diff --git a/work/2024/phil-1/paper-1/main.pdf b/work/2024/phil-1/paper-1/main.pdf index 651b443..fa24552 100644 Binary files a/work/2024/phil-1/paper-1/main.pdf and b/work/2024/phil-1/paper-1/main.pdf differ diff --git a/work/2024/phil-1/paper-1/main.typ b/work/2024/phil-1/paper-1/main.typ index 8b72688..00fae1b 100644 --- a/work/2024/phil-1/paper-1/main.typ +++ b/work/2024/phil-1/paper-1/main.typ @@ -156,11 +156,11 @@ example of Zeus. Zeus will only reward those who believe in him specifically with an eternal afterlife. So, if you believe in the wrong god, you don't go to the afterlife. The author concludes believing in either Zeus or the Christian God still result in expected utilities of $infinity$, while being an atheist -always has a finite expected utility. Therefore, you should still believe in +always has a finite expected utility. Therefore, you should always believe in _some_ god that could grant you an eternal afterlife, although no argument is made for _which_ god. -However, this leaves out the possibility of gods who instead punish you for +However, this leaves out the possibility of a god who instead punishes you for eternity. For instance, suppose there exists an _Evil God_ who sends any theist to hell for eternity, and does nothing to atheists. That is, the Evil God will punish anyone who believes in _any_ god, including those who believe in the @@ -214,11 +214,14 @@ usual method. We have $0.333 times infinity + 0.333 times 1 + 0.333 times infinity is not a number in the traditional sense. It makes no sense to add or subtract infinite values. For instance, try and subtract the total amount of integers ($infinity$) from the total amount of real numbers (also $infinity$) -#footnote[Famously, this infinity is "larger" than the infinite number of -integers in the sense of cardinality (G. Cantor). But subtracting them still -makes no mathematical or physical sense.]. Clearly, this notion is meaningless -and we cannot obtain a solution. So, we consider $infinity - infinity$ an -_indeterminate form_. So, the expected utility is now _undefined_. +#footnote[Famously, the infinity of $RR$ is "larger" than the infinity of $ZZ$ +in the sense of cardinality, where $frak(c) > aleph_0$ (G. Cantor). However, +our familiar algebraic operations of $+$ and $-$ are still not defined on them. +Perhaps we could pursue a line of reasoning to rigorously define algebra with +infinity using the hyperreals $attach(RR, tl: *)$, but that is out of the scope +of this paper.]. Clearly, this notion is meaningless and we cannot obtain a +solution. So, we consider $infinity - infinity$ an _indeterminate form_. So, +the expected utility is now _undefined_. Consider the following Indeterminate Utilities argument: