Related papers: Intrinsic justifications for large-cardinal axioms
Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on the rule-following…
Computational modelling offers a powerful tool for formalising psychological theories, making them more transparent, testable, and applicable in digital contexts. Yet, the question often remains: how should one computationally model a…
This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\"odel's theorem). The fact, that a formal…
Since I first became enthralled with physics as a teenager, I've been intrigued by the philosophical aspects of the discipline. As I approached the end of my career as an experimental physicist and observational astronomer (I'm now…
Causal inference has been a pivotal challenge across diverse domains such as medicine and economics, demanding a complicated integration of human knowledge, mathematical reasoning, and data mining capabilities. Recent advancements in…
We propose a new type of self-aware systems inspired by ideas from higher-order theories of consciousness. First, we discussed the crucial distinction between introspection and reflexion. Then, we focus on computational reflexion as a…
In this paper we intend to connect two different strands of research concerning the origin of what I shall loosely call "formal" ideas: firstly, the relation between logic and rhetoric - the theme of the 2006 Cambridge conference to which…
Recent advances in long chain-of-thought (CoT) reasoning have largely prioritized answer accuracy and token efficiency, while overlooking aspects critical to trustworthiness. We argue that usable reasoning systems must be trustworthy,…
The general solutions of the reflection equation associated with Temperley-Lieb $R$-matrices are constructed. Their parametrization is defined and the Hamiltonians of corresponding integrable spin systems are given.
This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all…
While deep reasoning with long chain-of-thought has dramatically improved large language models in verifiable domains like mathematics, its effectiveness for open-ended tasks such as writing remains unexplored. In this paper, we conduct a…
In this paper, we described possible directions for deeper understanding, helping bridge the gap between psychology / cognitive science and computational approaches in sentiment/opinion analysis literature. We focus on the opinion holder's…
Chain-of-thought (CoT) reasoning has enabled large language models (LLMs) to utilize additional computation through intermediate tokens to solve complex tasks. However, we posit that typical reasoning traces contain many redundant tokens,…
Since the discovery of critical mistakes in Rauszer's work on bi-intuitionistic logics, solid foundations for these have progressively been rebuilt. However, the algebraic treatment of these logics has not yet been tended to. We fill this…
Large Reasoning Models (LRMs) have recently shown impressive performance on complex reasoning tasks, often by engaging in self-reflective behaviors such as self-critique and backtracking. However, not all reflections are beneficial-many are…
Conceptual reasoning, the ability to reason in abstract and high-level perspectives, is key to generalization in human cognition. However, limited study has been done on large language models' capability to perform conceptual reasoning. In…
We present three natural but distinct formalisations of Einstein's special principle of relativity, and demonstrate the relationships between them. In particular, we prove that they are logically distinct, but that they can be made…
A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and…
This is the second installment in a sequence of articles devoted to "explicit Chabauty-Kim theory" for the thrice punctured line. Its ultimate goal is to construct an algorithmic solution to the unit equation whose halting will be…
This thesis is situated within the context of quantum gravity, broadly understood as any effort to explore the interplay between gravitation and the quantum realm, without necessarily requiring the quantization of the gravitational field…