Related papers: The Mechanist's Challenge
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
We resolve some questions posed by Handelman in 1996 concerning log convex integrable functions. In particular, we give a negative answer to a question he posed concerning the integrability of $h^2(x)/h(2x)$ when $h$ is integrable and log…
We consider some critical claims concerning our above paper, and reply to these claims.
We give a new proof of Lucas' Theorem in elementary number theory.
We rebut Kowalenko's claims in 2010 that he proved the irrationality of Euler's constant, and that his rational series for it is new.
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards…
I use mechanized verification to examine several first- and higher-order formalizations of Anselm's Ontological Argument against the charge of begging the question. I propose three different but related criteria for a premise to beg the…
The crisis in the reproducibility of experiments invites a re-evaluation of methods of inquiry and validation procedures. The text challenges current assumptions of knowledge acquisition and introduces G-complexity for defining decidable…
This is a response to the article arXiv:1212.3130v1 by Xu-Jia Wang, where he attempted to address a mathematical question we raised. We point out that, and explain why, the article is far from answering our objections. Moreover, we have…
We respond briefly to the recent comment by Jay Lawrence, Marcin Markiewicz and Marek \'{Z}ukowski [arXiv:2210.09025 and Found. Phys. \textbf{54}, 45 (2024)] regarding our work defending RQM against their previous assessment. We refute the…
In a recent series of papers Wiseman, Cavalcanti, and Rieffel have outlined and contrasted two different views about what we now call Bell's theorem. They also assert that Bell presented these two different versions at different times. This…
Several arguments against the truth of the Riemann hypothesis are extensively discussed. These include the Lehmer phenomenon, the Davenport-Heilbronn zeta-function, large and mean values of $|\zeta(1/2+it)|$ on the critical line, and zeros…
Errors in Eberly's derivation of several Bell inequalities are pointed out: (1) it is based on an equation that is incorrect; (2) it uses neither two-particle states nor locality to derive Bell's inequalities and; (3) it does not use…
We close a gap appearing at the same time in the author's thesis "Iterated rings of bounded elements and generalizations of Schm\"udgen's theorem" [1] and in the author's article "Iterated rings of bounded elements and generalizations of…
In this note we show that Jackson's criticism (hep-ph/0203076) of our work "Necessity of simultaneous co-existence of..." is based on an inexact understanding of the basic assumptions and conclusions of our work.
In the recent work [1], authors discussed the relationship between the two of Euler angles assuming that it can be used to describe some effects in the theory of a rigid body. I show that this assumption is not properly justified.
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 show that the argument in Phys Rev Lett 70 (1993) 1360 is correct and consistent, and that Hagen & Sudarshan's solution has inconsistency leading to non-vanishing commutators of $[P^1, P^2]$ and $[P^j, H]$ even in physical states. This…
We introduce some early considerations of physical and mathematical impossibility as preludes to the Goedel incompleteness theorems. We consider some informal aspects of these theorems and their underlying assumptions and discuss some the…
F. Rohrlich has recently published two papers, including the paper under review, advocating a particular delay-differential equation as an approximate equation of motion for classical charged particles, which he characterizes as providing a…