Simplicity and Parsimony

Physical laws are strikingly simple, although there is no a priori reason they must be so. I propose that nomic realists of all types (Humeans and non-Humeans) should accept that simplicity is a fundamental epistemic guide for discovering and evaluating candidate physical laws. This principle of simplicity clarifies and addresses several problems of nomic realism and simplicity. A consequence is that the oft-cited epistemic advantage of Humeanism over non-Humeanism disappears, undercutting an influential epistemological argument for Humeanism. Moreover, simplicity is shown (...) to be more tightly connected to lawhood than to mere truth. (shrink)

Occam’s razor is frequently considered to be a cornerstone of the scientific method. Indeed, it was and remains a valuable tool for scientific and philosophical inquiry. However, we provided an overview of some historical instances in which it led science away from a reasonable and sound heuristic approach. Some words of caution are necessary to clarify how, contrary to common belief, a too strict adherence to such a principle did not guarantee scientific rigor but, rather, obstructed further progress.

In this note, I discuss the simplicity of rival statistical explanations of a correlation, couched in terms of Reichenbachian Common Cause Systems. Simplicity is analyzed in two components, the so-called intrinsic and contextual simplicity. I show that if one disentangles simplicity from explanatory power then the size of the system provides an adequate for simplicity in both of its dimensions.

given at the 2007 Formal Epistemology Workshop at Carnegie Mellon June 2nd. Good compression must track higher vs lower probability of inputs, and this is one way to approach how simplicity tracks truth.

This essay discusses Peter Langland-Hassan's approach to "explaining imagination" as it plays out in his recent book of that title. Langland-Hassan offers a theory of “attitude imagining” that avoids positing what he calls a “sui generis cognitive attitude.” This theory attempts to explain things like pretend play, hypothetical reasoning, and cognition of fiction; to explain them using only (what he calls) more “basic” mental states like beliefs and desires; and thus to explain them without positing a distinct cognitive attitude of (...) imagining, as many theorists do (including me). In other words, “attitude imagining,” for Langland-Hassan, is whatever explains those things (except for a distinct cognitive attitude of imagining itself). Despite the theoretical interest of this approach, I argue it is ontologically pennywise and pound foolish: for a slight savings in ontological complexity it dramatically reduces explanatory power. (shrink)

As Nelson Goodman highlighted, there are two main senses of “abstract” that can be found in discussions about abstract art. On the one hand, a representation is abstract if it leaves out certain features of its target. On the other hand, something can be abstract to the extent that it does not represent a concrete subject. The first sense of “abstract” is well-known in philosophy of science. For example, philosophers discuss mathematical models of physical, biological, and economic systems as being (...) abstract in this sense. However, it is the second sense that dominates discussions of abstract art in aesthetics. For example, abstract art was (and is) considered revolutionary precisely for being non-figurative. Through an analysis of artists including Kandinsky, Malevich, and Mondrian, we develop a reading of this second sense, which we call “generative abstraction,” as opposed to “subtractive” abstraction. Generative abstraction is a process in which a new artifact is created which does not represent the initial concrete target system that inspired it (if there was one), where the artifact’s features are explored for their own sake, and where the “language” of the new artifact is in some way more “universal.” Focusing on this sense of abstraction is helpful in revealing the complexity of the process of crafting an abstract artifact, in problematizing the notion that abstraction can always be un-done (or concretized), as well as revealing new ways for abstractions to be epistemically (un)successful. (shrink)

Metaphysicians often claim that some metaphysical theory should (or shouldn’t) be believed because it exhibits (or fails to exhibit) theoretical virtues such as simplicity. Metaphysicians also sometimes claim that the legitimacy of these sorts of appeals to theoretical virtues are vindicated by the similar appeals to theoretical virtues which scientists make in scientific theory choice. One objection to this methodological move is to claim that the metaphysician misdescribes the role that theoretical virtues play within science. In this paper I defend (...) the metaphysician’s use of theoretical virtues against this objection. (shrink)

