Bayesian confirmation theory—abbreviated to in these notes—is the predominant approach to confirmation in late twentieth century philosophy of science. It has many critics, but no rival theory can claim anything like the same following. The popularity of the Bayesian approach is due to its flexibility, its apparently effortless handling of various technical problems, the existence of various a priori arguments for its validity, and its injection of subjective and contextual elements into the process of confirmation in just the places where (...) critics of earlier approaches had come to think that subjectivity and sensitivity to context were necessary. (shrink)

A physical system has a chaotic dynamics, according to the dictionary, if its behavior depends sensitively on its initial conditions, that is, if systems of the same type starting out with very similar sets of initial conditions can end up in states that are, in some relevant sense, very different. But when science calls a system chaotic, it normally implies two additional claims: that the dynamics of the system is relatively simple, in the sense that it can be expressed in (...) the form of a mathematical expression having relatively few variables, and that the the geometry of the system’s possible trajectories has a certain aspect, often characterized by a strange attractor. (shrink)

Russell famously argued that causation should be dispensed with. He gave two explicit arguments for this conclusion, both of which can be defused if we loosen the ties between causation and determinism. I show that we can define a concept of causation which meets Russell’s conditions but does not reduce to triviality. Unfortunately, a further serious problem is implicit beneath the details of Russell’s arguments, which I call the causal exclusion problem. Meeting this problem involves deploying a minimalist pragmatic account (...) of the nature and function of modal language. Russell’s scruples about causation can be accommodated, even as we partially legitimise the pervasive causal explanations in folk and scientific practice. (shrink)

The concept of randomness has been unjustly neglected in recent philosophical literature, and when philosophers have thought about it, they have usually acquiesced in views about the concept that are fundamentally flawed. After indicating the ways in which these accounts are flawed, I propose that randomness is to be understood as a special case of the epistemic concept of the unpredictability of a process. This proposal arguably captures the intuitive desiderata for the concept of randomness; at least it should suggest (...) that the commonly accepted accounts cannot be the whole story and more philosophical attention needs to be paid. 1. Randomness in science1.1Random systems1.2Random behaviour1.3Random sampling1.4Caprice, arbitrariness and noise2. Concepts of randomness2.1Von Mises/church/martin-löf randomness2.2KCS-randomness3. Randomness is unpredictability: preliminaries3.1Process and product randomness3.2Randomness is indeterminism?4. Predictability4.1Epistemic constraints on prediction4.2Computational constraints on prediction4.3Pragmatic constraints on prediction4.4Prediction defined5. Unpredictability6. Randomness is unpredictability6.1Clarification of the definition of randomness6.2Randomness and probability6.3Subjectivity and context sensitivity of randomness7. Evaluating the analysis[R]andomness … is going to be a concept which is relative to our body of knowledge, which will somehow reflect what we know and what we don't know. Henry E. Kyburg, Jr ([1974], p. 217)Phenomena that we cannot predict must be judged random. Patrick Suppes ([1984], p. 32). (shrink)

Recent debate on the nature of probabilities in evolutionary biology has focused largely on the propensity interpretation of fitness (PIF), which defines fitness in terms of a conception of probability known as “propensity”. However, proponents of this conception of fitness have misconceived the role of probability in the constitution of fitness. First, discussions of probability and fitness have almost always focused on organism effect probability, the probability that an organism and its environment cause effects. I argue that much of the (...) probability relevant to fitness must be organism circumstance probability, the probability that an organism encounters particular, detailed circumstances within an environment, circumstances which are not the organism’s effects. Second, I argue in favor of the view that organism effect propensities either don’t exist or are not part of the basis of fitness, because they usually have values close to 0 or 1. More generally, I try to show that it is possible to develop a clearer conception of the role of probability in biological processes than earlier discussions have allowed. (shrink)

Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the thermodynamic arrow of time can be grounded on typicality within statistical mechanics. This account, which I will call typicality frequentism, will evade the major criticisms raised against previous forms of frequentism. In this theory, probabilities arise within a physical theory from statistical (...) behavior of almost all initial conditions. The main advantage of typicality frequentism is that it shows which kinds of probabilities (that also have empirical relevance) can be derived from physics. Although one cannot recover all probability talk in this account, this is rather a virtue than a vice, because it shows which types of probabilities can in fact arise from physics and which types need to be explained in different ways, thereby opening the path for a pluralistic account of probabilities. (shrink)

Toy models are highly idealized and extremely simple models. Although they are omnipresent across scientific disciplines, toy models are a surprisingly under-appreciated subject in the philosophy of science. The main philosophical puzzle regarding toy models concerns what the epistemic goal of toy modelling is. One promising proposal for answering this question is the claim that the epistemic goal of toy models is to provide individual scientists with understanding. The aim of this article is to precisely articulate and to defend this (...) claim. In particular, we will distinguish between autonomous and embedded toy models, and then argue that important examples of autonomous toy models are sometimes best interpreted to provide how-possibly understanding, while embedded toy models yield how-actually understanding, if certain conditions are satisfied. _1_ Introduction _2_ Embedded and Autonomous Toy Models _2.1_ Embedded toy models _2.2_ Autonomous toy models _2.3_ Qualification _3_ A Theory of Understanding for Toy Models _3.1_ Preliminaries and requirements _3.2_ The refined simple view _4_ Two Kinds of Understanding with Toy Models _4.1_ Embedded toy models and how-actually understanding _4.2_ Against a how-actually interpretation of all autonomous toy models _4.3_ The how-possibly interpretation of some autonomous toy models _5_ Conclusion. (shrink)

One currently popular view about the nature of objective probabilities, or objective chances, is that they – or some of them, at least – are primitive features of the physical world, not reducible to anything else nor explicable in terms of frequencies, degrees of belief, or anything else. In this paper I explore the question of what the semantic content of primitive chance claims could be. Every attempt I look at to supply such content either comes up empty-handed, or begs (...) important questions against the skeptic who doubts the meaningfulness of primitive chance claims. In the second half of the paper I show that, by contrast, there are clear, and clearly contentful, ways to understand objective chance claims if we ground them on deterministic physical underpinnings. (shrink)

I present an account of deterministic chance which builds upon the physico-mathematical approach to theorizing about deterministic chance known as 'the method of arbitrary functions'. This approach promisingly yields deterministic probabilities which align with what we take the chances to be---it tells us that there is approximately a 1/2 probability of a spun roulette wheel stopping on black, and approximately a 1/2 probability of a flipped coin landing heads up---but it requires some probabilistic materials to work with. I contend that (...) the right probabilistic materials are found in reasonable initial credence distributions. I note that, with some normative assumptions, the resulting account entails that deterministic chances obey a variant of Lewis's 'principal principle'. I additionally argue that deterministic chances, so understood, are capable of explaining long-run frequencies. (shrink)

It is an ongoing controversy whether natural selection is a cause of population change, or a mere statistical description of how individual births and deaths accumulate. In this paper I restate the problem in terms of the reference class problem, and propose how the structure of stable equilibrium can provide a solution in continuity with biological practice. Insofar natural selection can be understood as a tendency towards equilibrium, key statisticalist criticisms are avoided. Further, in a modification of the Newtonian-force analogy, (...) it can be suggested that a better metaphor for natural selection is that of an emergent force, similar in nature to entropic forces: with magnitude and direction, but lacking a spatiotemporal origin or point of application. (shrink)

The authors survey some debates about the nature and structure of physical theories and about the connections between our physical theories and naturalized metaphysics. The discussion is organized around an “ideal view” of physical theories and criticisms that can be raised against it. This view includes controversial commitments regarding the best analysis of physical modalities and intertheory relations. The authors consider the case in favor of taking laws as the primary modal notion, discussing objections related to alleged violations of the (...) laws, the apparent need to appeal to causality, and the status of probability. The “ideal view” includes a commitment that fundamental physical theories are explanatorily sufficient. The authors discuss several challenges to recovering the manifest image from fundamental physics, along with a distinct challenge to reductionism based on acknowledging the contributions of less fundamental theories in physical explanations. (shrink)

