The Open Systems View Quantum theory is commonly understood as a theory of closed, isolated systems, with open systems treated as merely effective descriptions obtained by embedding them into larger …

[Revised entry by Hannes Leitgeb and André Carus on July 2, 2026. Changes to: Main text, Bibliography, aufbau.html, carnap-quine.html, inductive-logic.html, methodology.html, reconstruct-sci-theories.html, semantics.html, syntax.html, tolerance-metaphysics.html] Rudolf Carnap (1891 - 1970) was...

The article argues for a system of axioms that is meant to capture the logic of normative reasons for belief. The system concerns a primitive direct-reason relation, a defined doxastic-reason relatio...

This paper demonstrates that in an important class of data-integration problems even Big Data cannot speak for itself: marginal probabilities provided by large and unbiased datasets do not determine a unique joint probability distribution. Big Data must instead be accompanied by further reasoning methodologies for handling unavoidable uncertainties. I assess how Bayesian approaches handle this underdetermination and argue that they face practical challenges when dealing with Big Data that does not speak for itself.

This paper demonstrates that in an important class of data-integration problems even Big Data cannot speak for itself: marginal probabilities provided by large and unbiased datasets do not determine a unique joint probability distribution. Big Data must instead be accompanied by further reasoning methodologies for handling unavoidable uncertainties. I assess how Bayesian approaches handle this underdetermination and argue that they face practical challenges when dealing with Big Data that does not speak for itself.

Hilbert’s (arithmetical) Axiom of Completeness asserts that the structure of the real numbers $$\mathbb {R}$$ R is maximal in the sense of not having a proper extension to an Archimedean ordered field. The more recent works of Ehrlich (2001), McGee (1997) and Aczel (1988) show that certain maximality conditions modeled upon Hilbert’s axiom provide unique characterizations of, respectively, the s-hierarchical ordered field of surreal numbers No, the well-founded hierarchy of pure sets $$\mathbb {V}_{\!k}$$ V k , and the non-well-founded hierarchy of Finsler-extensional sets $$\mathbb {V}_{\scriptscriptstyle \!F\!A\!F\!A}$$ V F A F A . The paper provides a comprehensive historical and theoretical reconstruction of this often overlooked chapter in the history of the axiomatic method. The historical reconstruction suggests that the maximality condition of non-extensibility arises as a natural axiom in the unique characterization of mathematical structures, as illustrated by the theories of (s-hierarchical non-)Archimedean continua and (non-)well-founded sets. The theoretical reconstruction argues that the maximality condition of non-extensibility is the formal explication of the heuristic principle of Plenitude, as usually adopted to describe the intuitive ‘‘fullness” of punctiform continua and the cumulative hierarchy of sets.

Hilbert’s (arithmetical) Axiom of Completeness asserts that the structure of the real numbers $$\mathbb {R}$$ R is maximal in the sense of not having a proper extension to an Archimedean ordered field. The more recent works of Ehrlich (2001), McGee (1997) and Aczel (1988) show that certain maximality conditions modeled upon Hilbert’s axiom provide unique characterizations of, respectively, the s-hierarchical ordered field of surreal numbers No, the well-founded hierarchy of pure sets $$\mathbb {V}_{\!k}$$ V k , and the non-well-founded hierarchy of Finsler-extensional sets $$\mathbb {V}_{\scriptscriptstyle \!F\!A\!F\!A}$$ V F A F A . The paper provides a comprehensive historical and theoretical reconstruction of this often overlooked chapter in the history of the axiomatic method. The historical reconstruction suggests that the maximality condition of non-extensibility arises as a natural axiom in the unique characterization of mathematical structures, as illustrated by the theories of (s-hierarchical non-)Archimedean continua and (non-)well-founded sets. The theoretical reconstruction argues that the maximality condition of non-extensibility is the formal explication of the heuristic principle of Plenitude, as usually adopted to describe the intuitive ‘‘fullness” of punctiform continua and the cumulative hierarchy of sets.

LMU - China Academic Network Workshop

At Cambridge, LMU alumnus Neil Dewar explores how physical theories represent the world.

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Michael Titelbaum introduced a variant of the Sleeping Beauty problem in which a coin is tossed on both Monday and Tuesday, with the Tuesday toss not affecting Beauty's condition. Titelbaum argues th....

Based on work from the International Association for Computing and Philosophy’s (IACAP) Awards Committee, the executive board of IACAP has selected Tom F. S ...

YouTube video by Munich Center for Mathematical Philosophy

Articulating Invariantism

Andrew Stephenson has joined the faculty at LMU. The philosopher researches Kant and how humans obtain knowledge of the world.

European Journal for Philosophy of Science - Sometimes we try to explain one thing but end up explaining something else. In this paper, I address when this is a problem, which I call the...

This paper presents a new solution to the preface paradox (Makinson, 1965). It makes use of a fragmented account of justification, and thus, unlike existing solutions, employs the central concept invo...

Abstract. Suppose a committee, expert panel or other group is making judgements on some issues, where these may be not just yes/no questions, such as wheth

Does philosophy make scientific progress, and if yes, how much? As Dellsén, Firing, and Norton have recently argued, to answer this, we need to consider both empirical questions about the history of philosophy and theoretical questions about the definition of scientific progress. In this paper, I develop a case study about the origin of analytic philosophy—focusing on Frege—to show that in this period we can document what I call a clear case for scientific progress in philosophy. That is, philosophy made scientific progress over this period no matter what definitions of scientific progress we consider, even by the very high standards of scientific progress that pessimists about progress in philosophy endorse. Thus, if any of the existing accounts of progress are correct, philosophy made progress at the origin of analytic philosophy.

Explicating the concept of coherence and establishing a measure for assessing the coherence of an information set are two of the most important tasks of coherentist epistemology. To this end, several ...

My essay "Keeping Your Distance" has been shortlisted for the inaugural Aeon Philosophy Prize as one of five finalists selected from several hundred submissions. The essay argues that a history of be...

Andrew Stephenson has joined the faculty at LMU. The philosopher researches Kant and how humans obtain knowledge of the world.