this book. But what is someone trying to figure out when they conduct a practical inquiry? I used to think that they were trying to figure out which option maximised expected utility, and to a first approximation identified knowledge with those things one could conditionalise on without changing the option that maximised expected utility. As noted in the previous paragraph, I no longer think that we can identify knowledge with what doesn’t change our verdicts. But more importantly, I no longer think that expected utility maximisation is as central to practical inquiry as I once did. There are some theoretical reasons from game theory that raise some doubts about expected utility maximisation. Weak dominance reasoning is part of our theory of rational choice, and can’t be modelled as expected utility maximisation. Perhaps some kinds of equilibrium seeking are parts of practical inquiry, and can’t be modelled as expected utility maximisation. But there are also very practical reasons to think that practical inquiry doesn’t aim at expected utility maximisation. When there are a lot of very similar options - think about selecting a can from a supermarket shelf - and it’s more trouble than it’s worth to figure out which of them maximises expected utility, it’s best to ignore the differences between them and just pick. As I’ll argue in Chapter 6, this makes a big difference to how interests and knowledge interact. -/- In the version of interest-relativity that I’m defending here, everything in epistemology is interest-relative. Knowledge, rational belief, and evidence are all interest-relative. But they are all interest-relative in slightly different ways. The main aim here is to defend the interest-relativity of knowledge. A common objection to interest-relative theories of knowledge is that they can’t be extended into theories of all the things we care about in epistemology. Here I try to meet that challenge. The way I do so is a little messy. It would be nice if there was some part of epistemology that’s interest-invariant, as I used to think, or if all the interest-relative notions were interest-relative in the same way, as other interest-relative epistemologists argue. For better or worse, that’s not the view I’m defending. Interests matter throughout epistemology, and we just have to go case by case to figure out how and why they matter. (shrink)

The prospects of a causal interpretation of probability are examined. Various accounts both from the history of scientific method and from recent developments in the tradition of the method of arbitrary functions, in particular by Strevens, Rosenthal, and Abrams, are briefly introduced and assessed. I then present a specific account of causal probability with the following features: First, the link between causal probability and a particular account of induction and causation is established, namely eliminative induction and the related difference-making account (...) of causation in the tradition of Bacon, Herschel, and Mill. Second, it is shown how a causal approach is useful beyond applications of the method of arbitrary functions and is able to deal with various shades of both ontic and epistemic probabilities. Furthermore, I clarify the notion of causal symmetry as a central element of an objective version of the principle of indifference and relate probabilistic independence to causal irrelevance. (shrink)