This article investigates a problem for statistical model evaluation, in particular for curve fitting: by employing a different family of curves we can fit any scatter plot almost perfectly at apparently minor cost in terms of model complexity. The problem is resolved by an appeal to prior probabilities. This leads to some general lessons about how to approach model evaluation.

Competition between scientific hypotheses is not always a matter of mutual exclusivity. Consistent hypotheses can compete to varying degrees either directly or indirectly via a body of evidence. We motivate and defend a particular account of hypothesis competition by showing how it captures these features. Computer simulations of Bayesian inference are used to highlight the limitations of adopting mutual exclusivity as a simplifying assumption to model scientific reasoning, particularly due to the exclusion of hypotheses that may be true. We end with a case study demonstrating the subtleties involved in hypothesis competition in scientific practice.

The no free lunch theorem is a radicalized version of Hume’s induction skepticism. It asserts that relative to a uniform probability distribution over all possible worlds, all computable prediction algorithms—whether ‘clever’ inductive or ‘stupid’ guessing methods (etc.)—have the same expected predictive success. This theorem seems to be in conflict with results about meta-induction. According to these results, certain meta-inductive prediction strategies may dominate other (non-meta-inductive) methods in their predictive success (in the long run). In this article this conflict is analyzed and dissolved, by means of probabilistic analysis and computer simulation.

Data from medical research are typically summarized with various types of outcome measures. We present three arguments in favor of absolute over relative outcome measures. The first argument is from cognitive bias: relative measures promote the reference class fallacy and the overestimation of treatment effectiveness. The second argument is decision-theoretic: absolute measures are superior to relative measures for making a decision between interventions. The third argument is causal: interpreted as measures of causal strength, absolute measures satisfy a set of desirable properties, but relative measures do not. Absolute outcome measures outperform relative measures on all counts.

Hacking’s Law of Likelihood says—paraphrasing—that data support hypothesis H1 over hypothesis H2 whenever the likelihood ratio (LR) for H1 over H2 exceeds 1. But Hacking later noted a seemingly fatal flaw in the LR itself: it cannot be interpreted as the degree of “evidential significance” across applications. I agree with Hacking about the problem, but I do not believe the condition is incurable. I argue here that the LR can be properly calibrated with respect to the underlying evidence, and I sketch the rudiments of a methodology for so doing.

Newton’s earliest publications contained scandalous epistemological claims: not only did he aim for certainty; he also claimed success. Some commentators argue that Newton ultimately gave up claims of certainty in favor of a high degree of probability. I argue that no such shift occurred. I examine the evidence of a probabilistic shift: a passage from query 23/31 of the Opticks and rule 4 of the Principia. Neither passage supports a probabilistic approach to natural philosophy. The aim of certainty, then, was an enduring feature of Newton’s methodology.

In discussion of mechanisms, philosophers often debate about whether quantitative descriptions of generalizations or qualitative descriptions of operations are explanatorily fundamental. I argue that these debates have erred by conflating the explanatory roles of generalizations and patterns. Patterns are types of variations within or between quantities in a mechanism over time or across conditions. While these patterns must often be represented in addition to descriptions of operations in order to explain a phenomenon, they are not equivalent to generalizations because their explanatory role does not depend on any specific facts about their scope or domain of invariance.

I examine explanations’ realist commitments in relation to dynamical systems theory. First I rebut an ‘explanatory indispensability argument’ for mathematical realism from the explanatory power of phase spaces. Then I critically consider a possible way of strengthening the indispensability argument by reference to attractors in dynamical systems theory. The take-home message is that understanding of the modal character of explanations (in dynamical systems theory) can undermine Platonist arguments from explanatory indispensability.

I defend the theory that the reasons why some event occurred are its causes. Many “counterexamples” to this theory turn on confusing two levels of reasons. We should distinguish the reasons why an event occurred (“first-level reasons”) from the reasons why those reasons are reasons (“second-level reasons”). An example that treats a second-level reason as a first-level reason will look like a counterexample if that second-level reason is not a cause. But second-level reasons need not be first-level reasons.

