Troy Dana

We examine several new and underexplored arguments for the finitude of the past and the impossibility of Hilbert’s Hotel. The first argument concludes that Hilbert’s Hotel is impossible due to an alleged contradiction arising from the causal powers of infinitely many guests. A second argument contends that if the past is infinite, then it would be possible to construct Hilbert’s Hotel. Since that’s not possible, the past is finite. A third argument is based on a thought experiment involving Methuselah’s diary and likewise concludes that the past is finite. Each argument fails, but their flaws are quite instructive. We also develop novel future-oriented parodies for each argument with the implausible conclusion that the future will (and perhaps must) come to an end.

Benardete paradoxes involve infinite collections of Grim Reapers, assassins, demons, deafening peals, or even sentences. These paradoxes have recently been used in arguments for finitist metaphysical theses such as temporal finitism, causal finitism, and discrete views of time. Here we develop a new finite Benardete-like paradox. We then use this paradox to defend a companions in guilt argument that challenges recent applications of patchwork principles on behalf of the aforementioned finitist arguments. Finally, we develop another problem for those applications by examining the notion of exact duplication.