youwen5/alexandria
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

update draft of paper 1

Browse source
This commit is contained in:
Youwen Wu 2024-10-18 22:49:20 -07:00
parent a2f5f23749
commit d2c948b18b
Signed by: youwen5
GPG key ID: 865658ED1FE61EC3
3 changed files with 117 additions and 94 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

BIN
work/2024/phil-1/paper-1/main.pdf
View file

Binary file not shown.

209
work/2024/phil-1/paper-1/main.typ
View file

@ -8,10 +8,17 @@
bibliography: bibliography("refs.bib"), bibliography: bibliography("refs.bib"),
) )
#show: word-count.with(exclude: (heading, <wordcount-exclude>, table)) #show: word-count.with(exclude: (
heading,
<wordcount-exclude>,
table,
figure,
footnote,
))
#set cite(style: "institute-of-electrical-and-electronics-engineers") #set cite(style: "institute-of-electrical-and-electronics-engineers")
#set text(fractions: true) #set text(fractions: true)
#set table(inset: 8pt, align: center)
#align( #align(
@ -28,7 +35,7 @@
#footnote[ #footnote[
Figure computed programmatically during document compilation. Discounts Figure computed programmatically during document compilation. Discounts
content in tables and the AI contribution statement. content in tables and the AI contribution statement.
]<wordcount-exclude> ]
], ],
), ),
), ),
@ -38,11 +45,11 @@
= Introduction = Introduction
The argument for Betting on God says that you should believe in God, regardless The argument for Betting on God says that you should believe in God, regardless
of other evidence, purely out of self-interest. In this paper, I challenge this of other evidence, purely out of rational self-interest. In this paper, I
argument by assessing the premise that believing in a particular God always challenge this argument by assessing the premise that believing in a particular
guarantees the greatest expected utility. God always guarantees the greatest expected utility.
The author's argument for belief in God #cite(supplement: [p. 38], The author's argument for belief in God on #cite(supplement: [p. 38],
<Korman2022-KORLFA>) goes as follows: <Korman2022-KORLFA>) goes as follows:
#indented-argument( #indented-argument(
@ -53,21 +60,29 @@ The author's argument for belief in God #cite(supplement: [p. 38],
[So, you should believe in God.], [So, you should believe in God.],
) )
BG1 should be uncontroversial. If you expect an action to bring you the most BG1 should be uncontroversial. If you expect that an action will bring you the
utility (i.e. be the most useful), it's rational to do it. most utility (i.e. be the most useful), it's rational to choose to do it.
// To justify BG2, the author uses a so-called "decision matrix" to compute the
// expected utility of each combination of action and possible outcome. The
// possible actions are placed on the rows, and the possible outcomes are placed
// on the columns, except for the last column, which is the calculated expected
// utility. At each intersection of a row and column, we place the utility gained
// from that combination of action and outcome. The expected utility for a given
// action is computed by multiplying the utility of each action-outcome pair in
// that action's row by the probability of the corresponding outcome occurring,
// and summing up all of those values.
To justify BG2, the author uses a so-called "decision matrix" to compute the To justify BG2, the author uses a so-called "decision matrix" to compute the
expected utility of each combination of action and possible outcome. The expected utility of either belief or disbelief in God. Both possible actions
possible actions are placed on the rows, and the possible outcomes are placed are placed on the first column, and the possible outcomes (God existing or God
on the columns, except for the last column, which is the calculated expected not existing) are placed on the first row. The last column of the matrix
utility. At each intersection of a row and column, we place the utility we gain represents the expected utility of the action in its corresponding row. At each
from that combination of action and outcome. The expected utility for a given intersection of action and outcome, we write the utility gained from that
action is computed by multiplying the utility of each action-outcome pair in action-outcome combination.
that row by the probability of the corresponding outcome occurring, and summing
up all of those values.
Here is the decision matrix the author proposes on #cite(supplement: [p. 38], Here is the decision matrix the author proposes on #cite(supplement: [p. 38],
<Korman2022-KORLFA>) which gives the expected utility for believing or not <Korman2022-KORLFA>) which gives the expected utilities for believing or not
believing in God. believing in God.
#show table.cell.where(x: 0): strong #show table.cell.where(x: 0): strong
@ -97,51 +112,59 @@ believing in God.
), ),
) )
Note that the numerical utility values themselves have no meaning, and they are Note that utility doesn't provide an empirical measure of "usefulness" or
