In his recent interview on the 80000 Hours Podcast, Toby Ord discussed how nonstandard analysis and its notion of hyperreals may help resolve some apparent issues arising from infinite ethics (link to transcript). For those interested in learning more about nonstandard analysis, there are various books and online resources. Many involve fairly high-level math as they are aimed at putting what was originally an intuitive but imprecise idea onto rigorous footing. Instead of those, you might want to check out a book like that of H. Jerome Keisler’s Elementary Calculus: An Infinitesimal Approach, which is freely available online. This book aims to be an introductory calculus textbook for college students, which uses hyperreals instead of limits and delta-epsilon proofs to teach the essential ideas of calculus such as derivatives and integrals. I haven’t actually read this book but believe it is the best known book of this sort. Here’s another similar-seeming book by Dan Sloughter.
In his recent interview on the 80000 Hours Podcast, Toby Ord discussed how nonstandard analysis and its notion of hyperreals may help resolve some apparent issues arising from infinite ethics (link to transcript). For those interested in learning more about nonstandard analysis, there are various books and online resources. Many involve fairly high-level math as they are aimed at putting what was originally an intuitive but imprecise idea onto rigorous footing. Instead of those, you might want to check out a book like that of H. Jerome Keisler’s Elementary Calculus: An Infinitesimal Approach, which is freely available online. This book aims to be an introductory calculus textbook for college students, which uses hyperreals instead of limits and delta-epsilon proofs to teach the essential ideas of calculus such as derivatives and integrals. I haven’t actually read this book but believe it is the best known book of this sort. Here’s another similar-seeming book by Dan Sloughter.