Daniel Saudek

How does causation in the physical world relate to implication in logic? This article presents implication as fundamentally a relation of inclusion between propositions. Given this, it is argued that an event cannot “causally imply” another, also given the laws of nature. Then, by applying the notion of inclusion to physical objects, a relation “within the possibilities of” is developed, which generates a partial order on sets of entities and is independent of time. Based on this, it is shown that changes of physical objects in time (at any rate, a great many of them) imply, and thus counterfactually depend on, what we call “causes” – an asymmetric dependence which is robust despite the perspectival nature of the concept of “cause”.

This article proposes a “third way” in the philosophy of time beyond A-theory and the block universe, in which time is understood as a purely local phenomenon. It does so by starting with simple metaphysical assumptions about substances and their properties. Based on these assumptions, the notions of “before”, of change, and of time as local quantification of change can be derived non-circularly, i.e. without invoking temporal concepts. I then proceed to prove the irreversibility of local time by showing that the propositional content of the local past cannot be changed, since this would imply a contradiction, whereas that of the future can. Time’s familiar asymmetric character, in particular the difference between the fixed past and the open or “branching” future, is therefore a non-illusory but purely local phenomenon. Such a model requires no past-present-future distinction valid for the entire cosmos, and is therefore consistent with special and general relativity.

The aim of this article is to spell out the relationship between miracles and violations of laws of nature. I argue that the former do not necessarily entail the latter, even in the case of the type of miraculous event which cannot be brought about by natural operations alone. The idea that they do is based on a deterministic assumption which is too often overlooked. The article also explores the reverse implication, i.e. the question whether violations of laws of nature entail miracles. It turns out that there are conceptual difficulties in defining what sort of events would qualify as such violations in the first place, but that a more general notion of God’s action contravening nature is viable. However, there are theological reasons against the assumption that God ever acts in this way.