Sleeping Beauty
The Sleeping Beauty problem is a puzzle in decision theory. Here is the problem, from Wikipedia:
Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details: On Sunday she will be put to sleep. Once or twice, during the experiment, Sleeping Beauty will be awakened, interviewed, and put back to sleep with an amnesia-inducing drug that makes her forget that awakening. A fair coin will be tossed to determine which experimental procedure to undertake:
If the coin comes up heads, Sleeping Beauty will be awakened and interviewed on Monday only.
If the coin comes up tails, she will be awakened and interviewed on Monday and Tuesday.
In either case, she will be awakened on Wednesday without interview and the experiment ends.
Any time Sleeping Beauty is awakened and interviewed she will not be able to tell which day it is or whether she has been awakened before. During the interview Sleeping Beauty is asked: "What is your credence now for the proposition that the coin landed heads?"
The problem is unsolved and philosophers are in disagreement, but there are two common answers. “Halvers” believe the answer is ½, and “thirders” believe the answer is ⅓.
Thirders argue that, given that the coin landed tails, when you wake up during the experiment you can’t distinguish between the days, so your belief that it’s Monday should equal the belief that it’s Tuesday: P(tails, Monday) = P(tails, Tuesday). Additionally, if you were to wake up and find out that it is Monday, you’d be indifferent between heads and tails: P(heads, Monday) = P(tails, Monday). Therefore, P(heads, Monday) = P(tails, Monday) = P(tails, Tuesday), and the probabilities must add up to 100%, so there is a ⅓ chance the coin landed heads.
Halvers argue that the probability of a fair coin landing on heads is ½, and she gets no new information about the coin flip when she wakes up, so she should still believe there is a ½ chance that the coin landed heads.
In his book Anthropic Bias, philosopher Nick Bostrom outlines two different ways you might reason about this.
The self-sampling assumption (SSA) says that you should reason as if you are selected from the set of all actually existing members of your reference class.
The self-indication assumption (SIA) says that you should reason as if you are selected from the set of all possible members of your reference class.
The self-sampling assumption leads to the ½ solution to the Sleeping Beauty problem, and the self-indication assumption leads to the ⅓ solution. One important difference between the two is that the SIA implies that you should be more willing to believe in theories that imply you are likelier to exist (because you get to exist and think about them if they’re true, but you’re less likely to exist and think about them if they’re false), whereas the SSA implies that the truth or falsehood of a theory is independent of whether you exist, even if you’d be more likely to exist if it were true.
Answer to Job
(See also: Answer to Job, Unsong, Bentham’s Bulldog arguments for god)
The problem of evil is an argument against the existence of god that says that there is evil in the world, which contradicts the claim that the universe is controlled by an omnipotent, benevolent god who works against evil. The usual theist response is that evil is caused not by god but by people misusing their free will to hurt others. The usual atheist response is to bring up the problem of natural evil, which is the same as the above but using examples of evil existing in nature, caused by natural disasters or by animals which do not have free will.
According to Wikipedia, “a theodicy is an argument that attempts to resolve the problem of evil that arises when all power and all goodness are simultaneously ascribed to God.”
Many-worlds theodicy is a theodicy that explains the existence of evil by the claim that, if god is infinitely benevolent, he would want to create as many happy beings as possible so that they all get to experience the blessing of life. He wouldn’t create a world filled with people who are constantly suffering, but obviously he would create a world full of rejoicing and happiness, and less obviously he would also create worlds with some suffering and some blessings - as long as there is more good than evil in the world, a benevolent god would still want it to exist.
You might sometimes ask yourself, “Why do we exist?” Well, atheists say we exist because of evolution and theists say we exist because god created us. Substack blogger Bentham’s Bulldog uses many-worlds theodicy in his anthropic argument for god, with the further detail that god would create not just infinity but an uncountably infinite number of worlds. Combined with the self-indication assumption (which says that you should give more credence to theories that imply you are more likely to exist), the ratio of existing beings in a universe ruled by god (uncountably infinite) to beings that exist in a universe with no god (finite or countably infinite) is infinity to one, so the evidence is overwhelmingly in favor of the theist explanation for existence. You are forced to conclude that the probability that god exists is 100% and the probability that there is no god is 0%.
Of course, this logic is entirely correct and there are absolutely no problems with it. But I regrettably must point out one unfortunate fact that he forgot to account for.
