Related papers: Mathematical Models of Consciousness
This review presents recent and older results on elementary quantitative and qualitative aspects of consciousness and cognition and tackles the question "What is consciousness?" conjointly from biological, neuroscience-cognitive, physical…
The complexity of human cognition has meant that psychology makes more use of theory and conceptual models than perhaps any other biomedical field. To enable precise quantitative study of the full breadth of phenomena in psychological and…
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…
Evaluating artificial systems for signs of consciousness is increasingly becoming a pressing concern, and a rigorous psychometric measurement framework may be of crucial importance in evaluating large language models in this regard. Most…
The Common Model of Cognition (CMC) provides an abstract characterization of the structure and processing required by a cognitive architecture for human-like minds. We propose a unified approach to integrating metacognition within the CMC.…
A series of examples of computational models is provided, where the model aim is to interpret numerical results in terms of internal states of agents minds. Two opposite strategies or research can be distinguished in the literature. First…
Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…
We review the philosophical framework of mathematical conceptualism as an alternative to set-theoretic foundations and show how mainstream mathematics can be developed on this basis. The paper includes an explicit axiomatization of the…
In the present work, quantum theory is founded on the framework of consciousness, in contrast to earlier suggestions that consciousness might be understood starting from quantum theory. The notion of streams of consciousness, usually…
A formal but intuitive framework is introduced to bridge the gap between data obtained from empirical studies and that generated by agent-based models. This is based on three key tenets. Firstly, a simulation can be given multiple formal…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
Objects are a centerpiece of the mathematical realm and our interaction with and reasoning about it, just as they are of the physical one (if not more). And humans' mathematical reasoning must ultimately be grounded in our general…
This article presents a heuristic view that shows that the inner states of consciousness experienced by every human being have a physical but imaginary hypercomplex basis. The hypercomplex description is necessary because certain processes…
Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…
Quantum theory, originally proposed as a physical theory to describe the motions of microscopic particles, has been applied to various non-physics domains involving human cognition and decision-making that are inherently uncertain and…
We formulate five basic tenets of enactivist cognitive science that we have carefully identified in the relevant literature as the main underlying principles of that philosophy. We then develop a mathematical framework to talk about…
We introduce a new mathematical framework for the probabilistic description of an experiment on a system of any type in terms of information representing this system initially. Based on the notions of an information state and a generalized…