相关论文: Godel's theorem is invalid

An ultimate universal theory -- a complete theory that accounts, via few and simple first principles, for all the phenomena already observed and that will ever be observed -- has been, and still is, the aspiration of most physicists and…

Although the categorical arithmetic is not effectively axiomatizable, the belief that the incompleteness Theorems can be apply to it is fairly common. Furthermore, the so-called "essential" (or "inherent") semantic incompleteness of the…

The prevalent interpretation of G\"odel's Second Theorem states that a sufficiently adequate and consistent theory does not prove its consistency. It is however not entirely clear how to justify this informal reading, as the formulation of…

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…

We take an argument of G\"odel's from his ground-breaking 1931 paper, generalize it, and examine its validity. The argument in question is this: the sentence $G$ says about itself that it is not provable, and $G$ is indeed not provable;…

We present a version of G\"odel's Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic version of the derivability conditions. We also argue that…

A century ago, discoveries of a serious kind of logical error made separately by several leading mathematicians led to acceptance of a sharply enhanced standard for rigor within what ultimately became the foundation for Computer Science. By…

This paper gives a counterexample to the impossibility, by G\"odel's second incompleteness theorem, of proving a formula expressing the consistency of arithmetic in a fragment of arithmetic on the assumption that the latter is consistent.…

If we apply an extension of the Deduction meta-Theorem to Goedel's meta-reasoning of "undecidability", we can conclude that Goedel's formal system of Arithmetic is not omega-consistent. If we then take the standard interpretation…

We investigate the eliminability of the absoluteness operator Delta in Goedel logics. While Delta is not definable from the standard connectives and disrupts important proof-theoretic properties, we show that it becomes eliminable at the…

Classical interpretations of Goedel's formal reasoning imply that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is essentially unverifiable. However, a language of general,…

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,…

This is an examination, a commentary, of links between some philosophical views ascribed to G\"odel and general proof theory. In these views deduction is of central concern not only in predicate logic, but in set theory too, understood from…

Despite the failure of the integral Hodge conjecture, we show that the rational Hodge conjecture implies an integral version (modulo torsion) of the absolute Hodge conjecture.

Some common fallacies about fundamental themes of Logic are exposed: the First and Second incompleteness Theorem interpretations, Chaitin's various superficialities and the usual classification of the axiomatic Theories in function of its…

We demonstrate that, in itself and in the absence of extra premises, the following argument scheme is fallacious: The sentence A says about itself that it has a certain property F, and A does in fact have the property F; therefore A is…

The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…

There are countless examples in the history of science that not only were the laws of physics often incomplete and more limited in their domain of validity than was realized, but at times they missed the mark completely. Despite this, our…

I investigate the question whether G\"odel's undecidability theorems play a crucial role in the search for a unified theory of physics. I conclude that unless the structure of space-time is fundamentally discrete we can never decide whether…

It is generally accepted that the incompleteness of first-order number theory (PA) is established by an application of Godel's proof. This paper shows that the arithmetization of the syntax of PA implies that the hypothesised class of PA…