•  22
    Vindicating the verifiability criterion
    Philosophical Studies 181 (1): 223-245. 2024.
    The aim of this paper is to argue for a revised and precisified version of the infamous Verifiability Criterion for the meaningfulness of declarative sentences. The argument is based on independently plausible premises concerning probabilistic confirmation and meaning as context-change potential, it is shown to be logically valid, and its ramifications for potential applications of the criterion are being discussed. Although the paper is not historical but systematic, the criterion thus vindicat…Read more
  •  69
    Reduction, Abstraction, Analysis (edited book)
    Ontos. 2009.
    This volume collects contributions comprising all these topics, including articles by Alexander Bird, Jaakko Hintikka, James Ladyman, Rohit Parikh, Gerhard ...
  •  4
  • How Similarities Compose
    In Markus Werning, Edouard Machery & Gerhard Schurz (eds.), The Compositionality of Meaning and Content. Volume I - Foundational Issues,, De Gruyter. pp. 147-168. 2005.
  •  5
    How Abstraction Works
    with Leon Horsten
  •  20
    Neural Network Models of Conditionals
    In Sven Ove Hansson & Vincent F. Hendricks (eds.), Introduction to Formal Philosophy, Springer. pp. 147-176. 2012.
    This chapter explains how artificial neural networks may be used as models for reasoning, conditionals, and conditional logic. It starts with the historical overlap between neural network research and logic, it discusses connectionism as a paradigm in cognitive science that opposes the traditional paradigm of symbolic computationalism, it mentions some recent accounts of how logic and neural networks may be combined, and it ends with a couple of open questions concerning the future of this area …Read more
  •  50
    Circular languages
    Journal of Logic, Language and Information 13 (3): 341-371. 2004.
    In this paper we investigate two purely syntactical notions ofcircularity, which we call ``self-application'''' and ``self-inclusion.'''' Alanguage containing self-application allows linguistic items to beapplied to themselves. In a language allowing for self-inclusion thereare expressions which include themselves as a proper part. We introduceaxiomatic systems of syntax which include identity criteria andexistence axioms for such expressions. The consistency of these axiomsystems will be shown …Read more
  •  105
    Revision Revisited
    with Leon Horsten, Graham E. Leigh, and Philip Welch
    Review of Symbolic Logic 5 (4): 642-664. 2012.
    This article explores ways in which the Revision Theory of Truth can be expressed in the object language. In particular, we investigate the extent to which semantic deficiency, stable truth, and nearly stable truth can be so expressed, and we study different axiomatic systems for the Revision Theory of Truth.
  •  74
    No future
    Journal of Philosophical Logic 30 (3): 259-265. 2001.
    The difficulties with formalizing the intensional notions necessity, knowability and omniscience, and rational belief are well-known. If these notions are formalized as predicates applying to (codes of) sentences, then from apparently weak and uncontroversial logical principles governing these notions, outright contradictions can be derived. Tense logic is one of the best understood and most extensively developed branches of intensional logic. In tense logic, the temporal notions future and past…Read more
  •  63
    Probability for the Revision Theory of Truth
    Journal of Philosophical Logic 48 (1): 87-112. 2019.
    We investigate how to assign probabilities to sentences that contain a type-free truth predicate. These probability values track how often a sentence is satisfied in transfinite revision sequences, following Gupta and Belnap’s revision theory of truth. This answers an open problem by Leitgeb which asks how one might describe transfinite stages of the revision sequence using such probability functions. We offer a general construction, and explore additional constraints that lead to desirable prop…Read more
  •  12
    1. Not a Sure Thing: Fitness, Probability, and Causation Not a Sure Thing: Fitness, Probability, and Causation (pp. 147-171) (review)
    with Denis M. Walsh, Leah Henderson, Noah D. Goodman, Joshua B. Tenenbaum, James F. Woodward, Richard Pettigrew, Brad Weslake, and John Kulvicki
    Philosophy of Science 77 (2): 172-200. 2010.
    Hierarchical Bayesian models provide an account of Bayesian inference in a hierarchically structured hypothesis space. Scientific theories are plausibly regarded as organized into hierarchies in many cases, with higher levels sometimes called ‘paradigms’ and lower levels encoding more specific or concrete hypotheses. Therefore, HBMs provide a useful model for scientific theory change, showing how higher-level theory change may be driven by the impact of evidence on lower levels. HBMs capture fea…Read more
  •  2
    Editorial
    with Hans Rott
    Erkenntnis 75 (1): 1-3. 2011.
