相关论文: Mathematical Foundations of Consciousness
We tackle the problem of consciousness by taking the naturally selected, embodied organism as our starting point. We provide a formalism describing how biological systems such as human bodies self-organize to hierarchically interpret…
Foundation models are powerful yet often opaque in their decision-making. A topic of continued interest in both neuroscience and artificial intelligence is whether some neurons behave like grandmother cells, i.e., neurons that are…
Abstract axiomatic formulation of mathematical structures are extensively used to describe our physical world. We take here the reverse way. By making basic assumptions as starting point, we reconstruct some features of both geometry and…
Operational frameworks are very useful to study the foundations of quantum mechanics, and are sometimes used to promote antirealist attitudes towards the theory. The aim of this paper is to review three arguments aiming at defending an…
This is an introduction to the set-theoretic method of forcing, including its application in proving the independence of the Continuum Hypothesis from the Zermelo-Fraenkel axioms of set theory. I presuppose no particular mathematical…
This talk presents foundations of mathematics as a historically variable set of principles appealing to various modes of human intuition and devoid of any prescriptive/prohibitive power. At each turn of history, foundations crystallize the…
The Neurobiology Of Thinking, Identity, And Geniality Abstract: Mathematically the axioms of representation are subtle, and critical. The CNS expresses its function via its internal neuronal networks in multidimensional, intrinsic frames.…
What is it about human brains that allows us to reason symbolically whereas most other animals cannot? There is evidence that dynamic binding, the ability to combine neurons into groups on the fly, is necessary for symbolic thought, but…
Ernst Zermelo's axiomatization of set theory (1908) did not exclude `a set that is a member of itself'. We call a set that is a member of itself `an individual'. In this article we prove the elimination of Russell's paradox is equivalent to…
It is well known that ZFC, despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to its infinitely many axioms, and it has a countable model due to the…
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…
Large Language Models (LLMs) exhibit persistent logical failures in complex reasoning due to the lack of an internal axiomatic framework. We propose Mathesis, a neuro-symbolic architecture that encodes mathematical states as higher-order…
How perception and reasoning arise from neuronal network activity is poorly understood. This is reflected in the fundamental limitations of connectionist artificial intelligence, typified by deep neural networks trained via gradient-based…
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 scientific community is becoming more and more interested in the research that applies the mathematical formalism of quantum theory to model human decision-making. In this paper, we provide the theoretical foundations of the quantum…
Fairly deep results of Zermelo-Frenkel (ZF) set theory have been mechanized using the proof assistant Isabelle. The results concern cardinal arithmetic and the Axiom of Choice (AC). A key result about cardinal multiplication is K*K = K,…
We recently performed cognitive experiments on conjunctions and negations of two concepts with the aim of investigating the combination problem of concepts. Our experiments confirmed the deviations (conceptual vagueness, underextension,…
If we take the subjective character of consciousness seriously, consciousness becomes a matter of "being" rather than "doing". Because "doing" can be dissociated from "being", functional criteria alone are insufficient to decide whether a…
Neurophenomenal structuralism posits that conscious experiences are defined relationally and that their phenomenal structures are mirrored by neural structures. While this approach offers a promising framework for identifying neural…
In "Object generators, relaxed sets, and a foundation for mathematics", we introduced ``object generators'', a logical environment much more general than set theory. Inside this we found a `relaxed' version of set theory. That paper is…