The framework of Solomonoff prediction assigns prior probability to hypotheses inversely proportional to their Kolmogorov complexity. There are two well-known problems. First, the Solomonoff prior is relative to a choice of Universal Turing machine. Second, the Solomonoff prior is not computable. However, there are responses to both problems. Different Solomonoff priors converge with more and more data. Further, there are computable approximations to the Solomonoff prior. I argue that there is a tension between these two responses. This is because computable (...) approximations to Solomonoff prediction do not always converge. (shrink)

The idea that “simplicity is a sign of truth”, and the related “Occam’s razor” principle, stating that, all other things being equal, simpler models should be preferred to more complex ones, have been long discussed in philosophy and science. We explore these ideas in the context of supervised machine learning, namely the branch of artificial intelligence that studies algorithms which balance simplicity and accuracy in order to effectively learn about the features of the underlying domain. Focusing on statistical learning theory, (...) we show that situations exist for which a preference for simpler models provably slows down, instead of favoring, the supervised learning process. Our results shed new light on the relations between simplicity and truth approximation, which are briefly discussed in the context of both machine learning and the philosophy of science. (shrink)

In this article, I will provide a critical overview of the form of non-deductive reasoning commonly known as “Inference to the Best Explanation” (IBE). Roughly speaking, according to IBE, we ought to infer the hypothesis that provides the best explanation of our evidence. In section 2, I survey some contemporary formulations of IBE and highlight some of its putative applications. In section 3, I distinguish IBE from C.S. Peirce’s notion of abduction. After underlining some of the essential elements of IBE, (...) the rest of the entry is organized around an examination of various problems that IBE confronts, along with some extant attempts to address these problems. In section 4, I consider the question of when a fact requires an explanation, since presumably IBE applies only in cases where some explanation is called for. In section 5, I consider the difficult question of how we ought to understand IBE in light of the fact that among philosophers, there is significant disagreement about what constitutes an explanation. In section 6, I consider different strategies for justifying the truth-conduciveness of the explanatory virtues, e.g., simplicity, unification, scope, etc., criteria which play an indispensable role in any given application of IBE. In section 7, I survey some of the most recent literature on IBE, much of which consists of investigations of the status of IBE from the standpoint of the Bayesian philosophy of science. (shrink)

In recent discussions of the Humean Theory of Motivation (HTM), several authors – not to mention other philosophers around the proverbial water cooler – have appealed to the simplicity of the theory to defend it. But the argument from simplicity has rarely been explicated or received much critical attention – until now. I begin by reconstructing the argument and then argue that it suffers from a number of problems. Most importantly, first, I argue that HTM is unlikely to be simpler (...) than even close competing theories, and second, it is unlikely that a plausible version of the theory will be very simple. Moreover, I argue that a convincing case for HTM is likely to have to show that it is more virtuous than defenders have done so far. (shrink)

It is a common view among philosophers of science that theoretical virtues (also known as epistemic or cognitive values), such as simplicity and consistency, play an important role in scientific practice. In this article, I set out to study the role that theoretical virtues play in scientific practice empirically. I apply the methods of data science, such as text mining and corpus analysis, to study large corpora of scientific texts in order to uncover patterns of usage. These patterns of usage, (...) in turn, might shed some light on the role that theoretical virtues play in scientific practice. Overall, the results of this empirical study suggest that scientists invoke theoretical virtues explicitly, albeit rather infrequently, when they talk about models (less than 30%), theories (less than 20%), and hypotheses (less than 15%) in their published works. To the extent that they are mentioned in scientific publications, the results of this study suggest that accuracy, consistency, and simplicity are the theoretical virtues that scientists invoke more frequently than the other theoretical virtues tested in this study. Interestingly, however, depending on whether they talk about hypotheses, theories, or models, scientists may invoke one of those theoretical virtues more than the others. (shrink)

This paper argues that all of the standard theories about the divisions of space and time can benefit from, and may need to rely on, parsimony considerations. More specifically, whether spacetime is discrete, gunky or pointy, there are wildly unparsimonious rivals to standard accounts that need to be resisted by proponents of those accounts, and only parsimony considerations offer a natural way of doing that resisting. Furthermore, quantitative parsimony considerations appear to be needed in many of these cases.

