By "an infinite series of contingent beings" is meant a beginningless succession of modally contingent beings, such that the succession of beings occupies an infinite number of equal-lengthened temporal intervals (e.g. an aleph-zero number of past years).

where ds is the space-time interval between two events, a the scale factor representing the radius of the universe at a given time, and do is the line element of a space with constant curvature. The application of this metric to the field equations provides us with the Friedmann’s solutions, which are the heart of big bang cosmology. With the cosmological constant omitted, these solutions read.

Kalam cosmological arguments have recently been the subject of criticisms, at least inter alia, by physicists---Paul Davies, Stephen Hawking---and philosophers of science---Adolf Grunbaum. In a series of recent articles, William Craig has attempted to show that these criticisms are “superficial, iII-conceived, and based on misunderstanding.” I argue that, while some of the discussion of Davies and Hawking is not philosophically sophisticated, the points raised by Davies, Hawking and Grunbaum do suffice to undermine the dialectical efficacy of kalam cosmological arguments.

Hypotheses about the shape of causal reality admit of both theistic and non-theistic interpretations. I argue that, on the simplest hypotheses about the causal shape of reality—infinite regress, contingent initial boundary, necessary initial boundary—there is good reason to suppose that non-theism is always either preferable to, or at least the equal of, theism, at least insofar as we restrict our attention merely to the domain of explanation of existence. Moreover, I suggest that it is perfectly proper for naturalists to be (...) undecided between these simple hypotheses about the causal shape of reality: contrary to the proponents of cosmological arguments, there are no decisive objections to any of these simple hypotheses. (I argue this case in detail in connection with objections offered by William Lane Craig; however, I believe that the case holds quite generally.). (shrink)

Recent models in quantum cosmology make use of the concept of imaginary time. These models all conjecture a join between regions of imaginary time and regions of real time. We examine the model of James Hartle and Stephen Hawking to argue that the various no-boundary attempts to interpret the transition from imaginary to real time in a logically consistent and physically significant way all fail. We believe this conclusion also applies to quantum tunneling models, such as that proposed by Alexander (...) Vilenkin. We conclude, therefore, that the notion of emerging from imaginary time is incoherent. A consequence of this conclusion seems to be that the whole class of cosmological models appealing to imaginary time is thereby refuted. (shrink)

The theory of relativity is often regarded as inhospitable to the idea that there is an objective passage of time in the world. In light of this, many philosophers and physicists embrace a “block universe” view, according to which change and temporal passage are merely a subjective appearance or illusion. My aim in this paper is to argue against such a view, and show that we can make sense of an objective passage of time in the setting of relativity theory (...) by abandoning the assumption that the now must be global, and re-conceiving temporal passage as a purely local phenomenon. Various versions of local becoming have been proposed in the literature. Here I focus on the causal diamond theory proposed by Steven F. Savitt and Richard Arthur, which models the now in terms of a local structure called a causal diamond. After defending the reality of temporal passage and exploring its compatibility with relativity theory, I show how the causal diamond approach can be used to counter the argument for the ideality of time due to Kurt Gödel, based on his “rotating universe” solution to the Einstein field equations. I defend the second component of his argument, the modal step, against the consensus view that finds it wanting, and reject the first step, showing that the Gödel universe is compatible with an objective passage of time as long as the latter is construed locally, along the lines of the causal diamond approach. (shrink)