meant to be viewed relative to each other. Utility doesn't literally provide an "happiness," and should be viewed as a relative measurement.
empirical measure of "usefulness" or "happiness."
We assign the various finite utilities as we see fit, based on how much each We assign each action-outcome combination utilities as we see fit, based on how
scenario benefits us. In the case where God does exist, and you believed in much each scenario benefits us. You'll see shortly that the exact values we set
God, then you are rewarded with an eternal afterlife of bliss and pleasure in for the finite utilities don't matter when infinite utility is introduced.
heaven. This reward is infinitely greater than any possible reward on earth, so
it has a utility of $infinity$.
So, the expected utility for not believing is $0.5 times 1 + 0.5 times 3 = 2$, In the specific case where God does exist, and you believed in God, you
and the expected utility is $0.5 times infinity + 0.5 times 2 = infinity$. If, are rewarded with an eternal afterlife of bliss and pleasure in heaven. This
according to BG1, you should pick the option with greatest expected utility, reward is infinitely greater than any possible reward on earth, so it has a
clearly you should choose to believe in God, because the expected utility is utility of $infinity$.
$infinity$.
The exact utilities don't matter much, since any finite utility you could gain
for atheism cannot possibly be greater than the infinite expected utility of To calculate the expected utility of a given action, we first multiply the
believing in God. Also, as the author points out on #cite(<Korman2022-KORLFA>, utility gained from each action-outcome combination in the action's row by the
supplement: [p. 40]), the exact probabilities don't matter either since probability of the corresponding outcome occurring. We then sum up all of these
multiplying them by $infinity$ still results in the expected utility of values to obtain the final expected utility.
So, the expected utility for disbelief is $0.5 times 1 + 0.5 times 3 = 2$, and
the expected utility for belief is $0.5 times infinity + 0.5 times 2 =
infinity$. If, according to BG1, you should pick the option with greatest
expected utility, you should clearly choose to believe in God, because the
expected utility is $infinity$.
Also, as the author points out on #cite(<Korman2022-KORLFA>, supplement: [p.
40]), the exact probabilities don't matter either since multiplying even the
smallest percentage by $infinity$ still results in the expected utility of
$infinity$. $infinity$.
I will show that the Argument for Betting on God fails because BG2 fails. In I will show that the Argument for Betting on God fails because BG2 fails. In
section 2, I argue you cannot determine whether or not believing in God has the section 2, I argue you cannot determine whether or not believing in God has the
greatest expected utility because the decision matrix approach fails when greatest expected utility because the decision matrix approach fails when
possible outcomes involving infinitely negative utilities are introduced. In possible outcomes involving infinitely negative utilities are introduced. In
section 3, I address a possible response to this objection. section 3, I address a few possible responses to this objection.
= Possibility of Infinite Suffering = Possibility of Infinite Suffering
It is possible there are more gods than just the one that sends you to an I propose that there is the possibility of more gods than just the Christian one that
eternal afterlife for believing? The author partially addresses this in sends you to an eternal afterlife for believing. The author partially addresses
#cite(<Korman2022-KORLFA>, supplement: [pp. 43-44]), using the example of Zeus. this concern on #cite(<Korman2022-KORLFA>, supplement: [pp. 43-44]), using the
Zeus will only reward those who believe in him with an eternal afterlife of example of Zeus. Zeus will only reward those who believe in him specifically
pleasure. So, if you believe in the wrong god, you don't go to the afterlife. with an eternal afterlife. So, if you believe in the wrong god, you don't go to
The author concludes either believing in Zeus or the Christian God still has the afterlife. The author concludes believing in either Zeus or the Christian
expected utilities of $infinity$, while being an atheist does has a finite God still result in expected utilities of $infinity$, while being an atheist
expected utility. Therefore, it is still preferable to believe in _some_ god always has a finite expected utility. Therefore, you should still believe in
that may grant you an eternal afterlife, although no argument is made for _some_ god that could grant you an eternal afterlife, although no argument is
_which_ god. made for _which_ god.
However, this leaves out the possibility of gods who punish you for some However, this leaves out the possibility of gods who instead punish you for
