Benardete paradoxes involve a beginningless set each member of which satisfies some predicate just in case no earlier member satisfies it. Such paradoxes have been wielded on behalf of arguments for the impossibility of an infinite past. These arguments often deploy patchwork principles in support of their key linking premise. Here I argue that patchwork principles fail to justify this key premise.

It is often said that time must have a beginning because otherwise the series of past events would have the paradoxical features of an actual infinite. In the present paper, we show that, even given a dynamic theory of time, the cardinality of an endless series of events, each of which will occur, is the same as that of a beginningless series of events, each of which has occurred. Both are denumerably infinite. So if an endless series of events is (...) possible, then the possibility of a beginningless series of past events should not be rejected merely on the ground that it would be an actual infinite. What would be required to rebut our argument is a symmetry breaker – something that motivates treating the past relevantly differently to the future. We consider several attempts to provide a symmetry breaker and show that none of them is successful. (shrink)

In a recent paper published in 2020, Alex Malpass & Wes Morriston discuss the difference between beginningless past and an endless future and try to show that beginningless series of past events and an endless series of future ones are in the same boat. So if (as they believe) an endless series of events is possible, then the possibility of a beginningless series of past events should not be rejected merely on the ground that it would be an actual infinite. (...) I will show in this paper that Malpass and Morriston’s refutations are flawed and that their argument does not provide any evidence that a beginningless past is possible. (shrink)

Yishai Cohen raises three related objections to the kalam cosmological argument. Firstly, Cohen argues that, if the argument against the possibility of an actual infinite, which is used to support the kalam cosmological argument, is sound, then a predetermined endless future must also be impossible. Secondly, Cohen argues that the possibility of a predetermined endless future entails the possibility of an actual infinite. Finally, Cohen maintains that Robert C. Koons’ Grim Reaper paradox shows that a predetermined endless future is impossible. (...) I intend to show that Cohen’s three arguments are not sound and that the possibility of an endless future is not a thorn in the kalam cosmological argument. (shrink)