Related papers: In whose mind is Mathematics an "a priori cognitio…
We explore in the framework of Quantum Computation the notion of {\em Computability}, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert's tenth problem, which is equivalent to…
It is argued that the problem of interpreting quantum mechanics, and the philosophical problem of consciousness, both have their roots in the same set of misguided Cartesian assumptions. The confusions underlying those assumptions are…
With his General Theory of Relativity, Albert Einstein produced a revolution in our conception of reality and of the knowledge we can obtain from it. This revolution can be viewed from philosophy as leading to one of the great paradigms in…
It is suggested that the "B" in QBism rightfully stands for Bohr. The paper begins by explaining why Bohr seems obscure to most physicists. Having identified the contextuality of physical quantities as Bohr's essential contribution to…
A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…
QBism may be the most significant contribution to the search for meaning in quantum mechanics since Bohr, even as Bohr's philosophy remains the most significant revision of Kant's theory of science. There are two ironies here. Bohr failed…
A number of philosophers and scientists have discussed the possibility of inseparability between the subject (i.e., the observer) and the object (i.e., the observed universe). In particular, it has recently been proposed that this…
This text tries to give an elementary introduction to the mathematical properties of infinite sets. The aim is to keep the approach as simple as possible. Advanced knowledge of mathematics is not necessary for a proper understanding, and…
The only acceptable reason why measurements are irreversible and outcomes definite is the intrinsic definiteness and irreversibility of human sensory experience. While QBists deserve credit for their spirited defense of this position, Niels…
Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the…
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…
The aim of this article is twofold. First, we shall review and analyse the Neo-Kantian justification for the application of probabilistic concepts in physics that was defended by Hans Reichenbach early in his career, notably in his…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
Any problem is concerned with the mind, but what do minds make a decision on? Here we show that there are three conditions for the mind to make a certain answer. We found that some difficulties in physics and mathematics are in fact…
The purpose of this project is to outline various philosophies on the metaphysics of mathematics that have been prominent since the time of Cantor, highlighting some biographical aspects that have influenced these ideas as well. The main…
The classical platonist / formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: \emph{Is new mathematics discovered or invented? Using examples from my own mathematical work during the…
Analogies between quantum mechanics and sociology lead to the hypothesis that quantum objects are complex products of evolution. Like biological objects they are able to receive, to work on, and to spread semantic information. In general…
In the process of evolution, the brain has achieved such perfection that artificial intelligence systems do not have and which needs its own mathematics. The concept of cognitome, introduced by the academician K.V. Anokhin, as the cognitive…
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning…
I argue that Immanuel Kant's critical philosophy -- in particular the doctrine of transcendental idealism which grounds it -- is best understood as an `epistemic' or `metaphilosophical' doctrine. As such it aims to show how one may engage…