Related papers: G\"odel's incompleteness theorem and universal phy…
The tremendous popular success of Chaos Theory shares some common points with the not less fortunate Relativity: they both rely on a misunderstanding. Indeed, ironically , the scientific meaning of these terms for mathematicians and…
G{\"o}del's second incompleteness theorem forbids to prove, in a given theory U, the consistency of many theories-in particular, of the theory U itself-as well as it forbids to prove the normalization property for these theories, since this…
The main aim of this paper is to make a remark about the relation between (i) dualities between theories, as `duality' is understood in physics and (ii) equivalence of theories, as `equivalence' is understood in logic and philosophy. The…
The basic notions of logic-predicate logic, Peano arithmetic, incompleteness theorems, etc.-have for long been an advanced topic. In the last decades, they became more widely taught, inphilosophy, mathematics, and computer science…
General relativity, despite its profound successes, fails as a complete theory due to presence of singularities. While it is widely believed that quantum gravity has the potential to be a complete theory, in which spacetime consistently…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
The principle which allows to construct new physical theories on the basis of classical mechanics by reduction of the number of its axiom without engaging new postulates is formulated. The arising incompleteness of theory manifests itself…
In human consciousness perceptions are distinct or atomistic events despite being perceived by an apparently undivided inner observer. This paper applies both classical (Boolean) and quantum logic to analysis of the Liar paradox which is…
We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest…
Goedel's completeness theorem is concerned with provability, while Girard's theorem in ludics (as well as full completeness theorems in game semantics) are concerned with proofs. Our purpose is to look for a connection between these two…
The overarching theme of the following pages is that mathematical logic -- centered around the incompleteness theorems -- is first and foremost an investigation of $\textit{computation}$, not arithmetic. Guided by this intuition we will…
We argue by using Godel's incompletness theorems in logic that platonism is the best metaphysics for science. This is based on the fact that a natural law in a platonic metaphysics represents a timeless order in the motion of matter, while…
In this essay we'll prove G\"odel's incompleteness theorems twice. First, we'll prove them the good old-fashioned way. Then we'll repeat the feat in the setting of computation. In the process we'll discover that G\"odel's work, rightly…
In physics, there is the prevailing intuition that we are part of a unique external world, and that the goal of physics is to understand and describe this world. This assumption of the fundamentality of objective reality is often seen as a…
We discuss some physical consequences of what might be called ``the ultimate ensemble theory'', where not only worlds corresponding to say different sets of initial data or different physical constants are considered equally real, but also…
In this paper I propose a new principle in physics: the principle of "finiteness". It stems from the definition of physics as a science that deals (among other things) with measurable dimensional physical quantities. Since measurement…
A rather easy yet rigorous proof of a version of G\"odel's first incompleteness theorem is presented. The version is "each recursively enumerable theory of natural numbers with 0, 1, +, *, =, logical and, logical not, and the universal…
The 20th century has revealed two important limitations of scientific knowledge. On the one hand, the combination of Poincar\'e's nonlinear dynamics and Heisenberg's uncertainty principle leads to a world picture where physical reality is,…
G\"odel's Incompleteness Theorems suggest that no single formal system can capture the entirety of one's mathematical beliefs, while pointing at a hierarchy of systems of increasing logical strength that make progressively more explicit…
This essay discusses the idea that a Theory of Everything would not be complete without a theory of consciousness as one of its parts, and the suggestion that new physics may be needed to describe consciousness. I argue that the motivations…