Related papers: Intrinsic justifications for large-cardinal axioms

Large language models (LLMs) have achieved strong performance on complex reasoning tasks using techniques such as chain-of-thought and self-consistency. However, ensemble-based approaches, especially self-consistency which relies on…

This paper aims to systematically study mystic reflection groups that emerged independently in the paper [Selecta Math. (N.S.) 14 (2009), 325-372, arXiv:0806.0867] by the authors and in the paper [Algebr. Represent. Theory 13 (2010),…

In these lectures we review the motivation, principles of and (circumstantial) evidence for the program of unification of the fundamental forces. In an appendix, we review the group theory pertinent to the program.

"Intrinsic motivation" refers to the capacity for intelligent systems to be motivated endogenously, i.e. by features of agential architecture itself rather than by learned associations between action and reward. This paper views active…

A fascinating hypothesis is that human and animal intelligence could be explained by a few principles (rather than an encyclopedic list of heuristics). If that hypothesis was correct, we could more easily both understand our own…

We present Russell's antinomy using three distinct deductive systems, which are then compared to deepen the logical deductions that lead to the contradiction. Some inferential paths are then presented, alternative to the commonly accepted…

Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here. Axiomatizations are provided for three successively more general classes of causal models: (1) the class of recursive theories (those…

Recently I posted a paper entitled "External observer reflections on QBism". As any external observable, I was not able to reflect some features of QBism properly. Therefore comments which I received from one of its creators, C. Fuchs, are…

Previous studies proposed that the reasoning capabilities of large language models (LLMs) can be improved through self-reflection, i.e., letting LLMs reflect on their own output to identify and correct mistakes in the initial responses.…

Reasoning models have demonstrated remarkable progress in solving complex and logic-intensive tasks by generating extended Chain-of-Thoughts (CoTs) prior to arriving at a final answer. Yet, the emergence of this "slow-thinking" paradigm,…

How does a cause lead to an effect, and which intermediate causal steps explain their connection? This work scrutinizes the mechanistic causal reasoning capabilities of large language models (LLMs) to answer these questions through the task…

This paper presents correct algorithms for answering the following two questions; (i) Does there exist a causal explanation consistent with a set of background knowledge which explains all of the observed independence facts in a sample?…

Some formulas and speculations are presented relative to integrable systems and quantum mechanics.

Although most theories posit that natural behavior can be explained as maximizing some form of extrinsic reward, often called utility, some behaviors appear to be reward independent. For instance, spontaneous motor babbling in human…

Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…

We present some arguments for the thesis that a set-theoretic inspired faith, in the ability of intuitive truth to faithfully reflect relationships between elements of a Platonic universe, may be as misplaced as an assumption that such…

In this article, we consider iteration principles for contraction, with the goal of identifying properties for contractions that respect conditional beliefs. Therefore, we investigate and evaluate four groups of iteration principles for…

The reflection capacity of Large Language Model (LLM) has garnered extensive attention. A post-hoc prompting strategy, e.g., reflexion and self-refine, refines LLM's response based on self-evaluated or external feedback. However, recent…

Large language models (LLMs) with Chain-of-Thought (CoT) reasoning have achieved strong performance across diverse tasks, including mathematics, coding, and general reasoning. A distinctive ability of these reasoning models is…

In Mathematical Thought and Its Objects, Charles Parsons argues that our knowledge of the iterability of functions on the natural numbers and of the validity of complete induction is not intuitive knowledge; Brouwer disagrees on both…