Related papers: The Mechanist's Challenge
Can we really falsify truth by dictat? A critical note on J. R. Lucas' 1996 remarks concerning non-standard models of first-order Peano Arithmetic.
The only fault we can fairly lay at Lucas' and Penrose's doors, for continuing to believe in the essential soundness of the Goedelian argument, is their naive faith in, first, non-verifiable assertions in standard expositions of classical…
An attempt is made to remedy confusing treatments of some basic relativistic concepts and results in recent papers by Franklin (2010 {\it Eur. J. Phys.} {\bf 31} 291-8) and by McGlynn and van Kampen (2008 {\it Eur. J. Phys.} {\bf 29}…
Goedel's explicit thesis was that his undecidable formula GUS is a well-formed, well-defined formal sentence in any formalisation of Intuitive Arithmetic IA in which the axioms and rules of inference are recursively definable. His implicit…
Translation of 'Die Logik Nicht Gleichzeitig Entscheidbarer Aussagen' by Ernst Specker, Dialectica, vol. 14, 239 - 246 (1960).
We argue that, although Wittgenstein's reservations on Goedel's interpretation of his own formal reasoning are, indeed, of historical importance, the uneasiness that academicians and philosophers continue to sense, and express, over…
Standard expositions of Goedel's 1931 paper on undecidable arithmetical propositions are based on two presumptions in Goedel's 1931 interpretation of his own, formal, reasoning - one each in Theorem VI and in Theorem XI - which do not meet…
The aim of this article is twofold. First, we shall review and analyse the Neo-Kantian justification for the application of probabilistic concepts in physics that was defended by Hans Reichenbach early in his career, notably in his…
We argue that several apparently distinct responses to the hole argument, all invoking formal or mathematical considerations, should be viewed as a unified "mathematical response". We then consider and rebut two prominent critiques of the…
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…
In the Comment [Eur. J. Phys., to be published] on our paper [Eur. J. Phys. 19 (1998) 1-6], the author declares that we claim that the ratio of inertial mass to gravitational mass can be derived ex nihilo and that our paper was published…
We respond to the criticism raised in the paper arXiv:1704.07831.
Some years ago I demonstrated a simulated annealing heuristic for the Hamiltonian cycle problem (Science 273, 413 (1996)). Here I propose an improved version of this heuristic.
In 1651 the Italian astronomer Giovanni Battista Riccioli published within his Almagestum Novum, a massive 1500 page treatise on astronomy, a discussion of 126 arguments for and against the Copernican hypothesis (49 for, 77 against). A…
We comment on some apparently weak points in the novel strategies recently developed by various authors aiming at a proof of the Riemann hypothesis. After noting the existence of relevant previous papers where similar tools have been used,…
A Comment on the Letter by C. R. Galley, Phys. Rev. Lett. 110, 174301 (2013).
We are pleased to see that Jeckelmann has made many changes to the original version of his comment on our paper as a result of our response. Here is a copy of this powerful response that reveals problems in his previous results. However,…
The equation derived by F. Rohrlich (Phys. Rev. E 77, 046609 (2008)) has been known for 60 years (C. J. Eliezer, Proc. Royal Soc. London. Ser. A 194, 543 (1948)). For a long time this equation has been considered to be incorrect. If there…
Some personal thoughts on Sklar's theorem and copulas after reading the original paper (Sklar, 1959) in French.
L. E. Ballentine's remarks in Physics Today about the QBist interpretation of quantum mechanics are generally wide of the mark.