Related papers: Computational Platonism
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
While philosophy of science is the study of problems of knowledge concerning science in general, there also exists - or should exist - a '' philosophy in science'' directed at finding out in what ways our actual scientific knowledge may…
Computation is commonly defined as the execution of abstract algorithms over symbolic representations, with physical systems treated as substrates that realise predefined operations. While effective for engineered machines, this separation…
We consider a definition of mathematics as the art of thinking in terms of formalized systems, and the science of relations, structures and algorithms. We also touch upon the relation of mathematics to other sciences, in particular through…
In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…
In this essay we describe a platonic metaphysics where time is a fundamental idea such that the passage of time is independent of observers and the laws of physics. Furthermore, time serves to distinguish between a real and an abstract…
After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth"…
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more…
Some notes about quantum physics, an interpretation if one wishes, are put forward, insisting on `closely following the mathematics/formalism, the `nuts and bolts of what quantum physics says'. These, basically well-known, issues seem to…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any…
Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…
In this paper, epistemology and ontology of quantum states are discussed based on a completely new way of founding quantum theory. The fundamental notions are conceptual variables in the mind of an observer or in the joint minds of a group…
In this paper, we analyze axiomatic issues of unconventional computations from a methodological and philosophical point of view. We explain how the new models of algorithms changed the algorithmic universe, making it open and allowing…
There are inherent limits in classical computation for it to serve as an adequate model of human cognition. In particular, non-commutativity, while ubiquitous in physics and psychology, cannot be sufficiently handled. We propose that we…
Quantum information and computation may serve as a source of useful axioms and ideas for the quantum logic/quantum structures project of characterizing and classifying types of physical theories, including quantum mechanics and classical…
We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as…
This paper surveys some recent developments towards a dynamic quantum logic and outlines its explicite construction -- some analogies and contrasts with other logics of dynamics are indicated. Abstract: The development of ``(static)…