Path-dependence offers a promising way of understanding the role historicity plays in explanation, namely, how the past states of a process can matter in the explanation of a given outcome. The two main existing accounts of path-dependence have sought to present it either in terms of dynamic landscapes or branching trees. However, the notions of landscape and tree both have serious limitations and have been criticized. The framework of causal networks is both more fundamental and more general that that of (...) landscapes and trees. Within this framework, I propose that historicity in networks should be understood as symmetry breaking. History matters when an asymmetric bias towards an outcome emerges in a causal network. This permits a quantitative measure for how path-dependence can occur in degrees, and offers suggestive insights into how historicity is intertwined both with causal structure and complexity. (shrink)

Contemporary complexity theory has been instrumental in providing novel rigorous definitions for some classic philosophical concepts, including emergence. In an attempt to provide an account of emergence that is consistent with complexity and dynamical systems theory, several authors have turned to the notion of constraints on state transitions. Drawing on complexity theory directly, this paper builds on those accounts, further developing the constraint-based interpretation of emergence and arguing that such accounts recover many of the features of more traditional accounts. We (...) show that the constraint-based account of emergence also leads naturally into a meaningful definition of self-organization, another concept that has received increasing attention recently. Along the way, we distinguish between order and organization, two concepts which are frequently conflated. Finally, we consider possibilities for future research in the philosophy of complex systems, as well as applications of the distinctions made in this paper. (shrink)

Climatology is a paradigmatic complex systems science. Understanding the global climate involves tackling problems in physics, chemistry, economics, and many other disciplines. I argue that complex systems like the global climate are characterized by certain dynamical features that explain how those systems change over time. A complex system's dynamics are shaped by the interaction of many different components operating at many different temporal and spatial scales. Examining the multidisciplinary and holistic methods of climatology can help us better understand the nature (...) of complex systems in general. -/- Questions surrounding climate science can be divided into three rough categories: foundational, methodological, and evaluative questions. "How do we know that we can trust science?" is a paradigmatic foundational question (and a surprisingly difficult one to answer). Because the global climate is so complex, questions like "what makes a system complex?" also fall into this category. There are a number of existing definitions of `complexity,' and while all of them capture some aspects of what makes intuitively complex systems distinctive, none is entirely satisfactory. Most existing accounts of complexity have been developed to work with information-theoretic objects (signals, for instance) rather than the physical and social systems studied by scientists. -/- Dynamical complexity, a concept articulated in detail in the first third of the dissertation, is designed to bridge the gap between the mathematics of contemporary complexity theory (in particular the formalism of "effective complexity" developed by Gell-Mann and Lloyd [2003]) and a more general account of the structure of science generally. Dynamical complexity provides a physical interpretation of the formal tools of mathematical complexity theory, and thus can be used as a framework for thinking about general problems in the philosophy of science, including theories, explanation, and lawhood. -/- Methodological questions include questions about how climate science constructs its models, on what basis we trust those models, and how we might improve those models. In order to answer questions about climate modeling, it's important to understand what climate models look like and how they are constructed. Climate model families are significantly more diverse than are the model families of most other sciences (even sciences that study other complex systems). Existing climate models range from basic models that can be solved on paper to staggeringly complicated models that can only be analyzed using the most advanced supercomputers in the world. I introduce some of the central concepts in climatology by demonstrating how one of the most basic climate models might be constructed. I begin with the assumption that the Earth is a simple featureless blackbody which receives energy from the sun and releases it into space, and show how to model that assumption formally. I then gradually add other factors (e.g. albedo and the greenhouse effect) to the model, and show how each addition brings the model's prediction closer to agreement with observation. After constructing this basic model, I describe the so-called "complexity hierarchy" of the rest of climate models, and argue that the sense of "complexity" used in the climate modeling community is related to dynamical complexity. -/- With a clear understanding of the basics of climate modeling in hand, I then argue that foundational issues discussed early in the dissertation suggest that computation plays an irrevocably central role in climate modeling. "Science by simulation" is essential given the complexity of the global climate, but features of the climate system--the presence of non-linearities, feedback loops, and chaotic dynamics--put principled limits on the effectiveness of computational models. This tension is at the root of the staggering pluralism of the climate model hierarchy, and suggests that such pluralism is here to stay, rather than an artifact of our ignorance. Rather than attempting to converge on a single "best fit" climate model, we ought to embrace the diversity of climate models, and view each as a specialized tool designed to predict and explain a rather narrow range of phenomena. Understanding the climate system as a whole requires examining a number of different models, and correlating their outputs. This is the most significant methodological challenge of climatology. -/- Climatology's role contemporary political discourse raises an unusually high number of evaluative questions for a physical science. The two leading approaches to crafting policy surrounding climate change center on mitigation (i.e. stopping the changes from occurring) and adaptation (making post hoc changes to ameliorate the harm caused by those changes). Crafting an effective socio-political response to the threat of anthropogenic climate change, however, requires us to integrate multiple perspectives and values: the proper response will be just as diverse and pluralistic as the climate models themselves, and will incorporate aspects of both approaches. I conclude by offering some concrete recommendations about how to integrate this value pluralism into our socio-political decision making framework. (shrink)