Over the past decade, in contrast to the traditional analytic version of metaphysics, a brand of metaphysics that prioritizes collaboration and corroboration with sciences has emerged in the form of scientific metaphysics. While there has been a shift from the methodological dependence of analytic metaphysis on intuition, and conceptual analysis to the methodological preference for empirically-motivated metaphysical insights in scientific metaphysics, such a shift has not penetrated the foundational aims. Scientific metaphysics continues to probe the nature and structure of reality, (...) much like its analytic counterpart and in this process, develops ontologies. Broadly two kinds of ontologies are furnished - global metaphysical ontologies and local scientific ontologies. In this paper, I highlight the challenges with developing such ontologies in scientific metaphysics. With Ladyman-Ross’ Information Theoretic Structural Realism as a case in point, I contest that the former suffers from representational indeterminacy and redundancy. Further, I note the possibility that eventually, local scientific ontologies might be replaced by scientific theories and in such a scenario, the former are best conceived as interim metaphysical supports for the latter. (shrink)

Quine taught us the difference between a theory’s ontology and its ideology. Ontology is the things a theory’s quantifiers must range over if it is true, Ideology is the primitive concepts that must be used to state the theory. This allows us to split the theoretical virtue of parsimony into two kinds: ontological parsimony and ideological parsimony. My goal is help illuminate the virtue of ideological parsimony by giving a criterion for ideological innocence—a rule for when additional ideology does not (...) count against parsimony. I propose the expressive power innocence criterion: if the ideology of theory one is expressively equivalent to that of theory two, then neither is ideologically simpler than the other. In its favor I offer the argument from accuracy, showing that any account of a theoretical virtue that is supposed to make theories that have it more likely to be true than theories that do not must respect it. Next I consider its ramifications, eliminating rival views and passing judgment on some arguments from parsimony that can be found in the literature. Finally, I consider two objections. First: I address an objection arising from the possibility of languages with a ‘primitive’ operator that allows us to list a theory’s primitives in the object-language. Second: I address an objection raised by Nelson Goodman against attempts to reckon simplicity by expressive power. Both objections fail. (shrink)

Theoretical virtues play an important role in the acceptance and belief of theories in science and philosophy. Philosophers have well-developed views on which virtues ought and ought not to influence one’s acceptance and belief. But what do scientists think? This paper presents the results of a quantitative study with scientists from the natural and social sciences and compares their views to those held by philosophers. Some of the more surprising results are: all three groups have a preference order regarding theoretical (...) virtues, making theory choice a much more determinate matter than what has sometimes been suggested; the preference orders are very similar for the three groups; simplicity is viewed as an epistemic virtue particularly by social scientists ; and syntactic parsimony is preferred to ontological parsimony by all three groups. (shrink)

W. V. Quine calls some general methods of science maxims: general defeasible principles that call on us to approximate, maximize, or minimize a state and that are interpreted and weighed in context-sensitive ways. On my reading, his empiricism asks us to maximize accepting overall theories empirically equivalent to ours but to minimize accepting sentences that both do not affect the empirical content of our overall theory and do not simplify our overall theory. His naturalism asks us to maximize accepting sentences (...) that are solely supported by standards that support our best current scientific theory. Drawing on the Quine archive at Houghton Library at Harvard, I support and apply these interpretations by investigating his rapidly evolving later work on empirical content and empirical equivalence, including some of his views on translation in this later work and his vacillation between what he calls the ecumenical and sectarian attitudes. (shrink)

I articulate a Global Best-System Account (GBSA) of laws of nature along broadly Mill–Ramsey–Lewis lines. The guiding idea is that the job of laws is to capture real patterns across time—where a pattern is real if it allows to compress information about matters of particular fact. The GBSA’s key ingredient is a definition of ‘best system’ in terms of a ranking method that meets a number of desiderata: it is rigorously defined; it outputs the ranking based on the candidate systems’ (...) epistemic virtues; it is objective, in that the output does not depend on one’s choice of basic concepts; it avoids two trivialization results (by Lewis, and Arrow-Okasha); and it does not appeal to naturalness, or other metaphysical notions in that vicinity. Although the GBSA is independent of the controversial thesis of Humean Supervenience, it satisfies the weaker thesis that laws of nature supervene on the total physical state of the world. Moreover, the resulting notion of lawhood is hyperintensional, unlike the neighboring notion of nomological necessity. Finally, GBSA-laws do not track naturalness, contra the Lewisian orthodoxy. (shrink)

