As large language models (LLMs) continue to demonstrate remarkable abilities across various domains, computer scientists are developing methods to understand their cognitive processes, particularly concerning how (and if) LLMs internally represent their beliefs about the world. However, this field currently lacks a unified theoretical foundation to underpin the study of belief in LLMs. This article begins filling this gap by proposing adequacy conditions for a representation in an LLM to count as belief-like. We argue that, while the project of belief (...) measurement in LLMs shares striking features with belief measurement as carried out in decision theory and formal epistemology, it also differs in ways that should change how we measure belief. Thus, drawing from insights in philosophy and contemporary practices of machine learning, we establish four criteria that balance theoretical considerations with practical constraints. Our proposed criteria include accuracy, coherence, uniformity, and use, which together help lay the groundwork for a comprehensive understanding of belief representation in LLMs. We draw on empirical work showing the limitations of using various criteria in isolation to identify belief representations. (shrink)

Evaluative studies of inductive inferences have been pursued extensively with mathematical rigor in many disciplines, such as statistics, econometrics, computer science, and formal epistemology. Attempts have been made in those disciplines to justify many different kinds of inductive inferences, to varying extents. But somehow those disciplines have said almost nothing to justify a most familiar kind of induction, an example of which is this: “We’ve seen this many ravens and they all are black, so all ravens are black.” This is (...) enumerative induction in itsfullstrength. For it does not settle with a weaker conclusion (such as “the ravens observed in the future will all be black”); nor does it proceed with any additional premise (such as the statistical IID assumption). The goal of this paper is to take some initial steps toward a justification for the full version of enumerative induction, against counterinduction, and against the skeptical policy. The idea is to explore various epistemic ideals, mathematically defined as different modes of convergence to the truth, and look for one that is weak enough to be achievable and strong enough to justify a norm that governs both the long run and the short run. So the proposal is learning-theoretic in essence, but a Bayesian version is developed as well. (shrink)

This paper addresses the so-called Taurek debate on whether or not to save the greater number of victims in rescue conflicts. In this controversy we take a consequentialist and aggregationist pro-numbers position and defend it against various objections. In particular, we consider it to be compatible with the principle of equal concern. Given that the pro-numbers position hinges to a significant extent on the acceptance of the person-neutral value of personal well-being, we offer a coherentist justification for this value claim. (...) Systematically though, we argue that neither pure welfare aggregationism nor its strict rejection are convincing. Rather, rejoining the two ethical dimensions of individual claims and collective well-being requires a hybrid position. Identifying three possible ways of constructing such a position, we briefly defend them against a recent version of the charge that they cannot be coherently expressed in a rational choice framework. -/- / Zusammenfassung: Im Rahmen der sogenannten Taurek-Debatte wird die Frage diskutiert, ob in Rettungskonflikten die größere Anzahl an Opfern gerettet werden sollte oder nicht. Wir beziehen in dieser Kontroverse eine konsequentialistische und aggregationistische Pro-Anzahl-Position und verteidigen diese gegen verschiedene Einwände. Insbesondere halten wir die Position für kompatibel mit dem Prinzip gleicher Achtung. Angesichts des Umstandes, dass die Pro-Anzahl-Position in maßgeblicher Weise von der Annahme eines personenneutralen Wertes persönlichen Wohlergehens abhängt, bieten wir eine kohärentistische Rechtfertigung für diese Wertbehauptung. Systematisch argumentieren wir, dass weder ein reiner Wohlergehensaggregationismus noch seine komplette Zurückweisung überzeugend sein können. Die Vereinigung der beiden ethischen Dimensionen individueller Ansprüche und kollektiven Wohlergehens erfordert stattdessen eine hybride Position. Wir identifizieren drei mögliche Wege für die Konstruktion einer solchen Hybridposition und verteidigen diese abschließend kurz gegen einen aktuellen Vorwurf, demzufolge diese nicht auf kohärente Weise im Rahmen der rationalen Entscheidungstheorie abgebildet werden können. (shrink)

‘Bayesian epistemology’ became an epistemological movement in the 20th century, though its two main features can be traced back to the eponymous Reverend Thomas Bayes (c. 1701-61). Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic. (...) The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization. (shrink)

This is a comprehensive anthology of works concerning the nature of economics as a science, including classic texts and essays exploring specific branches and schools of economics. Apart from the classics, most of the selections in the third edition are new, as are the introduction and bibliography. No other anthology spans the whole field and offers a comprehensive introduction to questions about economic methodology.