According to one large family of views, scientific explanations explain a phenomenon (such as an event or a regularity) by subsuming it under a general representation, model, prototype, or schema (see Bechtel, W., & Abrahamsen, A. (2005). Explanation: A mechanist alternative. Studies in History and Philosophy of Biological and Biomedical Sciences, 36(2), 421–441; Churchland, P. M. (1989). A neurocomputational perspective: The nature of mind and the structure of science. Cambridge: MIT Press; Darden (2006); Hempel, C. G. (1965). Aspects of scientific (...) explanation. In C. G. Hempel (Ed.), Aspects of scientific explanation (pp. 331–496). New York: Free Press; Kitcher (1989); Machamer, P., Darden, L., & Craver, C. F. (2000). Thinking about mechanisms. Philosophy of Science, 67(1), 1–25). My concern is with the minimal suggestion that an adequate philosophical theory of scientific explanation can limit its attention to the format or structure with which theories are represented. The representational subsumption view is a plausible hypothesis about the psychology of understanding. It is also a plausible claim about how scientists present their knowledge to the world. However, one cannot address the central questions for a philosophical theory of scientific explanation without turning one’s attention from the structure of representations to the basic commitments about the worldly structures that plausibly count as explanatory. A philosophical theory of scientific explanation should achieve two goals. The first is explanatory demarcation. It should show how explanation relates with other scientific achievements, such as control, description, measurement, prediction, and taxonomy. The second is explanatory normativity. It should say when putative explanations succeed and fail. One cannot achieve these goals without undertaking commitments about the kinds of ontic structures that plausibly count as explanatory. Representations convey explanatory information about a phenomenon when and only when they describe the ontic explanations for those phenomena. (shrink)

I define a concept of causal probability and apply it to questions about the role of probability in evolutionary processes. Causal probability is defined in terms of manipulation of patterns in empirical outcomes by manipulating properties that realize objective probabilities. The concept of causal probability allows us see how probabilities characterized by different interpretations of probability can share a similar causal character, and does so in such way as to allow new inferences about relationships between probabilities realized in different chance (...) setups. I clarify relations between probabilities and properties defined in terms of them, and argue that certain widespread uses of computer simulations in evolutionary biology show that many probabilities relevant to evolutionary outcomes are causal probabilities. This supports the claim that higher-level properties such as biological fitness and processes such as natural selection are causal properties and processes, contrary to what some authors have argued. (shrink)

In the methodology of scientific research programs (MSRP) there are important features on the problem of prediction, especially regarding novel facts. In his approach, Imre Lakatos proposed three different levels on prediction: aim, process, and assessment. Chapter 5 pays attention to the characterization of prediction in the methodology of research programs. Thus, it takes into account several features: (1) its pragmatic characterization, (2) the logical perspective as a proposition, (3) the epistemological component, (4) its role in the appraisal of research (...) programs, and (5) its place as a value for scientific research. -/- The notion of “novel facts” is highly relevant in his conception, where several aspects are involved: the directions of novel facts, the different kinds of novelty, and the transition from six possible options of “novel facts” to four choices. Thereafter, the prediction of novel facts as the criterion of appraisal is considered. On the one hand, this requires analyzing the theoretical, empirical, and heuristic possibilities of appraisal; and, on the other, whether there is an overemphasis on the role of prediction in methodology of scientific research programs. As a consequence, there is an analysis of Lakatos’ criterion of appraisal in MSRP and economics. (shrink)

