Federico Viglione

Recently, it has been argued that nothing seems to logically or metaphysically prevent a traversal of the infinite (i.e., the completion of an infinite series of equally long successive additions) starting at some time. In this paper, I support a stronger claim: that physically reasonable models of general relativity (Malament-Hogarth models) provide reason to think such a traversal may be physically possible, at least in what I call a proxy fashion. Moreover, I advance a conjecture based on a speculative yet physically reasonable cosmological model (Conformal Cyclic Cosmology): that it may also be physically possible to traverse the infinite in a non-proxy fashion, i.e., by both starting and finishing at some time.

Cosmic simultaneity is the proposal that we can reconcile absolute simultaneity with relativity by means of the cosmic time function definable in certain cosmological models. In this paper, I add a new criticism to the debate on cosmic simultaneity: once the relevant notion of absoluteness is clarified, a seemingly appealing approach to cosmic simultaneity, the metaphysical approach, proves to be inconsistent. My overall argument proceeds as follows. First, I argue for what I call the Causal Connection Condition (CCC): the fact that two events stand in a certain temporal relation is absolute only if it obtains independently of the occurrence of any causally disconnected event. I then show that, according to metaphysical cosmic simultaneity, whether two events are cosmically simultaneous depends on causally disconnected events. I conclude that metaphysical cosmic simultaneity is inconsistent.

This paper offers a critical assessment of the Successive Addition Argument (SAA) in support of past finitism, i.e., the thesis that the past of the universe is finite in duration. This old philosophical argument, re-popularized by William Lane Craig in modern times, contends that the universe’s past cannot be infinite because an infinite series cannot be formed by successive addition. I first address a recently popular objection to the argument, namely the Zeno Objection, showing that it can be easily dismissed once each addition is taken to have the same duration. Nevertheless, I contend that the _onus_ of the proof lies on those who propose the SAA, and that their main argumentative strategies fail. Indeed, many of their arguments are based on the supposedly uncontroversial claim that one cannot traverse the infinite by starting somewhere. I argue that a complete traversal of the infinite, with a beginning infinitely far from its end, is logically and metaphysically possible. Other popular arguments against traversed infinities are based on thought experiments such as the backward counter or the Tristram Shandy thought experiments. I argue that, once infinitely far beginnings are granted, none of the arguments based on such thought experiments prove effective, so that the SAA must be rejected.