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.

The recent use of typicality in statistical mechanics for foundational purposes has stirred an important debate involving both philosophers and physicists. While this debate customarily focuses on technical issues, in this paper I try to approach the problem from an epistemological angle. The discussion is driven by two questions: (1) What does typicality add to the concept of measure? (2) What kind of explanation, if any, does typicality yield? By distinguishing the notions of `typicality-as-vast-majority' and `typicality-as-best-exemplar', I argue that the (...) former goes beyond the concept of measure. Furthermore, I also argue that typicality aims at providing us with a form of causal explanation of equilibrium. (shrink)

Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of typicality-based explanations (...) of thermodynamic behaviour and evaluate their respective success. My conclusion will be that the boldest version fails for technical reasons, while more prudent versions leave unanswered essential questions. (shrink)

I want to combine two hitherto largely independent research projects, scientific understanding and mechanistic explanations. Understanding is not only achieved by answering why-questions, that is, by providing scientific explanations, but also by answering what-questions, that is, by providing what I call scientific descriptions. Based on this distinction, I develop three forms of understanding: understanding-what, understanding-why, and understanding-how. I argue that understanding-how is a particularly deep form of understanding, because it is based on mechanistic explanations, which answer why something happens in (...) virtue of what it is made of. I apply the three forms of understanding to two case studies: first, to the historical development of thermodynamics and, second, to the differences between the Clausius and the Boltzmann entropy in explaining thermodynamic processes. (shrink)

The paper uses the concept of typicality to spell out an argument against Humean supervenience and the best system account of laws. It proves that, in a very general and robust sense, almost all possible Humean worlds have no Humean laws. They are worlds of irreducible complexity that do not allow for any systematization. After explaining typicality reasoning in general, the implications of this result for the metaphysics of laws are discussed in detail.

This paper contributes to the clarification of the concept of “typicality” discussed in contemporary philosophy of physics by conceiving the nomological status of a typical behaviour such as that expressed in the Second Law of Thermodynamics as a “minutis rectis law”. A brief sketch of the discovery of “typicality” shows that there were ideas of typical behaviour not only in physics but also in sociology. On this basis and in analogy to the Second Law of Thermodynamics, it is shown that (...) the nomological status of sociological laws such as Gresham’s Law can also be conceived as “minutis rectis laws”. (shrink)

This paper aims to investigate the so-called paradox of deterministic probabilities: in a deterministic world, all probabilities should be subjective; however, they also seem to play important explanatory and predictive roles which suggest they are objective. The problem is then to understand what these deterministic probabilities are. Recent proposed solutions of this paradox are the Mentaculus vision, the range account of probability and a version of frequentism based on typicality. All these approaches aim at defining deterministic objective probabilities as to (...) make them compatible with determinism. In this paper, I argue that one can think of the equivalent of subjective and objective deterministic probabilities in terms of typicality. Also, I show that only what I identify with objective probabilities plays the necessary explanatory and predictive roles, while the subjective components essentially guide beliefs. In this way, the paradox is solved. (shrink)

I develop an account of naturalness in physics which demonstrates that naturalness assumptions are not restricted to narrow cases in high-energy physics but are a ubiquitous part of how interlevel relations are derived in physics. After exploring how and to what extent we might justify such assumptions on methodological grounds or through appeal to speculative future physics, I consider the apparent failure of naturalness in cosmology and in the Standard Model. I argue that any such naturalness failure threatens to undermine (...) the entire structure of our understanding of intertheoretic reduction, and so risks a much larger crisis in physics than is sometimes suggested; I briefly review some currently-popular strategies that might avoid that crisis. (shrink)

The problem of reconciling a reversible micro-dynamics with the second law of thermodynamics has been a scientific and conceptual challenge for centuries and it continues to animate heated debate even today. In my opinion, one key point lays in the interrelation between the physical, the mathematical and the philosophical aspects of the problem. In many treatments those domains of knowledge dangerously mix, generating confusion and misunderstanding. In this short work I will show how disentangling these three domains for the problem (...) at hand will give a better understanding of the enigma of irreversibility and opens up possibility for future research. (shrink)

The present article proposes to re-examine the parity-of-reasoning or double-standard fallacy argument, which favours a time-symmetric Gold universe model over a cosmological arrow of time. There are two reasons for this re-examination. One is empirical: the recent discovery of an expanding and accelerating universe questions the symmetry assumption of the Gold universe on empirical grounds. The other is theoretical: the argument from t-symmetry fails to take into account some important aspects of the topology of phase space and recently developed typicality (...) arguments. If the parity-of-reasoning argument, which depends on the t-symmetry of probability, is reconsidered in terms of the topology of phase space and typicality arguments, the double-standard fallacy argument loses much of its appeal. The Gold universe model itself suffers from unexplained dynamic asymmetries. The upshot of this article is that the Gold universe model is implausible or far less plausible than asymmetric models. (shrink)

We critically examine the role and status probabilities, as they enter via the Quantum Equilibrium Hypothesis, play in the standard, deterministic interpretation of deBroglie’s and Bohm’s Pilot Wave Theory (dBBT), by considering interpretations of probabilities in terms of ignorance, typicality and Humean Best Systems, respectively. We argue that there is an inherent conflict between dBBT and probabilities, thus construed. The conflict originates in dBBT’s deterministic nature, rooted in the Guidance Equation. Inquiring into the latter’s role within dBBT, we find it (...) explanatorily redundant (in particular for dBBT’s solution of the Measurement Problem, which only requires that the corpuscles possess definite positions), and subject to a number of difficulties. Following a suggestion from Bell, we propose to abandon the Guidance Equation, whilst retaining dBBT’s point particle-based Primitive Ontology, with positions as local beables. The resultant theory, which we identify as a stochastic, minimally deBroglie-Bohmian theory, describes a random walk through configuration space. Its probabilities, we propose, are best understood as dispositions of possible corpuscle configurations to manifest themselves. We subsequently evaluate the merits of sdBBT vis-à-vis dBBT, such as the justification of the Symmetrisation Postulate and the violation of the Action-Reaction Principle. Not only is sdBBT an attractive Bohmian theory that, whilst retaining dBBT's virtues, overcomes many of its shortcomings; it also sparks off a number of exciting follow-up questions, such as a comparison between sdBBT and other stochastic hidden-variable theories, e.g. Nelson Stochastics, or between sdBBT and the Everett interpretation. (shrink)

We often use symmetries to infer outcomes’ probabilities, as when we infer that each side of a fair coin is equally likely to come up on a given toss. Why are these inferences successful? I argue against answering this with an a priori indifference principle. Reasons to reject that principle are familiar, yet instructive. They point to a new, empirical explanation for the success of our probabilistic predictions. This has implications for indifference reasoning in general. I argue that a priori (...) symmetries need never constrain our probability attributions, even when it comes to our initial credences. (shrink)

A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper attempts to fill this gap. The paper first argues that Pitowsky's (2012) justification of typicality measures does not fit the bill. Then a first proposal of how to justify typicality measures is presented. The (...) main premises are that typicality measures are invariant and are related to the initial probability distribution of interest (which are translation-continuous or translation-close). The conclusions are two theorems which show that the standard measures of statistical mechanics and dynamical systems are typicality measures. There may be other typicality measures, but they agree about judgements of typicality. Finally, it is proven that if systems are ergodic or epsilon-ergodic, there are uniqueness results about typicality measures. (shrink)