This article argues that holistic ecocentrism unnecessarily introduces elements to explain why we ought to halt biodiversity loss. I suggest that atomistic accounts can justify the same conclusion by utilising fewer elements. Hence, why we ought to preserve biodiversity can be made reasonable without adding elements such as intrinsic values of ecosystems or moral obligations to conserve collectives of organisms. Between two equally good explanations of the same phenomenon, the explanation utilising fewer elements, which speaks in favour of atomistic accounts, (...) will be the better one. (shrink)

The role of judgments of beauty in scientific theory evaluation is the subject of significant debate in contemporary philosophy of science. This book advances that debate by broadening its scope. In Judgments of Beauty in Theory Evaluation, the author argues that judgments of beauty are a justified part of theory evaluation of all sorts: not only scientific theory evaluation, but also philosophical theory evaluation. The author argues for this thesis by providing an account of beauty—inherited from Kant and Mothersill—on which (...) the distinctive nature of judgments of beauty is that they are unprincipled, yet possible. The author then analyzes two important methods of theory evaluation—reflective equilibrium and simplicity—and argues that these methods require making judgments of beauty so understood. Finally, the author argues that these methods of theory evaluation are not anomalies, but that they point to a deeper lesson about the nature of theorizing and the necessity of using judgments of beauty to evaluate systems, like theories. This conclusion has implications for the debate in philosophy of science over judgments of beauty, but also prompts a reckoning in philosophy itself over the use of judgments of beauty in philosophical theory evaluation. (shrink)

For computer simulation models to usefully inform climate risk management, uncertainties in model projections must be explored and characterized. Because doing so requires running the model many ti...

Nietzsche sometimes praises the drive to order—to simplify, organize, and draw clear boundaries—as expressive of a vital "classical" style, or an Apollonian artistic drive to calmly contemplate forms displaying "epic definiteness and clarity." But he also sometimes harshly criticizes order, as in the pathological dialectics or "logical schematism" that he associates paradigmatically with Socrates. I challenge a tradition that interprets Socratism as an especially one-sided expression of, or restricted form of attention to, the Apollonian: they are more radically disparate. Beyond (...) strengthening the case for this basic point, I develop a distinctive account of what, exactly, distinguishes the Apollonian-classical and Socratic forms of order. To this end, I advance interrelated interpretations of Apollonian-classical simplicity and the "cold" calm that it elicits, by contrast to superficially similar Socratic phenomena. This illuminates Nietzsche's broader ambivalence toward science, in part by clarifying the nature and value of an idealized Apollonian science. (shrink)

I argue that if simplicity is a theoretical virtue and some theoretical virtues are the constituents of the aims of theorizing in physics—i.e., theory choice and theory development in physics—and scientific rationality is instrumental rationality, then simplicity cannot be a mere means to achieve the aims. I do this by showing that considering simplicity as a mere means brings about counterintuitive ramifications concerning scientific rationality. These counterintuitive ramifications can be avoided if we consider simplicity a constituent of the aims of (...) theorizing in physics. (shrink)

The history of the philosophy of thought experiments has touched on the work of Kuhn, Popper, Duhem, Mach, Lakatos, and other big names of the 20th century, but so far, almost nothing has been written about Paul Feyerabend. His most influential work was Against Method, 8 chapters of which concern a case study of Galileo with a specific focus on Galileo’s thought experiments. In addition, the later Feyerabend was very interested in what might be called the epistemology of drama, including (...) stories and myths. This paper brings these different aspects of Feyerabend’s work together in an attempt to present what might have been his considered views on scientific thought experiments. I conclude by contrasting Feyerabend’s ideas with two modern currents in the debate surrounding thought experiments: 1) the claim that the epistemology of thought experiments is just the epistemology of deductive or inductive arguments, and 2) the claim that the specifically narrative quality of thought experiments must be taken into account if we want a complete epistemology of thought experiments. (shrink)

