The universe cannot have existed for ever, otherwise it would have reached its equilibrium end state an infinite time ago. Conclusion: the universe did not always exist." More recently though physicists have proposed various ideas for how the universe could have existed for an infinite time, such as eternal inflation. But in 2012, Alexander Vilenkin and Audrey Mithani of Tufts University wrote a paper claiming that in any such scenario past time could not have been infinite. It could however have been "before any nameable time", according to Leonard Susskind. Critical reception Kant's argument for finitism has been widely discussed, for instance Jonathan Bennett points out that Kant's argument is not a sound logical proof: His assertion that "Now the infinity of a series consists in the fact that it can never be completed through successive synthesis. It thus follows that it is impossible for an infinite world-series to have passed away", assumes that the universe was created at a beginning and then progressed from there, which seems to assume the conclusion. A universe that simply existed and had not been created, or a universe that was created as an infinite progression, for instance, would still be possible. Bennett quotes Strawson: Some of the criticism of William Lane Craig's argument for temporal finitism has been discussed and expanded on by Stephen Puryear. In this, he writes Craig's argument as: If the universe did not have a beginning, then the past would consist in an infinite temporal sequence of events. An infinite temporal sequence of past events would be actually and not merely potentially infinite. It is impossible for a sequence formed by successive addition to be actually infinite. The temporal sequence of past events was formed by successive addition. Therefore, the universe had a beginning. Puryear points out that Aristotle and Aquinas had an opposing view to point 2, but that the most contentious is point 3. Puryear says that many philosophers have disagreed with point 3, and adds his own objection: "Consider the fact that things move from one point in space to another. In so doing, the moving object passes through an actual infinity of intervening points. Hence, motion involves traversing an actual infinite ... Accordingly, the finitist of this stripe must be mistaken. Similarly, whenever some period of time elapses, an actual infinite has been traversed, namely, the actual infinity of instants that make up that period