This paper presents a new argument for the likelihood ratio measure of confirmation by showing that one of the adequacy criteria used in another argument can be replaced by a more plausible and better supported criterion which is a special case of the weak likelihood principle. This new argument is also used to show that the likelihood ratio measure is to be preferred to a measure that has recently received support in the literature.

To open a newspaper or turn on the television it would appear that science and religion are polar opposites - mutually exclusive bedfellows competing for hearts and minds. There is little indication of the rich interaction between religion and science throughout history, much of which continues today. From ancient to modern times, mathematicians have played a key role in this interaction. This is a book on the relationship between mathematics and religious beliefs. It aims to show that, throughout scientific history, (...) mathematics has been used to make sense of the 'big' questions of life, and that religious beliefs sometimes drove mathematicians to mathematics to help them make sense of the world. Containing contributions from a wide array of scholars in the fields of philosophy, history of science and history of mathematics, this book shows that the intersection between mathematics and theism is rich in both culture and character. Chapters cover a fascinating range of topics including the Sect of the Pythagoreans, Newton's views on the apocalypse, Charles Dodgson's Anglican faith and Gödel's proof of the existence of God. (shrink)

Two models are developed for updating opinions in social networks under situations where certain beliefs might be considered to be competing. These two models represent different attitudes of people towards the perceived conflict between beliefs. In both models agents have a degree of tolerance, which represents the extent to which the agent takes into account the differing beliefs of other agents, and a degree of conflict, which represents the extent to which two beliefs are considered to be competing. Computer simulations (...) are used to determine how the opinion dynamics are affected by the inclusion of conflict. Results show that conflict can enhance the formation of consensus within the network in certain circumstances according to one of the models. (shrink)

Two models are developed for updating opinions in social networks under situations where certain beliefs might be considered to be competing. These two models represent different attitudes of people towards the perceived conflict between beliefs. In both models agents have a degree of tolerance, which represents the extent to which the agent takes into account the differing beliefs of other agents, and a degree of conflict, which represents the extent to which two beliefs are considered to be competing. Computer simulations (...) are used to determine how the opinion dynamics are affected by the inclusion of conflict. Results show that conflict can enhance the formation of consensus within the network in certain circumstances according to one of the models. (shrink)