Related papers: The antinomy of Mr. G{\"o}del
This is a companion to a paper by the authors entitled "G\"odel's natural deduction", which presented and made comments about the natural deduction system in G\"odel's unpublished notes for the elementary logic course he gave at the…
This is a companion to a paper by the authors entitled "G\"odel on deduction", which examined the links between some philosophical views ascribed to G\"odel and general proof theory. When writing that other paper, the authors were not…
We give a proof of the inconsistency of PM arithmetic, classical set theory and related systems, incidentally exposing an error in Goedel's own proof of Goedel's Theorems. The inconsistency proof, that formulae of the form R and ~R occur as…
I attempted to write the full translation of this article to make the remarkable proof of Pierre Deligne available to a greater number of people. Overviews of the proofs can be found elsewhere. I especially recommend the notes of James…
English translation of "Bemerkungen zur allgemein-relativistischen Fassung der Quantentheorie", originally published in {\em Sitzber. kgl.-preu{\ss}. Akad. Wiss. Berlin, Sitzung der phys.-math. Klasse} {\bf XXIV} (1932) 346--354.
A new viewpoint of the G\"odel's incompleteness theorem be given in this article which reveals the deep relationship between the logic and computation. Upon the results of these studies, an algorithm be given which shows how to search a…
Annotated English translation of Duleau's "Notice sur A. Fresnel" in Revue encyclop\'edique, vol.39, pp.558-67 (September 1828), and of the shorter obituary for Fresnel in id., vol.37, pp.316-7.
I present a dialetheic solution to the Antinomy of the Liar and I evaluate the objection that, if the argument in Curry's paradox is valid, accepting this solution forces us to accept an analogous solution to Curry's, which I show to be…
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.…
This is a collection of variants of Schanuel's conjecture and the known dependencies between them. It was originally written in 2007, and made available for a time on my webpage. I have been asked by a few people to make it available again…
We provide a generalization of the Phragm\'en-Lindel\"of principal of Rademacher with the aim of correcting, or at least provide a pathway to correcting, several errors appearing in the literature.
Translation of 'Die Logik Nicht Gleichzeitig Entscheidbarer Aussagen' by Ernst Specker, Dialectica, vol. 14, 239 - 246 (1960).
In recent years, different types of adversarial examples from different fields have emerged endlessly, including purely natural ones without perturbations. A variety of defenses are proposed and then broken quickly. Two fundamental…
G\"odel's argument for the First Incompleteness Theorem is, structurally, a proof by contradiction. This article intends to reframe the argument by, first, isolating an additional assumption the argument relies on, and then, second, arguing…
We give a survey of current research on G\"{o}del's incompleteness theorems from the following three aspects: classifications of different proofs of G\"{o}del's incompleteness theorems, the limit of the applicability of G\"{o}del's first…
The famous G\"odel incompleteness theorem says that for every sufficiently rich formal theory (containing formal arithmetic in some natural sense) there exist true unprovable statements. Such statements would be natural candidates for being…
We present Russell's antinomy using three distinct deductive systems, which are then compared to deepen the logical deductions that lead to the contradiction. Some inferential paths are then presented, alternative to the commonly accepted…
This is a paper for a special issue of the journal "Studia Semiotyczne" devoted to Stanislaw Krajewski's paper [30]. This paper gives some supplementary notes to Krajewski's [30] on the Anti-Mechanist Arguments based on G\"{o}del's…
This is a slightly edited translation of a paper in Dutch which appeared in Nieuw Archief voor Wiskunde (5) 25 (2024), No.2, 87-90 on the occasion of I.G. Macdonald's death in 2023, and aimed at a very broad mathematical audience. First we…
This is an English translation of Raymond Debremaeker's 1976 Dutch-language dissertation "Cohomologie met waarden in een gekruiste groepenschoof op een situs" (Katholieke Universiteit te Leuven). I thank the University librarians for…