This model explores consensus among agents in a population in terms of two properties. The first is a probability of belief change. This value indicates how likely agents are to change their mind in interactions. The other is the size of the agents audience: the proportion of the population the agent has access to at any given time. In all instances, the agents converge on a single belief, although the agents are arational. I argue that this generates a skeptical hypothesis: (...) any instance of purportedly rational consensus might just as well be a case of arational belief convergence. I also consider what the model tells us about increasing the likelihood that one agent’s belief is adopted by the rest. Agents are most likely to have their beliefs adopted by the entire population when their value for PBC is low relative to the rest of the population and their audience sizes are roughly three-quarters of the largest possible audience. I further explore the consequences of dogmatists to the population; individuals who refuse to change their mind end up polarizing the population. I conclude with reflections on the supposedly special character of rationality in belief-spread. (shrink)

An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.

Unlike almost all other philosophers of science, Karl Popper sought to contribute to natural philosophy or cosmology – a synthesis of science and philosophy. I consider his contributions to the philosophy of science and quantum theory in this light. There is, however, a paradox. Popper’s most famous contribution – his principle of demarcation – in driving a wedge between science and metaphysics, serves to undermine the very thing he professes to love: natural philosophy. I argue that Popper’s philosophy of science (...) is, in this respect, defective. Science cannot proceed without making highly problematic metaphysical assumptions concerning the comprehensibility and knowability of the universe. Precisely because these assumptions are problematic, rigour requires that they be subjected to sustained critical scrutiny, as an integral part of science itself. Popper’s principle of demarcation must be rejected. Metaphysics and philosophy of science become a vital part of science. Natural philosophy is reborn. A solution to the problem of what it means to say a theory is unified is proposed, a problem Popper failed to solve. In The Logic of Scientific Discovery, Popper made important contributions to the interpretation of quantum theory, especially in connection with Heisenberg's uncertainty relations. Popper's advocacy of natural philosophy has important implications for education. (shrink)