Related papers: Intrinsic justifications for large-cardinal axioms

The notion of argumentation and the one of belief stand in a problematic relation to one another. On the one hand, argumentation is crucial for belief formation: as the outcome of a process of arguing, an agent might come to (justifiably)…

We study consequences of stationary and semi-stationary set reflection. We show that the semi stationary reflection principle implies the Singular Cardinal Hypothesis, the failure of weak square principle, etc. We also consider two cardinal…

As large language models (LLMs) increasingly exhibit human-like capabilities, a fundamental question emerges: How can we enable LLMs to learn the underlying patterns from limited examples in entirely novel environments and apply them…

I use mechanized verification to examine several first- and higher-order formalizations of Anselm's Ontological Argument against the charge of begging the question. I propose three different but related criteria for a premise to beg the…

This article presents a survey of computability logic: its philosophy and motivations, main concepts and most significant results obtained so far. A continuously updated online version of this article is maintained at…

Despite significant achievements and current interest in machine learning and artificial intelligence, the quest for a theory of intelligence, allowing general and efficient problem solving, has done little progress. This work tries to…

Can we trust the reasoning traces that large reasoning models (LRMs) produce? We investigate whether these traces faithfully reflect what drives model outputs, and whether models will honestly report their influence. We introduce Thought…

At the heart of intuitionistic type theory lies an intuitive semantics called the "meaning explanations"; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer "proof" but "verification".…

Reasoning, a fundamental cognitive process integral to human intelligence, has garnered substantial interest within artificial intelligence. Notably, recent studies have revealed that chain-of-thought prompting significantly enhances LLM's…

Large proprietary language models exhibit strong causal reasoning abilities that smaller open-source models struggle to replicate. We introduce a novel framework for distilling causal explanations that transfers causal reasoning skills from…

Reward models play a fundamental role in aligning large language models with human preferences. Existing methods predominantly follow two paradigms: scalar discriminative preference models, which are efficient but lack interpretability, and…

Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search…

Conceptual analysis -- proposing definitions and refining them through counterexamples -- is central to philosophical methodology. We study whether language models can perform this task through iterated analysis and repair chains: one model…

This paper has been withdrawn by the author. In this article I review W\"ust's recent handbook on mathematical physics from a philosophical standpoint. It emerges a structural approach to mathematics which evidences the utility of logic in…

The most important problems for society are describable only in vague terms, dependent on subjective positions, and missing highly relevant data. This thesis is intended to revive and further develop the view that giving non-trivial,…

Existing algorithms for explaining the outputs of image classifiers are based on a variety of approaches and produce explanations that frequently lack formal rigour. On the other hand, logic-based explanations are formally and rigorously…

Conversational implicatures are pragmatic inferences that require listeners to deduce the intended meaning conveyed by a speaker from their explicit utterances. Although such inferential reasoning is fundamental to human communication,…

This is the first of a series of papers that we intend to publish about the epistemology of fundamental physics in its current state. One of the main objectives of these papers is to improve our understanding of fundamental physics (and…

Introspection is a foundational cognitive ability, but its mechanism is not well understood. Recent work has shown that AI models can introspect. We study the mechanism of this introspection. We first extensively replicate Lindsey (2025)'s…

This note is a critical examination of the argument of Frauchiger and Renner (Nature Communications 9:3711 (2018)), in which they claim to show that three reasonable assumptions about the use of quantum mechanics jointly lead to a…