  •  10
    Philosophers often have tried to either reduce "disagreeable" objects or concepts to (more) acceptable objects or concepts. Reduction is regarded attractive by those who subscribe to an ideal of ontological parsimony. But the topic is not just restricted to traditional metaphysics or ontology. In the philosophy of mathematics, abstraction principles, such as Hume's principle, have been suggested to support a reconstruction of mathematics by logical means only. In the philosophy of language and t…Read more
  •  26
    Axioms for Type-Free Subjective Probability
    with Cezary Cieśliński and Leon Horsten
    Review of Symbolic Logic 1-16. forthcoming.
    We formulate and explore two basic axiomatic systems of type-free subjective probability. One of them explicates a notion of finitely additive probability. The other explicates a concept of infinitely additive probability. It is argued that the first of these systems is a suitable background theory for formally investigating controversial principles about type-free subjective probability.
  • A class of n-valued statement calculi: Many universes statement calculus
    Kriterion - Journal of Philosophy 1 (11): 3-15. 1997.
  •  68
    Ramsification and Semantic Indeterminacy
    Review of Symbolic Logic 16 (3): 900-950. 2022.
    Is it possible to maintain classical logic, stay close to classical semantics, and yet accept that language might be semantically indeterminate? The article gives an affirmative answer by Ramsifying classical semantics, which yields a new semantic theory that remains much closer to classical semantics than supervaluationism but which at the same time avoids the problematic classical presupposition of semantic determinacy. The resulting Ramsey semantics is developed in detail, it is shown to supp…Read more
  •  83
    A new justification of probabilism is developed that pays close attention to the structure of the underlying space of possibilities. Its central assumption is that rational numerical degrees of bel...
  •  86
    On Non-Eliminative Structuralism. Unlabeled Graphs as a Case Study, Part A†
    Philosophia Mathematica 28 (3): 317-346. 2020.
    This is Part A of an article that defends non-eliminative structuralism about mathematics by means of a concrete case study: a theory of unlabeled graphs. Part A summarizes the general attractions of non-eliminative structuralism. Afterwards, it motivates an understanding of unlabeled graphs as structures sui generis and develops a corresponding axiomatic theory of unlabeled graphs. As the theory demonstrates, graph theory can be developed consistently without eliminating unlabeled graphs in fav…Read more
  •  56
    This is Part B of an article that defends non-eliminative structuralism about mathematics by means of a concrete case study: a theory of unlabeled graphs. Part A motivated an understanding of unlabeled graphs as structures sui generis and developed a corresponding axiomatic theory of unlabeled graphs. Part B turns to the philosophical interpretation and assessment of the theory: it points out how the theory avoids well-known problems concerning identity, objecthood, and reference that have been …Read more
  •  35
    Correction to: HYPE: A System of Hyperintensional Logic
    Journal of Philosophical Logic 48 (2): 407-407. 2019.
    The original version of the article unfortunately contained a mistake. The author missed to mention the support by a EU-funded research network that he is involved in. See below. This work was supported by the Marie-Sklodowska-Curie Innovative Training Network DIAPHORA.
  •  127
    Pure mathematical truths are commonly thought to be metaphysically necessary. Assuming the truth of pure mathematics as currently pursued, and presupposing that set theory serves as a foundation of pure mathematics, this article aims to provide a metaphysical explanation of why pure mathematics is metaphysically necessary.
  •  259
    HYPE: A System of Hyperintensional Logic
    Journal of Philosophical Logic 48 (2): 305-405. 2019.
    This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositio…Read more
  •  72
    Imaging all the people
    Episteme 14 (4): 463-479. 2017.
    It is well known that aggregating the degree-of-belief functions of different subjects by linear pooling or averaging is subject to a commutativity dilemma: other than in trivial cases, conditionalizing the individual degree-of-belief functions on a piece of evidence E followed by linearly aggregating them does not yield the same result as rst aggregating them linearly and then conditionalizing the resulting social degree- of-belief function on E. In the present paper we suggest a novel way out…Read more
  • Inference on the Low Level: An Investigation into Deduction, Nonmonotonic Reasoning, and the Philosophy of Cognition
    Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 38 (2): 393-395. 2007.
  •  111
    This is a personal, incomplete, and very informal take on the role of logic in general philosophy of science, which is aimed at a broader audience. We defend and advertise the application of logical methods in philosophy of science, starting with the beginnings in the Vienna Circle and ending with some more recent logical developments