A note on Huemer’s Claim to immortality

According to Huemer (2019), existence is evidence of immortality, provided past time is infinite. The argument is based on, inter alia, an alleged contradiction between the fact of one’s existence now and its improbability. I suggest that Huemer’s argument is flawed in equating the infinitesimally small with its limit value, and in assuming a philosophically significant difference between the a priori probability of the occurrence of a unique incarnation and that of anyone among an infinite number.

Bayesian statistics in human genetics

Using of the Bayes’ method in genetic counseling allows clarifying of the probability of a disease in the offspring, which in some cases can save probands from additional laboratory diagnostic tests due to the extremely low risk which can be calculated. The article is devoted to the usage of the Bayes’ method in human genetics. The concepts of a priori, conditional, total and posterior probabilities are introduced. As an example, a pedigree with a monogenic recessive X-linked trait is considered. An algorithm for calculating of the probability that a patient is a carrier of a pathological gene is presented. The prediction of results made with help of using the classical method of calculations and the Bayesian method are compared. An example for calculation of the gene mutation rate based on epidemiological and genetic data is given. The discussed topic can be taken into account for presenting of courses in human genetics and medical genetics at classical and medical universities, and the given problem can serve as an example for drawing up of tasks for students with pedigrees of various configurations and other attributes. Keywords: Bayesian method, a priori probability, posterior probability, teaching of genetics, genetic counseling.

Nucleosynthesis and Kilonovae from Strange Star Mergers

In this talk, we summarize the work in progress toward a full characterization of strange star–strange star (SS–SS) mergers related to the GW/GRB/kilonova events. In addition, we show that the a priori probability constructed from the observed neutron star mass distribution points toward an asymmetric binary system as the progenitor of the GW170817 event.

In Defense of the Explanationist Response to Skepticism

A promising response to the threat of external world skepticism involves arguing that our commonsense view of the world best explains the sensory experiences that we have. Since our commonsense view of the world best explains our evidence, we are justified in accepting this commonsense view of the world. Despite the plausibility of this Explanationist Response, it has recently come under attack. James Beebe has argued that only a version of the Explanationist Response that provides an a priori justification of inference to the best explanation can hope to respond to two serious objections. Additionally, he has argued that providing such an a priori justification requires an acceptable account of a priori probability and that it is unclear whether such an account can be developed. In this paper I argue that Beebe fails to provide adequate support for either of these claims.

BEING LOW ALONG A SEQUENCE AND ELSEWHERE

Let an oracle be called low for prefix-free complexity on a set in case access to the oracle improves the prefix-free complexities of the members of the set at most by an additive constant. Let an oracle be called weakly low for prefix-free complexity on a set in case the oracle is low for prefix-free complexity on an infinite subset of the given set. Furthermore, let an oracle be called low and weakly for prefix-free complexity along a sequence in case the oracle is low and weakly low, respectively, for prefix-free complexity on the set of initial segments of the sequence. Our two main results are the following characterizations. An oracle is low for prefix-free complexity if and only if it is low for prefix-free complexity along some sequences if and only if it is low for prefix-free complexity along all sequences. An oracle is weakly low for prefix-free complexity if and only if it is weakly low for prefix-free complexity along some sequence if and only if it is weakly low for prefix-free complexity along almost all sequences. As a tool for proving these results, we show that prefix-free complexity differs from its expected value with respect to an oracle chosen uniformly at random at most by an additive constant, and that similar results hold for related notions such as a priori probability. Furthermore, we demonstrate that on every infinite set almost all oracles are weakly low but are not low for prefix-free complexity, while by Shoenfield absoluteness there is an infinite set on which uncountably many oracles are low for prefix-free complexity. Finally, we obtain no-gap results, introduce weakly low reducibility, or WLK-reducibility for short, and show that all its degrees except the greatest one are countable.

Quantum thermodynamics and canonical typicality

We present here a set of lecture notes on quantum thermodynamics and canonical typicality. Entanglement can be constructively used in the foundations of statistical mechanics. An alternative version of the postulate of equal a priori probability is derived making use of some techniques of convex geometry.