Large changes of financial market prices without exogenous causes deviate significantly from the Gaussian behavior of random variables. This indicates that financial markets should be treated as complex systems, for which nonlinear interactions of its subunits/agents are crucial. I focus on how the complex systems perspective impacts the notion of explanations in economics. The mechanistic model seems to fit the bill, but problems surface on closer scrutiny. One characteristic of complex systems is that their behavior is surprisingly independent from microscopic (...) details. Thus, mechanistic explanations in the microreductionist manner seem unavailable. Despite these conflicts, I defend a modified structural mechanistic approach. (shrink)

In their influential paper “Ceteris Paribus, There is No Problem of Provisos”, Earman and Roberts (Synthese 118:439–478, 1999) propose to interpret the non-strict generalizations of the special sciences as statistical generalizations about correlations. I call this view the “statistical account”. Earman and Roberts claim that statistical generalizations are not qualified by “non-lazy” ceteris paribus conditions. The statistical account is an attractive view, since it looks exactly like what everybody wants: it is a simple and intelligible theory of special science laws (...) without the need for mysterious ceteris paribus conditions. I present two challenges to the statistical account. According to the first challenge, the statistical account does not get rid of so-called “non-lazy” ceteris paribus conditions. This result undermines one of the alleged and central advantages of the statistical account. The second challenge is that the statistical account, qua general theory of special science laws, is weakened by the fact that idealized law statements resist a purely statistical interpretation. (shrink)

This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction.In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebuttal. I focus on limiting relations between theories and illustrate my claims with four examples, each (...) of them a model or a framework for modelling, from well-established mathematics or physics.I take emergence as behaviour that is novel and robust relative to some comparison class. I take reduction as, essentially, deduction. The main idea of my first rebuttal will be to perform the deduction after taking a limit of some parameter. Thus my first main claim will be that in my four examples (and many others), we can deduce a novel and robust behaviour, by taking the limit N→∞ of a parameter N.But on the other hand, this does not show that the N=∞ limit is “physically real”, as some authors have alleged. For my second main claim is that in these same examples, there is a weaker, yet still vivid, novel and robust behaviour that occurs before we get to the limit, i.e. for finite N. And it is this weaker behaviour which is physically real.My examples are: the method of arbitrary functions (in probability theory); fractals (in geometry); superselection for infinite systems (in quantum theory); and phase transitions for infinite systems (in statistical mechanics). (shrink)

This chapter will review selected aspects of the terrain of discussions about probabilities in statistical mechanics (with no pretensions to exhaustiveness, though the major issues will be touched upon), and will argue for a number of claims. None of the claims to be defended is entirely original, but all deserve emphasis. The first, and least controversial, is that probabilistic notions are needed to make sense of statistical mechanics. The reason for this is the same reason that convinced Maxwell, Gibbs, and (...) Boltzmann that probabilities would be needed, namely, that the second law of thermodynamics, which in its original formulation says that certain processes are impossible, must, on the kinetic theory, be replaced by a weaker formulation according to which what the original version deems impossible is merely improbable. Second is that we ought not take the standard measures invoked in equilibrium statistical mechanics as giving, in any sense, the correct probabilities about microstates of the system. We can settle for a much weaker claim: that the probabilities for outcomes of experiments yielded by the standard distributions are effectively the same as those yielded by any distribution that we should take as a representing probabilities over microstates. Lastly, (and most controversially): in asking about the status of probabilities in statistical mechanics, the familiar dichotomy between epistemic probabilities (credences, or degrees of belief) and ontic (physical) probabilities is insufficient; the concept of probability that is best suited to the needs of statistical mechanics is one that combines epistemic and physical considerations. (shrink)