Pure mathematics can play an indispensable role explaining empirical phenomena if recent accounts of insect evolution are correct. In particular, the prime life cycles of cicadas and the geometric structure of honeycombs are taken to undergird an inference to the best explanation about mathematical entities. Neither example supports this inference or the mathematical realism it is intended to establish. Both incorrectly assume that facts about mathematical optimality drove selection for the respective traits and explain why they exist. We show how this problem can be avoided, identify limitations of explanatory indispensability arguments, and attempt to clarify the nature of mathematical explanation.

Reductionist accounts of objective chance rely on a notion of fit, which ties the chances at a world to the frequencies at that world. Here, I criticize extant measures of the fit of a chance system and draw on recent literature in epistemic utility theory to propose a new model: chances fit a world insofar as they are accurate at that world. I show how this model of fit does a better job of explaining the normative features of chance, its role in the laws of nature, and its status as an expert function than do previous accounts.

I argue against Matthew Slater’s rejection of what he calls the grounding claim in his stable property cluster (SPC) account of natural kinds. This claim states that the epistemic value of natural kinds depends on the existence of some ground to bind together a kind’s properties. Using two test cases from academic medicine, I show that grounds are genuinely explanatory of scientific epistemic practices and that the SPC account should not do without them in its philosophical analysis of natural kinds.

Counternomics—counterfactuals whose antecedents run contrary to the laws of nature—are commonplace in science but have enjoyed relatively little philosophical attention. This article discusses a puzzle about our counternomic epistemology, focusing on cases in which experimental observations are used as evidence for counternomic claims. I show that these cases resist being characterized in familiar interventionist lines, and I suggest a characterization of my own.

Callender and Cohen argue that there is no need for a special account of the constitution of scientific representation. I argue that scientific representation is communal and therefore deeply tied to the practice in which it is embedded. The communal nature is accounted for by licensing, the activities of scientific practice by which scientists establish a representation. A case study of the Lotka-Volterra model reveals how licensure is a constitutive element of the representational relationship. Thus, any account of the constitution of scientific representation must account for licensing, meaning that there is a special problem of scientific representation.

In this article I connect two debates in the philosophy of science: the questions of scientific representation and both model and theoretical equivalence. I argue that by paying attention to how a model is used to draw inferences about its target system, we can define a notion of theoretical equivalence that turns on whether models license the same claims about the same target systems. I briefly consider the implications of this for two questions that have recently been discussed in the context of the formal philosophy of science.

It has recently been suggested that realist responses to historical cases featured in pessimistic meta-inductions are not as successful as previously thought. In response, selective realists have updated the basic divide et impera strategy specifically to take such cases into account and to argue that more modern realist accounts are immune to the historical challenge. Using a case study—that of the nineteenth-century zymotic theory of disease—I argue that these updated proposals fail and that even the most sophisticated recent realist accounts remain vulnerable to the challenge from history.

Industry is a major source of funding for scientific research. There is also a growing concern for how it corrupts researchers faced with conflicts of interest. As such, the debate has focused on whether researchers have maintained their integrity. In this article we draw on both the history of medicine and formal modeling to argue that given methodological diversity and a merit-based system, industry funding can bias a community without corrupting any particular individual. We close by considering a policy solution (i.e., independent funding) that may seem to promote unbiased inquiry but that actually exacerbates the problem without additional restrictions.

The aim of this article is to critically build on Justin Biddle and Anna Leuschner’s characterization of epistemologically detrimental dissent (EDD) in the context of science. We argue that the presence of nonepistemic agendas and severe nonepistemic consequences offers neither necessary nor sufficient conditions for EDD to obtain. We clarify their role by arguing that they are contingent enabling factors, not stable difference-makers, in the production of EDD. We maintain that two stable difference-makers are core to the production of EDD: production of skewed science and effective public dissemination.

The reward system of science is the priority rule. The first scientist making a new discovery is rewarded with prestige, while second runners get little or nothing. Michael Strevens, following Philip Kitcher, defends this reward system, arguing that it incentivizes an efficient division of cognitive labor. I argue that this assessment depends on strong implicit assumptions about the replicability of findings. I question these assumptions on the basis of metascientific evidence and argue that the priority rule systematically discourages replication. My analysis leads us to qualify Kitcher and Strevens’s contention that a priority-based reward system is normatively desirable for science.