Related papers: Infinity and the Sublime

This pseudo-paper consists of excerpts drawn from two of my quantum-email samizdats. Section 1 draws a picture of a physical world whose essence is ``Darwinism all the way down.'' Section 2 outlines how quantum theory should be viewed in…

The basic notions of logic-predicate logic, Peano arithmetic, incompleteness theorems, etc.-have for long been an advanced topic. In the last decades, they became more widely taught, inphilosophy, mathematics, and computer science…

This paper formalizes religious epistemology through the mathematics of Variational Autoencoders. We model religious traditions as distinct generative mappings from a shared, low-dimensional latent space to the high-dimensional space of…

This paper looks at how ancient mathematicians (and especially the Pythagorean school) were faced by problems/paradoxes associated with the infinite which led them to juggle two systems of numbers: the discrete whole/rationals which were…

This article is a short review on the concept of information. We show the strong relation between Information Theory and Physics, beginning by the concept of bit and its representation with classical physical systems, and then going to the…

We rely on the strength of linguistic and philosophical perspectives in constructing a framework that offers a unified explanation for presuppositions and existential commitment. We use a rich ontology and a set of methodological principles…

Faithfulness evaluators based on large language models (LLMs) are often fooled by the fluency of the text and struggle with identifying errors in the summaries. We propose an approach to summary faithfulness evaluation in which multiple…

Construal of observable facts or events, that is, the manner in which we understand reality, is based not only on mathematical formulas of a theory suggested as a reasonable explanation for physical phenomena (like general relativity or…

Turing's (1936) paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure…

Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…

I propose a notion of theory motivated by Category theory.

The concept of infinity took centuries to achieve recognized status in the field of mathematics, despite the fact that it was implicitly present in nearly all mathematical endeavors. Here I explore the idea that a similar development might…

In a 1985 commentary to his collected works, Kolmogorov informed the reader that his 1932 paper 'On the interpretation of intuitionistic logic' "was written in hope that with time, the logic of solution of problems [i.e., intuitionistic…

This is a translation into English of my Masters thesis (hovedoppgave) from 1991. The main topic of the thesis is the relation between fundamental physics and philosophy, and a discussion of several possible ontologies of quantum field…

This paper undertakes a foundational inquiry into logical inferentialism with particular emphasis on the normative standards it establishes and the implications these pose for classical logic. The central question addressed herein is: 'What…

I deal with two approaches to proof-theoretic semantics: one based on argument structures and justifications, which I call reducibility semantics, and one based on consequence among (sets of) formulas over atomic bases, called base…

This article focuses on the problem of the authenticity of knowledge. It argues that the failure to integrate the observer into the act of observing is the main source of the disagreements and divisions in contemporary science and…

A central problem in proof-theory is that of finding criteria for identity of proofs, that is, for when two distinct formal derivations can be taken as denoting the same logical argument. In the literature one finds criteria which are…

The difference between object-language and metalanguage is crucial for logical analysis, but has yet not been examined for the field of computer science. In this paper the difference is examined with regard to inferential relations. It is…

As David Berlinski writes (1997), the existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself. Here we analyze the essence of mathematics making the main emphasis…