reason. For instance, suppose there exists an _Evil God_ who sends anyone who eternity. For instance, suppose there exists an _Evil God_ who sends any theist
believes in any god to hell for eternity, and does nothing to atheists. 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
Evil God themselves.
Let us modify our decision matrix to model an outcome where the Evil God Let us modify our decision matrix to model an outcome where the Evil God
exists. exists.
@ -158,7 +181,7 @@ exists.
table.header( table.header(
[], [],
[Correct god exists ($33.3%$)], [Correct god exists ($33.3%$)],
[No god exists ($33.3%$)], [No god or wrong god ($33.3%$)],
[Evil God exists ($33.3%$)], [Evil God exists ($33.3%$)],
[E.U.], [E.U.],
), ),
@ -179,19 +202,18 @@ We've added the new option to our matrix. For the sake of argument, let's say
each option has an equally likely outcome. Again, the exact probabilities don't each option has an equally likely outcome. Again, the exact probabilities don't
really matter when we're multiplying them by infinity. really matter when we're multiplying them by infinity.
The utilities are mostly the same as before. Not believing in any god and the The utilities are mostly the same as before. However, the theist now faces the
Evil God existing is now the best case for the atheist since they avoided possibility of the worst case of all: eternal punishment if the Evil God
infinite suffering. However, the theist now faces the possibility of the worst exists. If eternal bliss in heaven has a utility of $infinity$, then it follows
case of all: eternal punishment for believing in the wrong god. If eternal that we should represent eternal punishment in hell with a utility of
bliss in heaven has a utility of $infinity$, then it follows that we should $-infinity$.
represent eternal punishment in hell with a utility of $-infinity$.
There is a problem: how do we calculate the expected utility of believing in Let us attempt to calculate the expected utility of believing in god using our
god? We have $0.333 times infinity + 0.333 times 1 + 0.333 times -infinity$. usual method. We have $0.333 times infinity + 0.333 times 1 + 0.333 times
What is $infinity - infinity$? A naive answer might be 0, but infinity is not a -infinity$. What is $infinity - infinity$? A naive answer might be 0, but
number in the traditional sense. It makes no sense to add or subtract infinite infinity is not a number in the traditional sense. It makes no sense to add or
values. For instance, try and subtract the total amount of integers subtract infinite values. For instance, try and subtract the total amount of
($infinity$) from the total amount of real numbers (also $infinity$) integers ($infinity$) from the total amount of real numbers (also $infinity$)
#footnote[Famously, this infinity is "larger" than the infinite number of #footnote[Famously, this infinity is "larger" than the infinite number of
integers in the sense of cardinality (G. Cantor). But subtracting them still integers in the sense of cardinality (G. Cantor). But subtracting them still
makes no mathematical or physical sense.]. Clearly, this notion is meaningless makes no mathematical or physical sense.]. Clearly, this notion is meaningless
@ -204,13 +226,13 @@ Consider the following Indeterminate Utilities argument:
title: "The Indeterminate Utilities argument", title: "The Indeterminate Utilities argument",
abbreviation: "IU", abbreviation: "IU",
[If the expected utility of believing in god is undefined, then we [If the expected utility of believing in god is undefined, then we
cannot compare the expected utilities of believing in god or not believing cannot compare the expected utilities of believing in god and not believing
in god.], in god.],
[The expected utility of believing in god is undefined.], [The expected utility of believing in god is undefined.],
[So, we cannot compare the expected utilities of believing in god or [So, we cannot compare the expected utilities of believing in god and
not believing in god. not believing in god.
], ],
[If we cannot compare the expected utilities of believing in god or [If we cannot compare the expected utilities of believing in god and
not believing in god, then we cannot determine if believing in god has a not believing in god, then we cannot determine if believing in god has a
higher expected utility than not believing in god. higher expected utility than not believing in god.
], ],
@ -254,26 +276,26 @@ utility, it is a false premise.
One might argue that it is not plausible there is an Evil God who punishes all One might argue that it is not plausible there is an Evil God who punishes all
theists, including their own believers. Many religions present a god that theists, including their own believers. Many religions present a god that
rewards believers and at most punishes disbelievers. None of the major world rewards believers and at most punishes disbelievers, yet none of the major
religions propose an Evil God who punishes all believers. It's much more likely world religions propose an Evil God who punishes all believers
