The Principle of Indifference, which dictates that we ought to assign two outcomes equal probability in the absence of known reasons to do otherwise, is vulnerable to well-known objections. Nevertheless, the appeal of the principle, and of symmetry-based assignments of equal probability, persists. We show that, relative to a given class of symmetries satisfying certain properties, we are justified in calling certain outcomes equally probable, and more generally, in defining what we call relative probabilities. Relative probabilities are useful in providing (...) a generalized approach to conditionalization. The technique is illustrated by application to simple examples. (shrink)

In a random process, later events seem to be loosely attached to earlier ones; in other words, a substantial or tight relationship between the two is missing. This relationship is sometimes held to be the relation of cause and effect, so that random events are not caused by what preceded them. Richard Johns, however, adopts the original stance that random events are fully caused and lack only determination by their causes; according to his causal theory of chance, the physical chance (...) of an event is the degree to which the event is determined by its causes. -/- A Theory of Physical Probability addresses an important and, until now, poorly comprehended topic: chance, or physical probability. It puts forth Johns's theory of physical chance and demonstrates the implications of this theory in various areas of physics. Johns's is a novel approach to a fundamental topic in such disciplines as philosophy, philosophy of science, and physics, and it will be widely admired by scholars for its clarity and accessibility. (shrink)

Epistemic theories of objective chance hold that chances are idealised epistemic probabilities of some sort. After giving a brief history of this approach to objective chance, I argue for a particular version of this view, that the chance of an event E is its epistemic probability, given maximal knowledge of the possible causes of E. The main argument for this view is the demonstration that it entails all of the commonly-accepted properties of chance. For example, this analysis entails that chances (...) supervene on the physical facts, that the chance function is an expert probability, that the existence of stable frequencies results from invariant chances in repeated experiments, and that chances are probably close to long-run relative frequencies in repeated experiments. Despite these virtues, epistemic approaches to chance have been neglected in recent decades, on account of their conflict with accepted views about closely related topics such as causation, laws of nature, and epistemic probability. However, existing views on these topics are also very problematic, and I believe that the epistemic view of chance is a key piece of this puzzle that, once in place, allows all the other pieces to fit together into a new and coherent way. I also respond to some criticisms of the epistemic theory that I favour. (shrink)

The aim of this paper is to provide a mathematical basis for the plausible idea that regular dynamical laws can only produce (quickly and reliably) regular structures. Thus the actual laws, which are regular, can only produce regular objects, like crystals, and not irregular ones, like living organisms.

There is presently considerable interest in the phenomenon of "self-organisation" in dynamical systems. The rough idea of self-organisation is that a structure appears "by itself in a dynamical system, with reasonably high probability, in a reasonably short time, with no help from a special initial state, or interaction with an external system. What is often missed, however, is that the standard evolutionary account of the origin of multi-cellular life fits this definition, so that higher living organisms are also products of (...) self-organisation. Very few kinds of object can selforganise, and the question of what such objects are like is a suitable mathematical problem. Extending the familiar notion of algorithmic complexity into the context of dynamical systems, we obtain a notion of "dynamical complexity". A simple theorem then shows that only objects of very low dynamical complexity can self organise, so that living organisms must be of low dynamical complexity. On the other hand, symmetry considerations suggest that living organisms are highly complex, relative to the dynamical laws, due to their large size and high degree of irregularity. In particular, it is shown that since dynamical laws operate locally, and do not vary across space and time, they cannot produce any specific large and irregular structure with high probability in a short time. These arguments suggest that standard evolutionary theories of the origin of higher organisms are incomplete. (shrink)

What I’m calling “Subjective Logic” is a new approach to logic. Fundamentally it is a theory about what sentences mean, i.e. a theory of the proposition, but it includes an account of logical consequence, the propositional connectives, probability, and the nature of truth.

The Luck Argument seems to show that libertarianism is false, since indeterministic free will is impossible. We should be wary of this argument, however, since a very similar argument shows that indeterministic causation1 is impossible. Further, since chancy events require causes, but are not determined, it would also follow that chancy events do not exist. If we are to conclude that free actions are all deterministic (or nonexistent), then the same reasoning should also persuade us that events with physical chances (...) do not exist. The Luck Argument, in its various formulations, assumes that a human being, like any physical system, has a set of complete (or exact, or precise) possible states. The same assumption drives the similar argument against indeterministic causation. This spells disaster for both free actions and chancy events, as these require causes. The assumption that physical systems have precise states should therefore be subjected to the closest scrutiny, which is not usually the case. On the contrary, it enjoys a wide and uncritical acceptance. (shrink)

There is a long history of philosophical intuition that the human mind must be more than physical or mechanical. I argue that this intuition arises from the perfect “transparency” of physical and mechanical states, in the sense that such states have no obscure or occult elements, but are fully intelligible in mathematical terms. In the paper, I derive a contradiction from the claim that such a physical system has genuine intentionality, comparable with an intelligent human. The contradiction arises from the (...) fact that, according to physicalism, the physical properties of a brain state determine the narrow propositional content of any conscious thought occurring in that state. This fact allows a physical property of brain states to be defined using Cantor’s diagonal construction, and then a contradiction results if a physical system is assumed to form thoughts involving that property. (shrink)