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)

Ockham’s razor is the principle that, all other things being equal, scientists ought to prefer simpler theories. In recent years, philosophers have argued that simpler theories make better predictions, possess theoretical virtues like explanatory power, and have other pragmatic virtues like computational tractability. However, such arguments fail to explain how and why a preference for simplicity can help one find true theories in scientific inquiry, unless one already assumes that the truth is simple. One new solution to that problem is (...) the Ockham efficiency theorem, which states that scientists who heed Ockham’s razor retract their opinions less often and sooner than do their non-Ockham competitors. The theorem neglects, however, to consider competitors following random strategies and in many applications random strategies are known to achieve better worst-case loss than deterministic strategies. In this paper, we describe two ways to extend the result to a very general class of random, empirical strategies. The first extension concerns expected retractions, retraction times, and errors and the second extension concerns retractions in chance, times of retractions in chance, and chances of errors. (shrink)

Many philosophers and statisticians argue that risk assessors are morally obligated to evaluate the probabilities and consequences of methodological error, and to base their decisions of whether to adopt a given parameter value, model, or hypothesis on those considerations. This argument is couched within the rubric of null hypothesis testing, which I suggest is a poor descriptive and normative model for risk assessment. Risk regulation is not primarily concerned with evaluating the probability of data conditional upon the null hypothesis, but (...) rather with measuring risks, estimating the consequences of available courses of action and inaction, formally characterising uncertainty, and deciding what to do based upon explicit values and decision criteria. In turn, I defend an ideal of value-neutrality, whereby the core inferential tasks of risk assessment – such as weighing evidence, estimating parameters, and model selection – should be guided by the aim of correspondence to reality. This is not to say that value-judgments be damned, but rather that they should be accounted for within a structured approach to decision analysis, rather than embedded within risk assessment in an informal manner. (shrink)

Classic conceptions of model simplicity for machine learning are mainly based on the analysis of the structure of the model. Bayesian, Frequentist, information theoretic and expressive power concepts are the best known of them, which are reviewed in this work, along with their underlying assumptions and weaknesses. These approaches were developed before the advent of the Big Data deluge, which has overturned the importance of structural simplicity. The computational simplicity concept is presented, and it is argued that it is more (...) encompassing and closer to actual machine learning practices than the classic ones. In order to process the huge datasets which are commonplace nowadays, the computational complexity of the learning algorithm is the decisive factor to assess the viability of a machine learning strategy, while the classic accounts of simplicity play a surrogate role. Some of the desirable features of computational simplicity derive from its reliance on the learning system concept, which integrates key aspects of machine learning that are ignored by the classic concepts. Moreover, computational simplicity is directly associated with energy efficiency. In particular, the question of whether the maximum possibly achievable predictive accuracy should be attained, no matter the economic cost of the associated energy consumption pattern, is considered. (shrink)

Ockham’s razor is the characteristic scientific penchant for simpler, more testable, and more unified theories. Glymour’s early work on confirmation theory eloquently stressed the rhetorical plausibility of Ockham’s razor in scientific arguments. His subsequent, seminal research on causal discovery still concerns methods with a strong bias toward simpler causal models, and it also comes with a story about reliability—the methods are guaranteed to converge to true causal structure in the limit. However, there is a familiar gap between convergent reliability and (...) scientific rhetoric: convergence in the long run is compatible with any conclusion in the short run. For that reason, Carnap suggested that the proper sense of reliability for scientific inference should lie somewhere between short-run reliability and mere convergence in the limit. One natural such concept is straightest possible convergence to the truth, where straightness is explicated in terms of minimizing reversals of opinion and cycles of opinion prior to convergence. We close the gap between scientific rhetoric and scientific reliability by showing that Ockham’s razor is necessary for cycle-optimal convergence to the truth, and that patiently waiting for information to resolve conflicts among simplest hypotheses is necessary for reversal-optimal convergence to the truth. (shrink)

There are at least twelve major virtues of good theories: evidential accuracy, causal adequacy, explanatory depth, internal consistency, internal coherence, universal coherence, beauty, simplicity, unification, durability, fruitfulness, and applicability. These virtues are best classified into four classes: evidential, coherential, aesthetic, and diachronic. Each virtue class contains at least three virtues that sequentially follow a repeating pattern of progressive disclosure and expansion. Systematizing the theoretical virtues in this manner clarifies each virtue and suggests how they might have a coordinated and cumulative (...) role in theory formation and evaluation across the disciplines—with allowance for discipline specific modification. An informal and flexible logic of theory choice is in the making here. Evidential accuracy, according to my systematization, is not a largely isolated trait of good theories, as some have made it out to be. Rather, it bears multifaceted relationships, constituting significant epistemic entanglements, with other theoretical virtues. (shrink)

A longstanding philosophical premise perceives simplicity as a desirable attribute of scientific theories. One of several raised justifications for this notion is that simple theories are more likely to indicate the true makeup of natural systems. Qualitatively parsimonious hypotheses and theories keep to a minimum the number of different postulated entities within a system. Formulation of such ontologically simple working hypotheses proved to be useful in the experimental probing of narrowly defined bio systems. It is less certain, however, whether qualitatively (...) parsimonious theories are effective indicators of the true nature of complex biological systems. This paper assesses the success of ontologically simple theories in envisaging the makeup of three complex systems in bacteriology, immunology, and molecular biology. Evidence shows that parsimonious theories completely misconstrued the actual ontologically complex constitutions of the three examined systems. Since evolution and selective pressures typically produce ontologically intricate rather than simple bio systems, qualitatively parsimonious theories are mostly inapt indicators of the true nature of complex biological systems. (shrink)

This paper discusses Kevin Kelly’s recent attempt to justify Ockham’s Razor in terms of truth-finding efficiency. It is argued that Kelly’s justification fails to warrant confidence in the empirical content of theories recommended by Ockham’s Razor. This is a significant problem if, as Kelly and many others believe, considerations of simplicity play a pervasive role in scientific reasoning, underlying even our best tested theories, for the proposal will fail to warrant the use of these theories in practical prediction.

Formal learning theory is the mathematical embodiment of a normative epistemology. It deals with the question of how an agent should use observations about her environment to arrive at correct and informative conclusions. Philosophers such as Putnam, Glymour and Kelly have developed learning theory as a normative framework for scientific reasoning and inductive inference.

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

Over the past two decades, several consistent procedures have been designed to infer causal conclusions from observational data. We prove that if the true causal network might be an arbitrary, linear Gaussian network or a discrete Bayes network, then every unambiguous causal conclusion produced by a consistent method from non-experimental data is subject to reversal as the sample size increases any finite number of times. That result, called the causal flipping theorem, extends prior results to the effect that causal discovery (...) cannot be reliable on a given sample size. We argue that since repeated flipping of causal conclusions is unavoidable in principle for consistent methods, the best possible discovery methods are consistent methods that retract their earlier conclusions no more than necessary. A series of simulations of various methods across a wide range of sample sizes illustrates concretely both the theorem and the principle of comparing methods in terms of retractions. (shrink)