For a long time, the accepted explanatory model of language acquisition was the so-called Principles and Parameters framework (P&P). P&P seemingly provides an elegant answer to the central puzzle of generative linguistics: How do children acquire their native language given the limited time and input resources available to them? Yet P&P tells a story that is evolutionarily implausible, and for this reason it has since been abandoned. I argue that this is an unwarranted move, and that it could and should (...) be avoided by reassessing the epistemic status of P&P. In particular, I argue that contrary to extant accounts, P&P ought to be retrospectively construed as a highly idealized (toy) model of language acquisition. The proposed reinterpretation is vindicated, I argue, insofar as it paves the way for a reconciliation of the two central explanatory challenges of modern generative linguistics. (shrink)

This paper is part of the general debate about the need to rethink economics as a human discipline using a heuristic to describe its object, about the need to explicitly reject the positivistic approach in neoclassical economics, and about the urgency to adopt a different methodology, grounded on a realistic set of initial assumptions able to cope with the complexity of the decision making process. The aim of this paper is to show the use of Occam's razor in the economic (...) debate around realism in economic modelling. Occam's razor can be intended as a principle of logic that emphasises simplicity, or as a heuristic tool that emphasises parsimony. Neoclassical economists, such as Samuelson, have explicitly used Occam's razor as a logical principle to highlight the strict logic and simplicity of neoclassical economics; neoclassical models, however, are based on unrealistic assumptions. Some approaches of heterodox economics, au contraire, have used Occam's razor as a powerful heuristic tool to emphasise parsimony, building up models grounded on realistic initial assumptions and capable of embedding complexity into the general explanation of economic behaviour, as in Simon's bounded rationality (1955; 1957) and Hayek's notion of human rationality (1948; 1952; 1974) and cultural and social evolution (1967; 1978). (shrink)

The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks what probabilities are (...) not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the “problem of the priors.”. (shrink)

Ockham’s Razor advises us to not multiply entities without necessity. Recently, Jonathan Schaffer and Karen Bennett have argued that we ought to replace Ockham’s Razor with the Laser, the principle that only advises us to not multiply fundamental entities without necessity. In this paper, I argue that Ockham’s Razor is preferable to the Laser. I begin by contending that the arguments offered for the Laser by Schaffer and Bennett are unpersuasive. Then I offer two cases of theory assessment that I (...) believe the Razor handles better than the Laser. Finally, I argue that accepting the Laser gives rise to a difficult explanatory challenge: It is difficult to explain why fundamental entities and non-fundamental entities ought to be treated differently in ontological parsimony assessments. A recurring secondary theme of the paper is that the most tempting ways of responding to my arguments frequently result in the Laser losing much of its significance for debates about ontology. Thus, not only is it difficult to defend a preference for the Laser over the Razor, but it is especially difficult to do so while maintaining the Laser’s dialectical significance. (shrink)

Computer scientists have provided a distinct justification of Occam’s Razor. Using the probably approximately correct framework, they provide a theorem that they claim demonstrates that we should favor simpler hypotheses. The argument relies on a philosophical interpretation of the theorem. I argue that the standard interpretation of the result in the literature is misguided and that a better reading does not, in fact, support Occam’s Razor at all. To this end, I state and prove a very similar theorem that, if (...) interpreted the same way, would justify the contradictory Anti-Occam’s Razor—the principle that we should favor more complex hypotheses. (shrink)

En metafísica contemporánea, es común trabajar bajo una metodología basada en virtudes teóricas. En caso de disputa, esta metodología nos aconseja elegir la teoría que mejor satisfaga las virtudes teóricas estándar: precisión empírica, fecundidad, poder unificador, consistencia y simplicidad. Sin embargo, no hay consenso sobre cómo deben frasearse tales virtudes, ni sobre cómo ponderarlas. Aquí me concentraré en ofrecer razones a favor de una manera de frasear el principio de parsimonia ideológica, una especie de simplicidad. Defiendo que dicho principio debería (...) decir que, dadas dos teorías T1 y T2, ceteris paribus, si T1 postula menos tipos de expresiones primitvas que T2, entonces es más probable que T1 sea una teoría fiel a que T2 lo sea. Se elabora en qué consiste la cláusula ceteris paribus, qué quiere decir "postular menos tipos de expresiones primitivas" (parsimonia ideológica cualitativa) y en qué consiste la fidelidad teórica. (shrink)

