Related papers: In whose mind is Mathematics an "a priori cognitio…
Constructivists (and intuitionists in general) asked what kind of mental construction is needed to convince ourselves (and others) that some mathematical statement is true. This question has a much more practical (and even cynical)…
One of the most complex systems is the human brain whose formalized functioning is characterized by decision theory. We present a "Quantum Decision Theory" of decision making, based on the mathematical theory of separable Hilbert spaces.…
We envision a machine capable of solving mathematical problems. Dividing the quantitative reasoning system into two parts: thought processes and cognitive processes, we provide probabilistic descriptions of the architecture.
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
In his late work (De venatione sapientiae), Cusanus unfolded basic ideas of his brilliant theology. After a long period, this ingenious teaching became clearly recognizable especially in our time. Forward with his face to the back, modern…
Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…
Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore,…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
We explore the different meanings of "quantum uncertainty" contained in Heisenberg's seminal paper from 1927, and also some of the precise definitions that were explored later. We recount the controversy about "Anschaulichkeit",…
We introduce and formalize a notion of "a priori knowledge" about a quantum system, and show some properties about this form of knowledge. Finally, we show that the Kochen-Specker theorem follows directly from this study. This version is a…
The ``Hard Problem" of consciousness refers to a long-standing enigma about how qualia emerge from physical processes in the brain. Building on insights from the development of non-Euclidean geometry, this paper seeks to present a…
There is no mysterious link between mathematics and physics, because both of them are human inventions designed to study the world.
This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all…
We look at consciousness through the lens of Theoretical Computer Science, a branch of mathematics that studies computation under resource limitations, distinguishing functions that are efficiently computable from those that are not. From…
It is known that Einstein's conceptual base for his theory of relativity was the philosophy formulated by Immanuel Kant. Things appear differently to observers in different frames. However, Kant's Ding-an-Sich leads to the existence of the…
We describe in dialogue form a possible way of discovering and investigating 10-adic numbers starting from the naive question about a `largest natural number'. Among the topics we pursue are possibilities of extensions to transfinite…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
We present a logical proof that computing machines, and by extension physical systems, can never be certain if they possess conscious awareness. This implies that human consciousness is associated with a violation of energy conservation. We…
We discuss the nature of reality in the ontological context of Penrose's math-matter-mind triangle. The triangle suggests the circularity of the widespread view that math arises from the mind, the mind arises out of matter, and that matter…
This article supports the epistemological claim that sound human reasoning about ultimate knowledge is either foundational or circularly justified. In particular, questions which naturally arise in theology, philosophy, and related…