I describe a realist, ontologically objective interpretation of probability, "far-flung frequency (FFF) mechanistic probability". FFF mechanistic probability is defined in terms of facts about the causal structure of devices and certain sets of frequencies in the actual world. Though defined partly in terms of frequencies, FFF mechanistic probability avoids many drawbacks of well-known frequency theories and helps causally explain stable frequencies, which will usually be close to the values of mechanistic probabilities. I also argue that it's a virtue rather than (...) a failing of FFF mechanistic probability that it does not define single-case chances, and compare some aspects of my interpretation to a recent interpretation proposed by Strevens. (shrink)

The concept of hierarchical organization is commonplace in science. Subatomic particles compose atoms, which compose molecules; cells compose tissues, which compose organs, which compose organisms; etc. Hierarchical organization is particularly prominent in ecology, a field of research explicitly arranged around levels of ecological organization. The concept of levels of organization is also central to a variety of debates in philosophy of science. Yet many difficulties plague the concept of discrete hierarchical levels. In this paper, we show how these difficulties undermine (...) various implications ascribed to hierarchical organization, and we suggest the concept of scale as a promising alternative to levels. Investigating causal processes at different scales offers a way to retain a notion of quasi-levels that avoids the difficulties inherent in the classic concept of hierarchical levels of organization. Throughout, our focus is on ecology, but the results generalize to other invocations of hierarchy in science and philosophy of science. (shrink)

This chapter explores a philosophical hypothesis about the nature of (some) probabilities encountered in social sciences. It should be of interest to those with philosophical concerns about the foundations of probability, and to social scientists and philosophers of science who are somewhat puzzled by the nature of probability in social domains. As will become clear below, the chapter is not intended as a contribution to an empirical methodology such as a particular way of applying statistics.

An historically important conception of the unity of science is explanatory reductionism, according to which the unity of science is achieved by explaining all laws of science in terms of their connection to microphysical law. There is, however, a separate tradition that advocates the unity of science. According to that tradition, the unity of science consists of the coordination of diverse fields of science, none of which is taken to have privileged epistemic status. This alternate conception has roots in Otto (...) Neurath’s notion of unified science. In this paper, I develop a version of the coordination approach to unity that is inspired by Neurath’s views. The resulting conception of the unity of science achieves aims similar to those of explanatory reductionism, but does so in a radically different way. As a result, it is immune to the criticisms facing explanatory reductionism. This conception of unity is also importantly different from the view that science is disunified, and I conclude by demonstrating how it accords better with scientific practice than do conceptions of the disunity of science. (shrink)

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

To understand the behavior of a complex system, you must understand the interactions among its parts. Doing so is difficult for non-decomposable systems, in which the interactions strongly influence the short-term behavior of the parts. Science's principal tool for dealing with non-decomposable systems is a variety of probabilistic analysis that I call EPA. I show that EPA's power derives from an assumption that appears to be false of non-decomposable complex systems, in virtue of their very non-decomposability. Yet EPA is extremely (...) successful. I aim to find an interpretation of EPA's assumption that is consistent with, indeed that explains, its success. (shrink)

Ruth Millikan and others advocate theories which attempt to naturalize wide mental content (e.g. beliefs.

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)

‘Those ice cubes melted because by melting total entropy increased and entropy increase has a very high objective chance.’ What role does the chance in this explanation play? I argue that it contributes to the explanation by entailing that the melting was almost necessary, and defend the claim that the fact that some event was almost necessary can, in the right circumstances, constitute a causal explanation of that event.