Ichneumonidae
The Ichneumonidae, also known as ichneumon wasps or Darwin wasps, are a family of parasitic wasps found in all continents except Antarctica. They have a very creepy life cycle. First, adult wasps mate, and the female needs somewhere to lay her eggs. So she finds a caterpillar, and stings it in the neck with her specialized venom, which will paralyze it so it stays alive but cannot run away. Next, she chews her way into the caterpillar’s abdomen and lays her eggs in the paralyzed caterpillar, where they hatch. As the larvae grow, they eat the caterpillar from the inside out, starting with the least essential organs first and ending with the most essential parts last, keeping the caterpillar alive as long as possible so that it stays fresh to feed the larvae. Unfortunately, the poor helpless caterpillar is not unconscious, only paralyzed, so it is aware of and feels the entire horrifying process of being stung, kidnapped, having eggs laid in its stomach, and being eaten alive by wasp larvae until they burst out of it and fly away to repeat the cycle with another caterpillar.
Charles Darwin was a highly devout Christian for almost all of his life, until he studied the ichneumon wasps shortly before he died. They are so disturbing that he lost his faith and became an atheist, unable to believe that a loving god could allow a creature as horrible as the ichneumonidae to exist. But actually, renouncing god is the wrong conclusion. Besides theism and atheism, there is another theory that better explains the evidence: maltheism, the proposition that the universe is ruled by an all-knowing, all-powerful, and infinitely evil god.
r/K selection theory
In r/K selection theory, selective pressures are hypothesised to drive evolution in one of two generalized directions: r- or K-selection. r and K are terms in a differential equation, the Verhulst model of population dynamics:
dN/dt = r N (1 - N/K)
where N is the population, r is the maximum growth rate, K is the carrying capacity of the local environment, and dN/dt is the rate of change of the population.
K-selected species display traits associated with living at densities close to carrying capacity and are typically strong competitors in such crowded niches, that invest more heavily in fewer offspring, each of which has a relatively high probability of surviving to adulthood (i.e., low r, high K). Examples of K-selected species include elephants, whales, and humans.
r-selected species are those that emphasize high growth rates, typically exploit less-crowded ecological niches, and produce many offspring, each of which has a relatively low probability of surviving to adulthood (i.e., high r, low K). Examples of r-selected species include dandelions, rabbits, and insects such as butterflies and caterpillars.
It’s bad for butterflies that wasps eat their baby caterpillars from the inside out. But evolution does not care if your kids are in pain, only how many of them make it to adulthood and reproduce. So the response of the butterflies is not to protect their caterpillars from flesh-eating wasps, but to lay more eggs and hope that the wasps don’t eat all of them.
This has disturbing implications for veganism, agriculture, and animal welfare.
If a population is stable, it’s neither growing nor shrinking over time, so the number of animals in each subsequent generation will be approximately the same as the number in the previous generation. But r-selected species have huge numbers of offspring: if a pair of adult flies gives birth to 1,000 children, on average only 2 will make it to adulthood and manage to have their own children. So for every individual that successfully reproduces, there were 499 others that starved to death, or died of disease, or were eaten by predators.
Unfortunately, most living things in the universe are r-selected, and most of the conscious ones probably have lives full of fear, starvation, sickness, and suffering.
Conclusion
Let’s revisit the three competing theories for why we exist and there is something rather than nothing. The theory of atheism says we happened to exist because there was the Big Bang and now there’s a planet with sunlight and water, so life evolved here. This might happen throughout the universe, so there might be an infinite number of beings if the universe is infinite, but within our observable universe there’s only a finite number. By contrast, theism (according to Bentham’s Bulldog and Klaas Kraay) argues that if god exists, there would be an uncountably infinite number of beings, living lives ranging from unimaginable bliss to slightly good. Finally, maltheism posits that there is an uncountably infinite number of beings, living lives ranging from extreme horror to slightly bad.
Here we have seen two key pieces of evidence that maltheism is true. One is that in our world, most beings live lives of suffering, but this isn’t decisive, because a benevolent god might make a world that starts out horrible but becomes good later on, and we don’t know what will happen in the future. The crucial thing to realize is that if a malevolent, all-powerful god existed, he would create an uncountably infinite number of suffering beings, which is infinitely many times as many beings as a benevolent god would make, so the theory of maltheism is infinitely more likely than the theory of theism. So thanks to Bentham’s Bulldog for convincing me that god exists and is evil.
Credits: Noah Kreutter and Sydney Brenner for the conversation that inspired this post; Scott Alexander for introducing me to many-worlds theodicy; Bentham’s Bulldog for the best versions of the fine-tuning and anthropic arguments I’ve ever heard, even though they’re still wrong.
I can’t figure out where “if a malevolent, all-powerful god existed, he would create an uncountably infinite number of suffering beings, which is infinitely many times as many beings as a benevolent god would make” comes from. It seems to me that the analyses of theism and maltheism are symmetrical.
Isn't this still only an argument for a god's existence rather than specifically for the malevolent god? Both the benevolent and malevolent gods create an uncountably infinite number of beings. So they're both infinitely more likely than the non-many-worlds theodicy, but equal in likelihood to each other.