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)

This paper argues that Duhem’s thesis does not decisively refute a corroboration-based account of scientific methodology (or ‘falsificationism’), but instead that auxiliary hypotheses are themselves subject to measurements of corroboration which can be used to inform practice. It argues that a corroboration-based account is equal to the popular Bayesian alternative, which has received much more recent attention, in this respect.

This paper presents a new 'discontinuous' view of Popper's theory of corroboration, where theories cease to have corroboration values when new severe tests are devised which have not yet been performed, on the basis of a passage from The Logic of Scientific Discovery. Through subsequent analysis and discussion, a novel problem for Popper's account of corroboration, which holds also for the standard view, emerges. This is the problem of the Big Test : that the severest test of any hypothesis is (...) actually to perform all possible tests. But this means that Popper's demand for 'the severest tests' amounts simply to a demand for 'all possible tests'. The paper closes by considering how this bears on accommodation vs. prediction, with respect to corroboration. (shrink)

Current methods of operationalizing concepts of misinformation in machine learning are often problematic given idiosyncrasies in their success conditions compared to other models employed in the natural and social sciences. The intrinsic value-ladenness of misinformation and the dynamic relationship between citizens' and social scientists' concepts of misinformation jointly suggest that both the construct legitimacy and the construct validity of these models needs to be assessed via more democratic criteria than has previously been recognized.

It is widely held that falsification of statistical hypotheses is impossible. This view is supported by an analysis of the most important theories of statistical testing: these theories are not compatible with falsificationism. On the other hand, falsificationism yields a basically viable solution to the problems of explanation, prediction and theory testing in a deterministic context. The present paper shows how to introduce the falsificationist solution into the realm of statistics. This is done mainly by applying the concept of empirical (...) content to statistical hypotheses. It is shown that empirical content is a substitute for ‘power’ as defined by Neyman and Pearson. Since the empirical content of a hypothesis is independent of alternative hypotheses, the proposed theory of statistical testing allows for tests of isolated hypotheses. (shrink)

The replication or reproducibility crisis in psychological science has renewed attention to philosophical aspects of its methodology. I provide herein a new, functional account of the role of replication in a scientific discipline: to undercut the underdetermination of scientific hypotheses from data, typically by hypotheses that connect data with phenomena. These include hypotheses that concern sampling error, experimental control, and operationalization. How a scientific hypothesis could be underdetermined in one of these ways depends on a scientific discipline’s epistemic goals, theoretical (...) development, material constraints, institutional context, and their interconnections. I illustrate how these apply to the case of psychological science. I then contrast this “bottom-up” account with “top-down” accounts, which assume that the role of replication in a particular science, such as psychology, must follow from a uniform role that it plays in science generally. Aside from avoiding unaddressed problems with top-down accounts, my bottom-up account also better explains the variability of importance of replication of various types across different scientific disciplines. (shrink)

In spite of the fact that the Neyman-Pearson theory of testing is the official theory of statistical testing, most research publications in the social sciences use a pattern of inductive reasoning that is characteristic of Fisherian tests of significance. The exact structure and rationale of this pattern of reasoning is widely misunderstood. The goal of the paper is to describe precisely the pattern and its rationale, and to show that while it is far more cogent than Fisher's critics have realized, (...) it does not logically sustain the inferences it sanctions. (shrink)

En este trabajo hago una comparación sistemática entre las dos teorías de la confirmación más populares en la actualidad: el método hipotético-deductivo y el bayesianismo. En primer lugar, enumero los cinco problemas fundamentales de la teoría hipotético-deductivista. Estos son el problema de las hipótesis estadísticas, el del grado de confirmación, el de la conjunción irrelevante, el del holismo epistemológico y el de las hipótesis alternativas. Luego, hago una presentación general de la epistemología bayesiana y muestro de qué manera estos problemas (...) resultan tratables en el marco bayesiano. Finalmente, concluyo que los tres primeros admiten una solución satisfactoria, sobre la base de algunos supuestos razonables. Los dos últimos, en cambio, todavía son problemas abiertos para la teoría bayesiana de la confirmación. Bayesians often affirm they have produced the best available theory of confirmation. In particular, they claim to have superseded the venerable hypothetico-deductive method. In this paper I intend to assess that claim by making a systematic comparison between both theories of confirmation. I begin by listing the main problems of hypothetico-deductive confirmation. I then show that this conception is incompatible with Hempel's conditions of adequacy for qualitative confirmation. I expound the Bayesian theory of confirmation with some detail in order to show that this theory is able to solve three out of the five fundamental problems of hypothetico-deductive confirmation. largue that the remaining two problems are still open questions for the Bayesians. (shrink)

Machine learning operates at the intersection of statistics and computer science. This raises the question as to its underlying methodology. While much emphasis has been put on the close link between the process of learning from data and induction, the falsificationist component of machine learning has received minor attention. In this paper, we argue that the idea of falsification is central to the methodology of machine learning. It is commonly thought that machine learning algorithms infer general prediction rules from past (...) observations. This is akin to a statistical procedure by which estimates are obtained from a sample of data. But machine learning algorithms can also be described as choosing one prediction rule from an entire class of functions. In particular, the algorithm that determines the weights of an artificial neural network operates by empirical risk minimization and rejects prediction rules that lack empirical adequacy. It also exhibits a behavior of implicit regularization that pushes hypothesis choice toward simpler prediction rules. We argue that taking both aspects together gives rise to a falsificationist account of artificial neural networks. (shrink)

Popper argued that a statistical falsification required a prior methodological decision to regard sufficiently improbable events as ruled out. That suggestion has generated a number of fruitful approaches, but also a number of apparent paradoxes and ultimately, no clear consensus. It is still commonly claimed that, since random samples are logically consistent with all the statistical hypotheses on the table, falsification simply does not apply in realistic statistical settings. We claim that the situation is considerably improved if we ask a (...) conceptually prior question: when should a statistical hypothesis be regarded as falsifiable. To that end we propose several different notions of statistical falsifiability and prove that, whichever definition we prefer, the same hypotheses turn out to be falsifiable. That shows that statistical falsifiability enjoys a kind of conceptual robustness. These notions of statistical falsifiability are arrived at by proposing statistical analogues to intuitive properties enjoyed by exemplary falsifiable hypotheses familiar from classical philosophy of science. That demonstrates that, to a large extent, this philosophical tradition was on the right conceptual track. Finally, we demonstrate that, under weak assumptions, the statistically falsifiable hypotheses correspond precisely to the closed sets in a standard topology on probability measures. That means that standard techniques from statistics and measure theory can be used to determine exactly which hypotheses are statistically falsifiable. In other words: the proposed notion of statistical falsifiability both answers to our conceptual demands and submits to standard mathematical techniques. (shrink)

According to Fisher, a hypothesis specifying a density function for X is falsified (at the level of significance ) if the realization of X is in the size- region of lowest densities. However, non-linear transformations of X can map low-density into high-density regions. Apparently, then, falsifications can always be turned into corroborations (and vice versa) by looking at suitable transformations of X (Neyman's Paradox). The present paper shows that, contrary to the view taken in the literature, this provides no argument (...) against a theory of statistical falsification. (shrink)