that a benevolent god exists than an evil one. indiscriminately. It's much more likely that a benevolent god exists than an
evil one.
I contend that it doesn't matter whether or not the Evil God is less plausible Notice that it doesn't actually matter how plausible the Evil God is. If a
than a benevolent god. Surely, if a rational atheist who is unconvinced by all rational atheist should concede there is at least a non-zero chance some god
the world's scriptures can still concede that there is at least a non-zero exists, then there must also be a non-zero chance the Evil God exists. After
chance that some god exists, the rational theist should also concede that there all, can you say for sure that the Evil God doesn't exist? All it takes is that
is a non-zero chance that the Evil God exists. All it takes is that non-zero non-zero chance, no matter how small, because multiplying it by $-infinity$
chance, no matter how small, because multiplying it by $-infinity$ still still results in the undefined expected utility.
results in the undefined expected utility.
== Finite utilities == Finite utilities
One might argue that we can avoid using $infinity$ to ensure that all expected One might argue that we can avoid using $infinity$ to ensure that all expected
utility calculations are defined. Instead, suppose that the utility of going to utility calculations are defined. Instead, suppose the utility of going to
heaven is just an immensely large finite number. The utility of going to hell heaven is just an immensely large finite number. The utility of going to hell
is likewise a very negative number. All of our expected utility calculations is likewise a very negative number. All of our expected utility calculations
will be defined, and given sufficiently large utilities, we should be able to will be defined, since infinity is not used. Given sufficiently large
make a similar argument for believing in god. utilities, we should be able to make a similar argument for believing in god.
// The problem with this argument is that we now open our expected utilities up to // The problem with this argument is that we now open our expected utilities up to
// individual subjective determination. A core feature of the previous argument // individual subjective determination. A core feature of the previous argument
@ -284,21 +306,24 @@ make a similar argument for believing in god.
// well. This greatly complicates the decision matrix. // well. This greatly complicates the decision matrix.
The problem with this argument is that infinity has a special property the The problem with this argument is that infinity has a special property the
argument relies on. Namely, any number multiplied by $infinity$ is still argument relies on that no finite numbers have. Namely, any number multiplied
$infinity$, so the exact probabilities we set for the existence of God don't by $infinity$ is still $infinity$, so the exact probabilities we set for the
matter. This is important for defending against the objection the author existence of God don't matter. This is important for defending against the
mentions on #cite(<Korman2022-KORLFA>, supplement: [p. 40]), that the objection that the probabilities are possibly incorrect which the author
probabilities are possibly incorrect, since the numbers don't matter anyways. mentions on #cite(<Korman2022-KORLFA>, supplement: [p. 40]). If the exact
numbers don't matter due to $infinity$, it doesn't matter if they might be
wrong (as long as they are non-zero).
If, instead, only finite utilities were used, then the theist must contend with If, instead, only finite utilities were used, the concern that the
the concern that the probabilities in the matrix are wrong. There could probabilities in the matrix are wrong cannot be resolved with the same argument
conceivably exist a matrix with probabilities for a benevolent god and an Evil as before. There could conceivably exist a matrix with probabilities for a
God such that the expected utility of atheism is actually higher. The issue is benevolent god and an Evil God such that the expected utility of atheism is
we cannot say for sure what the probabilities of the benevolent god and the actually higher. The issue is we cannot say for sure what the probabilities of
Evil God existing are. If we cannot know what the actual probabilities are, the benevolent god and the Evil God existing are. If we cannot know what the
then we cannot know the final outcome of our matrix. So, without knowing the actual probabilities are, then we cannot know the final outcome of our matrix.
final outcome of the matrix, we still cannot determine whether or not believing So, without knowing the final outcome of the matrix, we still cannot determine
in god has greater expected utility, and BG2 still fails. whether or not believing in god has greater expected utility, and BG2 still
fails.
#pagebreak() #pagebreak()

2
work/2024/phil-1/paper-1/prelude.typ
View file

@ -14,5 +14,3 @@
..args.pos(), ..args.pos(),
) )
] ]