This paper offers a metaphysics of physical probability in (or if you prefer, truth conditions for probabilistic claims about) deterministic systems based on an approach to the explanation of probabilistic patterns in deterministic systems called the method of arbitrary functions. Much of the appeal of the method is its promise to provide an account of physical probability on which probability assignments have the ability to support counterfactuals about frequencies. It is argued that the eponymous arbitrary functions are of little philosophical (...) use, but that they can be substituted for facts about frequencies without losing the ability to provide counterfactual support. The result is an account of probability in deterministic systems that has a “propensity-like” look and feel, yet which requires no supplement to the standard modern empiricist tool kit of particular matters of fact and principles of physical dynamics. (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)

Sciences of complex systems thrive on compositional theories – toolkits that allow the construction of models of a wide range of systems, each consisting of various parts put together in different ways. To be tractable, a compositional theory must make shrewd choices about the parts and properties that constitute its basic ontology. One such choice is to decompose a system into spatiotemporally discrete parts. Compositional theories in the high-level sciences follow this rule of thumb to a certain extent, but they (...) also make essential use of what I call distributed ontologies: divisions of the system into entities or states of affairs each depending on sets of fundamental-level facts that to a large extent overlap. The point is developed using the example of statistical theories in which the probabilities are ontologically distributed. (shrink)

In an influential paper, James Lenman argues that consequentialism can provide no basis for ethical guidance, because we are irredeemably ignorant of most of the consequences of our actions. If our ignorance of distant consequences is great, he says, we can have little reason to recommend one action over another on consequentialist grounds. In this article, I show that for reasons to do with statistical theory, the cluelessness objection is too pessimistic. We have good reason to believe that certain patterns (...) of action will tend to have better consequences, and we have good reason to recommend acting in accordance with strategies based on those advantageous patterns. I close by saying something about the strategies that this argument should lead us to favour. (shrink)

One of a pair of reviews of Michael Strevens’ book, Tychomancy: Inferring Probability from Causal Structure, Harvard University Press, Cambridge, MA, 2013, pp 265, $39.95 hbk, ISBN 978-0674073111. See also Bookstein (2014, this issue).

Renormalization group (RG) methods are an established strategy to explain how it is possible that microscopically different systems exhibit virtually the same macro behavior when undergoing phase-transitions. I argue – in agreement with Robert Batterman – that RG explanations are non-causal explanations. However, Batterman misidentifies the reason why RG explanations are non-causal: it is not the case that an explanation is non- causal if it ignores causal details. I propose an alternative argument, according to which RG explanations are non-causal explanations (...) because their explanatory power is due to the application mathematical operations, which do not serve the purpose of representing causal relations. (shrink)

International Studies in the Philosophy of Science, Volume 27, Issue 3, Page 273-293, September 2013.

Assumptions of stochastic independence are crucial to statistical models in science. Under what circumstances is it reasonable to suppose that two events are independent? When they are not causally or logically connected, so the standard story goes. But scientific models frequently treat causally dependent events as stochastically independent, raising the question whether there are kinds of causal connection that do not undermine stochastic independence. This paper provides one piece of an answer to this question, treating the simple case of two (...) tossed coins with and without a midair collision. (shrink)

Geologists, Paleontologists and other historical scientists are frequently concerned with narrative explanations targeting single cases. I show that two distinct explanatory strategies are employed in narratives, simple and complex. A simple narrative has minimal causal detail and is embedded in a regularity, whereas a complex narrative is more detailed and not embedded. The distinction is illustrated through two case studies: the ‘snowball earth’ explanation of Neoproterozoic glaciation and recent attempts to explain gigantism in Sauropods. This distinction is revelatory of historical (...) science. I argue that at least sometimes which strategy is appropriate is not a pragmatic issue, but turns on the nature of the target. Moreover, the distinction reveals a counterintuitive pattern of progress in some historical explanation: shifting from simple to complex. Sometimes, historical scientists rightly abandon simple, unified explanations in favour of disunified, complex narratives. Finally I compare narrative and mechanistic explanation, arguing that mechanistic approaches are inappropriate for complex narrative explanations. (shrink)

Kevin Davey claims that the justification of the second law of thermodynamics as it is conveyed by the “standard story” of statistical mechanics, roughly speaking, that lowentropy microstates tend to evolve to high-entropy microstates, is “unhelpful at best and wrong at worst.” In reply, I demonstrate that Davey’s argument for rejecting the standard story commits him to a form of skepticism that is more radical than the position he claims to be stating and that Davey places unreasonable demands on the (...) notion of justification in the physical sciences. (shrink)

Sewall Wright ’s FST is a mathematical test widely used in empirical applications to characterize genetic and other differences between subpopulations, and to identify causes of those differences. Cockerham and Weir’s popular approach to statistical estimation of FST is based on an assumption sometimes formulated as a claim that actual populations tested are sampled from.

