Related papers: Jacob's Ladder and Scientific Ontologies
There is a contemporary trend toward geometrizing all mathematical theories, as proposed by the Langlands program, and, by extension, physical theories as well. Within this paradigm, it becomes possible to represent physical objects as…
This article is dedicated to the investigation of difficulties involved in the understanding of the homomorphism concept. It doesn't restrict to group-theory but on the contrary raises the issue of developing teaching strategies aiming at…
This essay offers an epistemological reinterpretation of the foundational divide between matrix mechanics and wave mechanics. Though formally equivalent, the two theories embody distinct modes of knowing: procedural construction and…
A theorem, usually attributed to Barr, yields that (A) geometric implications deduced in classical L_{\infty\omega} logic from geometric theories also have intuitionistic proofs. Barr's theorem is of a topos-theoretic nature and its proof…
Epistemic uncertainty arises in lack of complete knowledge about the state of a system. There are multiple mathematical frameworks for measuring such uncertainty quantitatively, often referred to as imprecise probability theories. Inspired…
Herbrand's Fundamental Theorem provides a constructive characterization of derivability in first-order predicate logic by means of sentential logic. Sometimes it is simply called "Herbrand's Theorem", but the longer name is preferable as…
In this paper we discuss the so called "quantum omelette" created by Bohr and Heisenberg through the mix of (ontic) objective accounts and (epistemic) subjective ones within the analysis of Quantum Mechanics (QM). We will begin by…
This paper introduces a unifying framework that links the Context-Content Uncertainty Principle (CCUP) with optimal transport (OT) via primal-dual inference. We propose that cognitive representations are not static encodings but active dual…
A key problem in the description of language structure is to explain its contradictory properties of specificity and generality, the contrasting poles of formulaic prescription and generative productivity. I argue that this is possible if…
Cognition is not passive data accumulation but the active resolution of uncertainty through symmetry breaking. This paper argues that both cognitive evolution and development unfold via sequential symmetry-breaking transitions that disrupt…
This paper is motivated by the desire to study package management using the toolkit of the semantics of functional languages. As it transpires, this is deeply related to the semantics of concurrent computation. The models we produce are not…
This paper describes a new entropy-style of equation that may be useful in a general sense, but can be applied to a cognitive model with related processes. The model is based on the human brain, with automatic and distributed pattern…
Lawvere observed in his celebrated work on hyperdoctrines that the set-theoretic schema of comprehension can be elegantly expressed in the functorial language of categorical logic, as a comprehension structure on the functor…
In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…
The goal of this paper is to summarise the first steps in developing a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum…
Humans currently use arguments for explaining choices which are already made, or for evaluating potential choices. Each potential choice has usually pros and cons of various strengths. In spite of the usefulness of arguments in a decision…
Natural philosophy integrates scientific observation with abstract frameworks, often using a mathematical Ansatz to hypothesise about physical phenomena. Exploring the possibility of other universes, however, challenges assumptions that…
Quantum mechanics emerged as the result of a successful resolution of stringent empirical and profound conceptual conflicts within the development of atomic physics at the beginning of the last century. At first glance, it seems to be…
This paper introduces function alignment, a novel theory of mind and intelligence that is both intuitively compelling and structurally grounded. It explicitly models how meaning, interpretation, and analogy emerge from interactions among…
Knowledge is the most precious asset of humankind. People extract the experience from the data that provide for us the reality through the feelings. Generally speaking, it is possible to see the analogy of knowledge elaboration between…