This paper articulates a way to ground a relatively high prior probability for grand explanatory theories apart from an appeal to simplicity. I explore the possibility of enumerating the space of plausible grand theories of the universe by using the explanatory properties of possible views to limit the number of plausible theories. I motivate this alternative grounding by showing that Swinburne’s appeal to simplicity is problematic along several dimensions. I then argue that there are three plausible grand views—theism, atheism, and (...) axiarchism—which satisfy explanatory requirements for plausibility. Other possible views lack the explanatory virtue of these three theories. Consequently, this explanatory grounding provides a way of securing a nontrivial prior probability for theism, atheism, and axiarchism. An important upshot of my approach is that a modest amount of empirical evidence can bear significantly on the posterior probability of grand theories of the universe. (shrink)

In this paper significant challenges are raised with respect to the view that explanation essentially involves unification. These objections are raised specifically with respect to the well-known versions of unificationism developed and defended by Michael Friedman and Philip Kitcher. The objections involve the explanatory regress argument and the concepts of reduction and scientific understanding. Essentially, the contention made here is that these versions of unificationism wrongly assume that reduction secures understanding.

The Minimalist Program in generative linguistics is predicated on the idea that simplicity is a defining property of the human language faculty, on the one hand; on the other, a central aim of linguistic theorising. Worryingly, however, justifications for either claim are hard to come by in the literature. We sketch a proposal that would allow for both shortcomings to be addressed, and that furthermore honours the program’s declared commitment to naturalism. We begin by teasing apart and clarifying the different (...) conceptions of simplicity underlying generative inquiry, in both ontological and theoretical capacities. We then trace a path towards a more robust justification for each type of simplicity principle, drawing on recent work in cognitive science and in philosophy of science, respectively. The resulting proposal hinges on the idea that simplicity is an evolved, virtuous cognitive bias—one that is a condition of our scientific understanding and, ultimately, of successful scientific practice. Finally, we make a case for why minimalists should take this proposal seriously, on the one hand; and for why generative linguistics would make for an interesting case study for philosophy of science, on the other. (shrink)

The issue of the conservatism of scientific research questions the nature and the role of the internal and external forces controlling the emergence of new research questions or problems, the exploration of risky directions of research, or the use of risky research methods. This issue has recently gained a new framing in connection with the growing importance of the peer-review process and of the social and economic pressures weighing on the funding of scientific research. Current literature then interrogates the external (...) and internal features that promote what are described as conservative tendencies in scientific research. In this paper, I propose to contribute to this debate by clarifying what might be internal sources of conservatism in science; that is, that are inherent to the research process itself. I distinguish two possible understandings of the sources and manifestations of this internal conservatism. I first present a representational description of the nature and origin of conservatism in science, which brings to the fore the difficulties researchers find in setting aside their conceptual framework. I then offer for consideration a larger perspective on conservatism by arguing for the existence of a practical conservatism generated by all the dimensions of scientific activities. In this framework, conservatism in science can be explained by the tendency of all practices to close in on their own local objectives. I illustrate this view by reference to an historical episode: the discovery of the chemical nature of genes by Avery. (shrink)

It is sometimes claimed that the Bayesian framework automatically implements Ockham’s razor—that conditionalizing on data consistent with both a simple theory and a complex theory more or less inevitably favours the simpler theory. It is shown here that the automatic razor doesn’t in fact cut it for certain mundane curve-fitting problems.

