Related papers: The Mechanist's Challenge
We survey the impact of Lieb's influential paper "Proofs of some conjectures on permanents" [J. Math. Mech. 16 1966, 127-134], which introduced the famous permanental dominance conjecture. This conjecture has defied all attacks for over…
The Simulation Argument has gained significant traction in the public arena. It has offered a hypothesis based on probabilistic analysis of its assumptions that we are likely to exist within a computer simulation. This has been derived from…
A brief outline of the history of the discrepancies within Newtonian mechanics at the end of the nineteenth century is given. The framework of general relativity is described briefly and the famous 'tests' of general relativity are…
"The hardest logic puzzle ever" presented by George Boolos became a target for philosophers and logicians who tried to modify it and make it even tougher. I propose further modification of the original puzzle where part of the available…
Some of my previous publications were incomplete in the sense that non trivial zeros belonging to a particular type of fundamental domain have been inadvertently ignored. Due to this fact, I was brought to believe that computations done by…
French translation, by Henri Lombardi and Stefan Neuwirth, of the article "Did Euclid need the Euclidean algorithm to prove unique factorization?", American Mathematical Monthly 113 (2006), pages 196-205.
We consider a philosophical question that is implicit in Selmer Bringsjord's paper, "The narrational case against Church's Thesis": If, as Mendelson argues, the classically accepted definitions of foundational concepts such as "partial…
As a coauthor of the article mentioned in the title, I discuss the criticism in the comment of Aalseth et al. Part of the criticism is justified.
We present the intuitionistic version of PUC-Logic. After that, we present a constructive approach to Lewis' counterfactual abstraction to show that it does not require the classical absurd rule.
The Sylvester-Gallai Theorem, stated as a problem by J. J. Sylvester in 1893, asserts that for any finite, noncollinear set of points on a plane, there exists a line passing through exactly two points of the set. First, it is shown that for…
A critical reading of Lubin & Sandage's 2001 paper on the Tolman effect for the reality of the expansion of the universe clearly reveals that Sandage is far from winning the dispute with Hubble on the issue. After all the years, Hubble's…
The paper analizes a set of issues related to analogy and analogical reasoning, namely: 1) The problem of analogy and its duplicity; 2) The role of analogy in demonstrative reasoning; 3) The role of analogy in non-demonstrative reasoning;…
In this little non-technical piece, I argue that some of the lessons that can be learnt from the bold action carried out in 1996 by the physicist Alan Sokal and typically known as the "Sokal affair" not only apply to some sector of the…
Recently, in [18] the authors gave some results on the structure, capability and the Schur multiplier of generalized Heisenberg Lie superalgebra. In this work we try to extend these concepts to the case of generalized Heisenberg Lie…
An out of the box intellectual path exploring the foundations of quantum mechanics is discussed in some detail, in order to clarify why a possibly different way to look at the relevant fundamental questions can be identified and can support…
They are possible other cases at first done not contemplate. This paper has been withdrawn by the author due to a crucial sign error in equation 1 page 4
The problem of giving a computational meaning to classical reasoning lies at the heart of logic. This article surveys three famous solutions to this problem - the epsilon calculus, modified realizability and the dialectica interpretation -…
The paper is an extended version of the talk in the Logic Colloquium-2000 at Paris. We discuss a series of results and problems around Hrushovski's construction of counter-examples to the Trichotomy conjecture.
In a recent preprint, we discussed geometric lifts, and in particular the notion of St\"ackel lift. In this note, we wish to clarify several aspects raised in the comment arXiv:2511.05765.
This version corrects a number of mistakes that appeared in the previous draft. In particular, the (EU-LREM) condition is sufficient for existence and uniqueness but not necessary, as we had claimed. We are grateful to P. C. B. Phillips and…