Related papers: Towards a Coherent Theory of Physics and Mathemati…
Currently it is widely accepted that the language of science is mathematics. This book explores an alternative idea where the future of science is based on the language of algorithms and programs. How such a language can actually be…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
It is demonstrated that under the hypothesis of boundedness, the semantics appears as a property of spontaneous physical processes. It turns that both semantic structure and semantic meaning have their own physical agents each of which is…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
I distinguish two senses in which one can take a given physical theory to be `complete'. On the first, a complete physical theory is one that, in principle, completely describes physical reality. On the second, a complete physical theory is…
Practicing mathematicians often assume that mathematical claims, when they are true, have good reasons to be true. Such a state of affairs is "unreasonable", in Wigner's sense, because basic results in computational complexity suggest that…
Quantum mechanics led to spectacular technological developments, discovery of new constituents of matter and new materials. However there is still no consensus on its interpretation and limitations. Some scientists and scientific writers…
Measurement outcomes provide data for a physical theory. Unless they are objective they support no objective scientific knowledge. So the outcome of a quantum measurement must be an objective physical fact. But recent arguments purport to…
I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…
We show that the modern quantum mechanics, and particularly the theory of decoherence, allows for formulating a sort of a physical metatheory of consciousness. Particularly, the analysis of the necessary conditions for the occurrence of…
We show that the modern quantum mechanics, and particularly the theory of decoherence, allows formulating a sort of a physical metatheory of consciousness. Particularly, the analysis of the necessary conditions for the occurrence of…
String theory has not even come close to a complete formulation after half a century of intense research. On the other hand, a number of features of the theory suggest that the theory, once completed, may be a final theory. It is argued in…
Promoting a theory with a finite number of terms into an effective field theory with an infinite number of terms worsens simplicity, predictability, falsifiability, and other attributes often favored in theory choice. However, the…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
Various 'optimistic' attempts have been made to reasonably explain the undeniable effectiveness of mathematics in its application to physics. They range over retrospective, historical accounts of mathematical applicability based on…
Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But…
There is a longstanding debate in the logico-philosophical community as to why the G\"odelian sentences of a consistent and sufficiently strong theory are true. The prevalent argument seems to be something like this: since every one of the…
If gravity respects quantum mechanics, it is important to identify the essential postulates of a quantum framework capable of incorporating gravitational phenomena. Such a construct likely requires elimination or modification of some of the…
We identify the (filter representation of the) logic behind the recent theory of coherent sets of desirable (sets of) things, which generalise coherent sets of desirable (sets of) gambles as well as coherent choice functions, and show that…
I summarize a research program that aims to reconstruct quantum theory from a fundamental physical principle that, while a quantum system has no intrinsic hidden variables, it can be understood using a reference measurement. This program…