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Youwen Wu 2024-10-19 00:00:26 -07:00
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@ -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: