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I feel like this doesn't help. The only reason that time is finite is that we live in a non-classical universe (classical universes are infinite in time), and this poses a huge problem to any ethical theory that seeks to be global and consistent. Ethical theories typically assume something like a classical background context, because that's the only way to get ideas about e.g. causation or knowledge off the ground easily. By appealing to the finitude of time, you escape the St Petersburg Paradox but only at the expense of having to explain the structure of your decision-making in ways that are globally compatible with GR - and, well, good luck with that!

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