Executive summary: The post introduces a new paper arguing that many paradoxes in decision theory, economics, and ethics involving infinities can be resolved by replacing the extended reals with hyperreal numbers, which allow more nuanced evaluation and comparison of infinite sums and integrals, preserving intuitive values without resorting to discounting or bounded utility.
Key points:
Standard use of the extended reals forces divergent sums/integrals to collapse into +∞, which obscures meaningful comparisons and pressures theorists to artificially constrain models (e.g., bounded utility, discounting).
Hyperreal numbers provide a richer framework, enabling natural comparisons of infinite values (e.g., distinguishing between ω and ω², and allowing finite changes to matter).
The method has implications for statistics (handling infinite means/variances), decision theory (infinite expectations), economics (infinite utility streams), and ethics (evaluating infinite worlds).
By resolving the technical issue, the approach supports keeping intuitive stances on finite cases (e.g., harms matter equally regardless of when they occur) rather than distorting them to sidestep infinities.
The theory preserves the Pareto principle but not unrestricted permutation, and shows that many counterintuitive “infinite paradoxes” arise from overly coarse number systems.
Remaining issues are acknowledged, but the central result is that infinities can be treated in ways that behave much like finite values, avoiding paradoxes like ∞ + 1 = ∞ or Hilbert-hotel rearrangements.
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Executive summary: The post introduces a new paper arguing that many paradoxes in decision theory, economics, and ethics involving infinities can be resolved by replacing the extended reals with hyperreal numbers, which allow more nuanced evaluation and comparison of infinite sums and integrals, preserving intuitive values without resorting to discounting or bounded utility.
Key points:
Standard use of the extended reals forces divergent sums/integrals to collapse into +∞, which obscures meaningful comparisons and pressures theorists to artificially constrain models (e.g., bounded utility, discounting).
Hyperreal numbers provide a richer framework, enabling natural comparisons of infinite values (e.g., distinguishing between ω and ω², and allowing finite changes to matter).
The method has implications for statistics (handling infinite means/variances), decision theory (infinite expectations), economics (infinite utility streams), and ethics (evaluating infinite worlds).
By resolving the technical issue, the approach supports keeping intuitive stances on finite cases (e.g., harms matter equally regardless of when they occur) rather than distorting them to sidestep infinities.
The theory preserves the Pareto principle but not unrestricted permutation, and shows that many counterintuitive “infinite paradoxes” arise from overly coarse number systems.
Remaining issues are acknowledged, but the central result is that infinities can be treated in ways that behave much like finite values, avoiding paradoxes like ∞ + 1 = ∞ or Hilbert-hotel rearrangements.
This comment was auto-generated by the EA Forum Team. Feel free to point out issues with this summary by replying to the comment, and contact us if you have feedback.