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)

Complexity theory attempts to explain, at the most general possible level, the interesting behaviors of complex systems. Two such behaviors are the emergence of simple or stable high-level behavior from relatively complex low-level behavior, and the emergence of sophisticated high-level behavior from relatively simple low-level behavior; they are often found nested in the same system. Concerning the emergence of simplicity, this essay examines Herbert Simon's explanation from near-decomposability and a stochastic explanation that generalizes the approach of statistical physics. A more (...) general notion of an abstract difference-making structure is introduced with examples, and a discussion of evolvability follows. Concerning the emergence of sophistication, this essay focuses on, first, the energetics approach associated with dissipative structures and the fourth law of thermodynamics, and second, the notion of a complex adaptive system. (shrink)

There is something genuinely puzzling about large-scale simplicity emerging in systems that are complex at the small scale. Consider, for example, a population of hares. Clearly, the number of hares at any given time depends on hare fertility rates, the weather, the number of predators, the health of the predators, availability of hare resources, motor vehicle traffic, individual hare locations, colour of individual hares, and so on. Indeed, given the incredibly complexity of the hares’ environment at the small-scale, it is (...) amazing that anything can be said about hare abundances. But not only can we say something about hare abundances, we can formulate equations for hare abundance as a function of time that are remarkably accurate. But most amazing of all is that such equations have very few parameters—in the simplest cases, just the growth rate and an initial population abundance. How can this be? How can we ignore all the small-scale factors when they clearly play major roles in determining abundance? Put somewhat more grandiosely: How is population ecology possible? Of course it’s not just population ecology that exhibits such small-scale complexity and large-scale simplicity. Other important systems include the weather and gases in equilibrium. The examples can easily be multiplied. The general problem is the same: How can seemingly unpredictable and complex microbehaviour of complex systems result in predictable and simple macrobehaviour? Providing an answer to this question is the central task of Michael Strevens’ excellent book Bigger than Chaos : Understanding Complexity through Probability. (shrink)

Though some influentially critical objections have been raised during the ‘classical’ pre-computational simulation philosophy of science tradition, suggesting a more nuanced methodological category for experiments, it safe to say such critical objections have greatly proliferated in philosophical studies dedicated to the role played by computational simulations in science. For instance, Eric Winsberg suggests that computer simulations are methodologically unique in the development of a theory’s models suggesting new epistemic notions of application. This is also echoed in Jeffrey Ramsey’s notions of (...) “transformation reduction,”—i.e., a notion of reduction of a more highly constructive variety. Computer simulations create a broadly continuous arena spanned by normative and descriptive aspects of theory-articulation, as entailed by the notion of transformation reductions occupying a continuous region demarcated by Ernest Nagel’s logical-explanatory “domain-combining reduction” on the one hand, and Thomas Nickels’ heuristic “domain-preserving reduction,” on the other. I extend Winsberg’s and Ramsey’s points here, by arguing that in the field of computational fluid dynamics as well as in other branches of applied physics, the computer plays a constitutively experimental role—supplanting in many cases the more traditional experimental methods such as flow-visualization, etc. In this case, however CFD algorithms act as substitutes, not supplements when it comes to experimental practices. I bring up the constructive example involving the Clifford-Algebraic algorithms for modeling singular phenomena in CFD by Gerik Scheuermann and Steven Mann & Alyn Rockwood who demonstrate that their algorithms offer greater descriptive and explanatory scope than the standard Navier-Stokes approaches. The mathematical distinction between Navier-Stokes-based and Clifford-Algebraic based CFD has essentially to do with the regularization features exhibited to a far greater extent by the latter, than the former. Hence, CACFD indicate that the utilization of computational techniques can be based on principled reasons, as opposed to merely practical. CACFD hence exhibit a new generative role in the field of fluid mechanics, by offering categories of experimental evidence that are optimally descriptive and explanatory—i.e., pace Batterman can be both ontologically and epistemically fundamental. (shrink)