相关论文: A nonBayesian view of Hempel's paradox of the rave…
After long arguments between positivism and falsificationism, the verification of universal hypotheses was replaced with the confirmation of uncertain major premises. Unfortunately, Hemple discovered the Raven Paradox (RP). Then, Carnap…
Philosophers writing about the ravens paradox often note that Nicod's Condition (NC) holds given some set of background information, and fails to hold against others, but rarely go any further. That is, it is usually not explored which…
I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…
Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on the rule-following…
Consider an attributed graph whose vertices are colored green or red, but only a few are observed to be red. The color of the other vertices is unobserved. Typically, the unknown total number of red vertices is small. The vertex nomination…
The Fermi paradox is the conflict between an expectation of a high {\em ex ante} probability of intelligent life elsewhere in the universe and the apparently lifeless universe we in fact observe. The expectation that the universe should be…
A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours. The study of rainbow subgraphs goes back to the work of Euler on Latin squares and has been the focus of extensive research ever since. Many…
The rainbow arborescence conjecture posits that if the arcs of a directed graph with $n$ vertices are colored by $n-1$ colors such that each color class forms a spanning arborescence, then there is a spanning arborescence that contains…
Since the diagonal lemma plays a key role in the proof of the main limitative theorems of logic, its proof could shed light on the very essence of these fundamental theorems. Yet the lemma is often characterized as one of those important…
Can deception be detected solely from written text? Cues of deceptive communication are inherently subtle, even more so in text-only communication. Yet, prior studies have reported considerable success in automatic deception detection. We…
The concept of a judgment as a logical action which introduces new information into a deductive system is examined. This leads to a way of mathematically representing implication which is distinct from the familiar material implication,…
Recently, the educational initiative TED-Ed has published a popular brain teaser coined the 'frog riddle', which illustrates non-intuitive implications of conditional probabilities. In its intended form, the frog riddle is a reformulation…
The ubiquity of optical coherence arising from its importance in everything from astronomy to photovoltaics means that underlying assumptions such as stationarity and ergodicity can become implicit. When these assumptions become implicit,…
This paper describes Simpson's paradox, and explains its serious implications for randomised control trials. In particular, we show that for any number of variables we can simulate the result of a controlled trial which uniformly points to…
The way a rational agent changes her belief in certain propositions/hypotheses in the light of new evidence lies at the heart of Bayesian inference. The basic natural assumption, as summarized in van Fraassen's Reflection Principle…
Most stars in the Universe are red dwarfs. They outnumber stars like our Sun by a factor of 5 and outlive them by another factor of 20 (population-weighted mean). When combined with recent observations uncovering an abundance of temperate,…
A large number of essays address the Sleeping Beauty problem, which undermines the validity of Bayesian inference and Bas Van Fraassen's 'Reflection Principle'. In this study a straightforward analysis of the problem based on probability…
Nicod's criterion states that observing a black raven is evidence for the hypothesis H that all ravens are black. We show that Solomonoff induction does not satisfy Nicod's criterion: there are time steps in which observing black ravens…
A famous conjecture of Caccetta and H\"aggkvist is that in a digraph on $n$ vertices and minimum out-degree at least $\frac{n}{r}$ there is a directed cycle of length $r$ or less. We consider the following generalization: in an undirected…
Well known Simpson's paradox is puzzling and surprising for many, especially for the empirical researchers and users of statistics. However there is no surprise as far as mathematical details are concerned. A lot more is written about the…