In this paper, I discuss a specific approach to measuring and comparing the simplicity of theories that is based on Lewis’s notion of fundamental properties. In particular, I discuss the criterion of simplicity as stated by Williams. According to Williams, the best candidate for a theory is the one which has the shortest definition in terms of fundamental properties. The aim of this paper is to show that the criterion thus specified has two constraints. First, the criterion is not applicable (...) to cases in which candidates for theories that specify fundamental properties are compared. Secondly, the applicability of the criterion in social sciences seems to be unwarranted. (shrink)

Some physicalists (Balog 2012, Howell 2013), and most dualists, endorse the acquaintance response to the Knowledge Argument. This is the claim that Mary gains substantial new knowledge, upon leaving the room, because phenomenal knowledge requires direct acquaintance with phenomenal properties. The acquaintance response is an especially promising way to make sense of the Mary case. I argue that it casts doubt on two claims often made on behalf of physicalism, regarding parsimony and mental causation. I show that those who endorse (...) the acquaintance response face special obstacles to invoking parsimony in an argument for physicalism. And I show how acknowledging the phenomenon of acquaintance can ease the dualist’s problems with mental causation, by dispelling three key objections to epiphenomenalism. The most challenging of these objections is that epiphenomenalism blocks an evolutionary explanation of the so-called “hedonic/utility match”. I propose that pleasures and pains, while themselves epiphenomenal, can nonetheless explain positive and negative associations with stimuli, associations that can contribute to fitness. (shrink)

I argue that although Ockham’s Razor (OR) has its origins in a-priorist ontological mandates according to the purposes of natural theology and natural philosophy as influenced by it, the principle has taken on significant empirical and contingent materialist connotations and conceptual content since the scientific revolution. I briefly discuss the pluralism of the concept of OR historically and in contemporary science and philosophy. I then attempt to align scientific metaphysics with contemporary conceptions of OR, and to demonstrate that ontic parsimony (...) is an indispensable element of scientific (contingent and anti-a-priorist) metaphysics. I then further deploy that scientific metaphysics to propose a contingently grounded semi-formal approach, with set theoretic features, and then with information theoretic features, to provide a way of assessing when a scientific theory and its ontology are aligned with OR appropriately in the context of the proposed scientific metaphysics. (shrink)

The aim of this paper is to offer a formal criterion for physical computation that allows us to objectively distinguish between competing computational interpretations of a physical system. The criterion construes a computational interpretation as an ordered pair of functions mapping (1) states of a physical system to states of an abstract machine, and (2) inputs to this machine to interventions in this physical system. This interpretation must ensure that counterfactuals true of the abstract machine have appropriate counterparts which are (...) true of the physical system. The criterion proposes that rival interpretations be assessed on the basis of simplicity. Simplicity is construed as the Kolmogorov complexity of the interpretation. This approach is closely related to the notion of algorithmic information distance and draws on earlier work on real patterns. (shrink)

Ernst Mach’s defense of relativist theories of motion in Die Mechanik involves a well-known criticism of Newton’s theory appealing to absolute space, and of Newton’s “bucket” experiment. Sympathetic readers (Norton 1995) and critics (Stein 1967, 1977) agree that there’s a tension in Mach’s view: he allows for some constructed scientific concepts, but not others, and some kinds of reasoning about unobserved phenomena, but not others. Following Banks (2003), I argue that this tension can be interpreted as a constructive one, springing (...) from Mach’s approach to scientific reasoning. Mach’s “economy of science” allows for a principled distinction to be made, between natural and artificial hypothetical reasoning, and Mach defends a division of labor between the sciences in a 1903 paper for The Monist, “Space and Geometry from the Point of View of Physical Inquiry”. That division supports counterfactual reasoning in Mach’s system, something that’s long been denied is possible for him. (shrink)

I argue for patternism, a new answer to the question of when some objects compose a whole. None of the standard principles of composition comfortably capture our natural judgments, such as that my cat exists and my table exists, but there is nothing wholly composed of them. Patternism holds, very roughly, that some things compose a whole whenever together they form a “real pattern”. Plausibly we are inclined to acknowledge the existence of my cat and my table but not of (...) their fusion, because the first two have a kind of internal organizational coherence that their putative fusion lacks. Kolmogorov complexity theory supplies the needed rigorous sense of “internal organizational coherence”. (shrink)

