Related papers: Reflections on Russell's antinomy
We find it absurd that Walliser [1] essentially used the same analysis and obtained identical results as reported in [3], yet arrived at different conclusions. Namely, based on an incomplete theory and using erroneous arguments, he not only…
This work presents theorems which state (i) Z is a proper subset for any bijection f between A and Z, where Z is contained in P(A), A is a non-finite set and |Z|=|A|, and (ii) being Z a proper subset of P(A) nothing affirms or denies that…
We present a few charge distributions for which the application of Gauss' law in its integral form, as typically outlined in standard textbooks, results in a contradiction. We identify the root cause of such contradictions and put forward a…
In this paper a result of Latala about the tail behavior of Gaussian polynomials will be discussed. Latala proved an interesting result about this problem in paper [2]. But his proof applied an incorrect statement at a crucial point. Hence…
First a few reformulations of Frankl's conjecture are given, in terms of reduced families or matrices, or analogously in terms of lattices. These lead naturally to a stronger conjecture with a neat formulation which might be easier to…
One main goal of argumentation theory is to evaluate arguments and to determine whether they should be accepted or rejected. When there is no clear answer, a third option, being undecided, has to be taken into account. Indecision is often…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
In this paper, we consider the problem of making skeptical inferences for the multi-label ranking problem. We assume that our uncertainty is described by a convex set of probabilities (i.e. a credal set), defined over the set of labels.…
Results about the redundancy of circumscriptive and default theories are presented. In particular, the complexity of establishing whether a given theory is redundant is establihsed.
This paper undertakes a foundational inquiry into logical inferentialism with particular emphasis on the normative standards it establishes and the implications these pose for classical logic. The central question addressed herein is: 'What…
Algorithmic recourse aims to provide actionable recommendations to individuals to obtain a more favourable outcome from an automated decision-making system. As it involves reasoning about interventions performed in the physical world,…
The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…
The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes either contradiction or arbitrariness in other theoretical…
We produce an infinite family of transcendental numbers which, when raised to their own power, become rational. We extend the method, to investigate positive rational solutions to the equation $x^x = \alpha$, where $\alpha$ is a fixed…
We note the separation of a quantum description of an experiment into a statement of results (as probabilities) and an explanation of these results (in terms of linear operators). The inverse problem of choosing an explanation to fit given…
Consider the following story: A teacher announces to her students a test for the following week, such that the test will be ``surprising''. The students use this as the basis for a ``logical derivation'' and reach a contradiction, which…
A key challenge in causal inference from observational studies is the identification and estimation of causal effects in the presence of unmeasured confounding. In this paper, we introduce a novel approach for causal inference that…
New (infinitely many) rational approximants to \zeta(3) proving its irrationality are given. The recurrence relations for the numerator and denominator of these approximants as well as their continued fraction expansions are obtained. A…
We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…
Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses…