– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

Popper's account of science is an endeavour in establishing the relationship between universality and truth. The idea is that the more an empirical law is universal, by precluding certain realities from obtaining in an evidentially falsifiable way, the more the law is supported by instances of its predictions being evidentially verified. The logical structure of this dynamic is captured by Popper's notion of 'corroboration'. However, this notion is suspect, for, depending on one's interpretation of evidential givenness, the relation between a (...) law's degree of universality and evidential corroborability could instead invert, thereby contradicting Popper. This paper also explores how a conceptualization of universality in terms of necessary simplicity-i.e., a measure of simplicity that is also sensitive to the evidence at hand-can better recontextualize evidential givenness to be about evidential support for a theory's predictive truth conduciveness, against Popper's understanding of evidential support for a theory's veracity concerning the evidence at hand. However, it is argued that employing necessary simplicity to attain truth conduciveness in a theory's predictions must appeal to specific background assumptions concerning the state of affairs the evidence is supposed to be about. When these background assumptions are denied as being necessarily instantiated, then a relation between necessary simplicity and truth conduciveness becomes contingently uncertain. (shrink)

In this paper, I argue (i) that there are certain methodological practices that are epistemically significant, and (ii) that we can test for the success of these practices empirically by examining case-studies in the history of science. Analysing a particular episode from the history of medicine, I explain how this can help us resolve specific cases of underdetermination. I conclude that, while the anti-realist is (more or less legitimately) able to construct underdetermination scenarios on a case-by-case basis, he will have (...) to abandon the strategy of using algorithms to do so, thus losing the much needed guarantee that there will always be rival cases of the required kind. (shrink)

My talk will be guided by the idea that there are some familiar scientific practices that are epistemically significant. I will argue that we can test for the success of these practices empirically by examining cases in the history of science. Specifically, I will reconstruct one particular episode in the history of medicine – John Snow's reasoning concerning the infectiousness of cholera – and offer this case as a concrete example of the sort of empirical research that needs to be (...) done in order to discover what kinds of methodological practices and rules are actually of epistemic interest. Analysing this case, I will explain how it (and other cases like it) can help us resolve specific cases of underdetermination. After exploring some possible anti-realist responses to this argument, I will conclude that, while the anti-realist is (more or less legitimately) able to construct underdetermination scenarios on a case-by-case basis, he will likely have to abandon the strategy of using algorithms to do so, thus losing the much needed guarantee that there will always be rival cases of the required kind. (shrink)

In this paper I compare parametric and nonparametric regression models with the help of a simulated data set. Doing so, I have two main objectives. The first one is to differentiate five concepts of simplicity and assess their respective importance. The second one is to show that the scope of the existing philosophical literature on simplicity and model selection is too narrow because it does not take the nonparametric approach into account, S112–S123, 2002; Forster and Sober in The British Journal (...) for the Philosophy of Science 45, 1–35, 1994; Forster, 2001, in Philosophy of Science 74, 588–600, 2007; Hitchcock and Sober in The British Journal for the Philosophy of Science 55, 1–34, 2004; Mikkelson in Philosophy of Science 73, 440–447, 2006; Baker 2013). More precisely, I point out that a measure of simplicity in terms of the number of adjustable parameters is inadequate to characterise nonparametric models and to compare them with parametric models. This allows me to weed out false claims about what makes a model simpler than another. Furthermore, I show that the importance of simplicity in model selection cannot be captured by the notion of parametric simplicity. ‘Simplicity’ is an umbrella term. While parametric simplicity can be ignored, there are other notions of simplicity that need to be taken into consideration when we choose a model. Such notions are not discussed in the previously mentioned literature. The latter therefore portrays an incomplete picture of why simplicity matters when we choose a model. Overall I support a pluralist view according to which we cannot give a general and interesting justification for the importance of simplicity in science. (shrink)

The main point of this paper is to underscore the link between simplicity and truth in an unsupervised machine learning context. More precisely, we argue that parametric and dimensional simplicity are not indicators of truth but the methodological principle that urges us to pay attention to such notions of simplicity is truth conducive. The truth that we are looking for are specific geometrical shapes and we know which algorithm can find which shapes provided that we pay attention to parametric and (...) dimensional simplicity. (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)

In pedagogical contexts and in everyday life, we often come to believe something because it would best explain the data. What is it about the explanatory endeavor that makes it essential to everyday learning and to scientific progress? There are at least two plausible answers. On one view, there is something special about having true explanations. This view is highly intuitive: it’s clear why true explanations might improve one’s epistemic position. However, there is another possibility—it could be that the process (...) of seeking, generating, or evaluating explanations itself puts one in a better epistemic position, even when the outcome of the process is not a true explanation. In other words, it could be that accurate explanations are beneficial, or it could be that high-quality explaining is beneficial, where there is something about the activity of looking for an explanation that improves our epistemic standing. The main goal of this paper is to tease apart these two possibilities, both theoretically and empirically, which we align with “Inference to the Best Explanation” and “Explaining for the Best Inference”, respectively. We also provide some initial support for EBI and identify promising directions for future research. (shrink)

Explaining the connection, if any, between simplicity and truth is among the deepest problems facing the philosophy of science, statistics, and machine learning. Say that an efficient truth finding method minimizes worst case costs en route to converging to the true answer to a theory choice problem. Let the costs considered include the number of times a false answer is selected, the number of times opinion is reversed, and the times at which the reversals occur. It is demonstrated that (1) (...) always choosing the simplest theory compatible with experience, and (2) hanging onto it while it remains simplest, is both necessary and sufficient for efficiency. †To contact the author, please write to: Department of Philosophy, Carnegie Mellon University, Baker Hall 135, Pittsburgh, PA 15213-3890; e-mail: [email protected]. (shrink)

This paper challenges the appeal to theory virtues in theory choice as well as the appeal to the intellectual and moral virtues of an agent as determining unique choices between empirically equivalent theories. After arguing that theoretical virtues do not determine the choice of one theory at the expense of another theory, I argue that nor does the appeal to intellectual and moral virtues single out one agent, who defends a particular theory, and exclude another agent defending an alternative theory. (...) I analyse Duhem’s concept of good sense and its recent interpretation in terms of virtue epistemology. I argue that the virtue epistemological interpretation does not show how good sense leads to conclusive choices and scientific progress. (shrink)

Machine learning is a scientific discipline that can be divided into two main branches: supervised machine learning and unsupervised machine learning. In this paper, we aim to show just how simplicity matters in unsupervised contexts. This is important because unsupervised machine learning algorithms have barely received any attention in philosophy. Yet, there is a direct link between simplicity and truth in unsupervised contexts that we do not find in their supervised counterparts. This has thus far evaded philosophical discussions on simplicity.

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.