Occam’s razor directs us to adopt the simplest hypothesis consistent with the evidence. Learning theory provides a precise definition of the inductive simplicity of a hypothesis for a given learning problem. This definition specifies a learning method that implements an inductive version of Occam’s razor. As a case study, we apply Occam’s inductive razor to causal learning. We consider two causal learning problems: learning a causal graph structure that presents global causal connections among a set of domain variables, and learning (...) context-sensitive causal relationships that hold not globally, but only relative to a context. For causal graph learning, Occam’s inductive razor directs us to adopt the model that explains the observed correlations with a minimum number of direct causal connections. For expanding a causal graph structure to include context-sensitive relationships, Occam’s inductive razor directs us to adopt the expansion that explains the observed correlations with a minimum number of free parameters. This is equivalent to explaining the correlations with a minimum number of probabilistic logical rules. The paper provides a gentle introduction to the learning-theoretic definition of inductive simplicity and the application of Occam’s razor for causal learning. (shrink)

How should we reason in science? Jan Sprenger and Stephan Hartmann offer a refreshing take on classical topics in philosophy of science, using a single key concept to explain and to elucidate manifold aspects of scientific reasoning. They present good arguments and good inferences as being characterized by their effect on our rational degrees of belief. Refuting the view that there is no place for subjective attitudes in 'objective science', Sprenger and Hartmann explain the value of convincing evidence in terms (...) of a cycle of variations on the theme of representing rational degrees of belief by means of subjective probabilities (and changing them by Bayesian conditionalization). In doing so, they integrate Bayesian inference—the leading theory of rationality in social science—with the practice of 21st century science. Bayesian Philosophy of Science thereby shows how modeling such attitudes improves our understanding of causes, explanations, confirming evidence, and scientific models in general. It combines a scientifically minded and mathematically sophisticated approach with conceptual analysis and attention to methodological problems of modern science, especially in statistical inference, and is therefore a valuable resource for philosophers and scientific practitioners. (shrink)

Ockham's razor asks that we not multiply entities beyond necessity. The razor is a powerful methodological tool, enabling us to articulate reasons for preferring one theory to another. There are those, however, who would modify the razor. Schaffer, for one, tells us that, ‘I think the proper rendering of Ockham's razor should be ‘Do not multiply fundamental entities without necessity’’. Our aim, here, is to challenge such re-workings of Ockham's razor.

Occam's razor—the idea that all else being equal, we should pick the simpler hypothesis—plays a prominent role in ordinary and scientific inference. But why are simpler hypotheses better? One attractive hypothesis known as Bayesian Occam's razor is that more complex hypotheses tend to be more flexible—they can accommodate a wider range of possible data—and that flexibility is automatically penalized by Bayesian inference. In two experiments, we provide evidence that people's intuitive probabilistic and explanatory judgments follow the prescriptions of BOR. In (...) particular, people's judgments are consistent with the two most distinctive characteristics of BOR: They penalize hypotheses as a function not only of their numbers of free parameters but also as a function of the size of the parameter space, and they penalize those hypotheses even when their parameters can be “tuned” to fit the data better than comparatively simpler hypotheses. (shrink)

Should philosophers prefer simpler theories? Huemer (Philos Q 59:216–236, 2009) argues that the reasons to prefer simpler theories in science do not apply in philosophy. I will argue that Huemer is mistaken—the arguments he marshals for preferring simpler theories in science can also be applied in philosophy. Like Huemer, I will focus on the philosophy of mind and the nominalism/Platonism debate. But I want to engage with the broader issue of whether simplicity is relevant to philosophy.

Recent approaches to causal modelling rely upon the causal Markov condition, which specifies which probability distributions are compatible with a directed acyclic graph. Further principles are required in order to choose among the large number of DAGs compatible with a given probability distribution. Here we present a principle that we call frugality. This principle tells one to choose the DAG with the fewest causal arrows. We argue that frugality has several desirable properties compared to the other principles that have been (...) suggested, including the well-known causal faithfulness condition. _1_ Introduction _2_ The Causal Markov Condition _3_ Faithfulness _4_ Frugality _4.1_ Basic independences and frugality _4.2_ General properties of directed acyclic graphs satisfying frugality _4.3_ Connection to minimality assumptions _5_ Frugality as a Parsimony Principle _6_ Conclusion Appendix. (shrink)