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Suppose, I have a machine that accurately gives me the probability of any event occuring.

It's obvious what to do when

  1. The probabilities are 0.5 and 0.5 (Do nothing)
  2. The probabilities are 0 and 1 (Remain an atheist)
  3. The probabilities are 1 and 0 (Become a Muslim)

However, consider a more nuanced scenario. Say I obtained from that machine that the probability of Islam being true is 50.1%, and that the probability of Islam being false is 49.9%. What would you do in this situation? Would you become a Muslim or stay an atheist/agnostic?

Edit:

Some commenters have raised a very good point. Only taking actions based on probability is not prudent. You have to weigh the consequences too. "If there's a 40% chance of rain, it's still reasonable to take an umbrella, unless carrying the umbrella is an excessive burden." So, it seems like I am just heading towards a traditional Pascal's wager :-)

tryingtobeastoic
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  • It's the old, "Definite Maybe". – Scott Rowe May 18 '23 at 16:31
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    If there were truly a 50% chance that Islam is true, then you should become a Muslim, because of Pascal's wager. Even a 10% chance would warrant conversion, unless some other religion had an even higher chance. Rational atheism depends on the chance being very low, certainly <1%, which is usually justified by the excess complexity of supposed deities (in comparison to the formally much simpler laws of physics) interpreted through a Bayesian version of Occam's razor. Also, a sociological understanding of how religions form and evolve. – causative May 18 '23 at 17:29
  • Have mercy on us, finish the story! – Agent Smith May 18 '23 at 18:04
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    You also need a machine that accurately gives you payoffs of proposed decisions in each case, and their utilities. Then you calculate the [expected utilities](https://en.wikipedia.org/wiki/Expected_utility_hypothesis) and choose the decision with the highest one. If only life worked like math... What we learned from [Pascal's wager](https://plato.stanford.edu/entries/pascal-wager/) is that one should leave probability and payoffs out of religious decisions altogether. – Conifold May 18 '23 at 18:33
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    @Conifold Calculating utilities is one way to take a decision based on probabilities, but not the only one. – Frank May 18 '23 at 18:49
  • @Frank True. There's research in theoretical computer science about this, where AIXI, an ideal Bayesian reasoner that maximizes the expected value, will eventually drop an anvil on its head just to see what happens. Also Pascal's wager must be balanced with the reverse possibility that a deity exists that will reward you for being rational and punish you for believing without proof... or a million other possibilities where the reward/punishment works out the opposite of the Christian wager. – causative May 18 '23 at 18:53
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    The chance of what? The chance that another "probability" question gets asked tomorrow? – Boba Fit May 18 '23 at 19:42
  • have you thought of including the probability that christianism, budhism, paganism or zoroastrianism are true in your model? – armand May 19 '23 at 00:45
  • The easiest way to make Islam true 50% of the time is to have a second god that exists on average 50% of the time, so atheism doesn't seem like a reasonable alternative. You should really consider one-and-a-half-on-average-theism. – g s May 19 '23 at 06:50
  • This is a [false dilemma](https://en.m.wikipedia.org/wiki/False_dilemma) fallacy: you reduce a widely comprehensive set of considerations to a single number. If so, just follow the number. – RodolfoAP May 19 '23 at 06:57
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    If there's a 40% chance of rain, it's still reasonable to take an umbrella, unless carrying the umbrella is an excessive burden. – Barmar May 19 '23 at 15:08
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    What does it mean to say that the oracle **accurately** makes predictions, but then it assigns probabilities to those predictions? It seems like a contradiction. I can predict that a die will land 6 about 16% of the time, but that doesn't make it an accurate prediction for any particular throw. – Barmar May 19 '23 at 15:23
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    Saw the edit. You've got it! I hope ye're in a bathtub! Eureka time, buddy!! – Agent Smith May 20 '23 at 23:44
  • @AgentSmith Hahaha. Thank you :-) – tryingtobeastoic May 21 '23 at 06:16

5 Answers5

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I would first argue that there is no such thing, and that if a machine is trying to spit out a "true" probability of Islam being true, it would simply be wrong if it displayed 50.1, since the real answer should either be 0 or 1. Islam is or isn’t true. There's no in between.

Any “probability” of it being true or false is just a human guess that maps into getting into the thorny issue of when it’s considered justified or unjustified to believe in a statement like “Islam is true”.

There is no such thing as a “true” or “objective” probability, especially when it comes to existential matters such as the Islamic god existing.

tryingtobeastoic
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thinkingman
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  • "if a machine is trying to spit out a true probability of Islam being true, it would simply be wrong if it displayed 50.1 since the real answer should either be 0 or 1. Islam is or isn’t true. There’s no in between." I agree that there is no in-between between Islam being true and Islam being false. However, I never made the claim that there is something in-between Islam being false and Islam being true. I only stated that the *probability* of Islam being true/false is such and such. – tryingtobeastoic May 18 '23 at 16:16
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    @tryingtobeastoic Islam is a complicated theoretical system, and parts of it are true and parts of it are not, so the notion that it's all or nothing is [black and white thinking](https://en.wikipedia.org/wiki/False_dilemma). The [principle of bivalence](https://en.wikipedia.org/wiki/Principle_of_bivalence) doesn't always apply when making claims. – J D May 18 '23 at 16:19
  • @JD I am having trouble understanding how parts of Islam can be true and other parts false. Could you please give an example to elucidate the matter? – tryingtobeastoic May 18 '23 at 16:31
  • @tryingtobeastoic Islam is correct in that Muhammad is a great prophet. Many people follow his prophecies. The religion he led in founding conquered great swaths of North Africa, the Middle East, and parts of Europe. Arabic has become a lingua franca in many of those countries united by a common language and belief system. Islam recognizes Abraham and Jesus of Nazareth as fellow prophets, which is also true. Islam preaches tolerance, and tolerance is good for peace. These are all practically speaking truths. But, there are no supernatural gods. So, it gets that wrong. – J D May 18 '23 at 16:41
  • Islam is not true or false, it's a collection of truths and falsities. The same is true of all religions, indeed, of all belief systems. – J D May 18 '23 at 16:42
  • @tryingtobeastoic Even the sciences has falsities tucked in among it's truths. It's the duty of every scientist to hunt down and challenge those falsities. Thus modern biology, while it has many strong and obvious truths isn't free from falsities. Biologists know that, and they are constantly challenging each other to prove that claims are true. In philosophy, this is called [fallibilism (IEP)](https://iep.utm.edu/fallibil/). – J D May 18 '23 at 16:44
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    @JD We are arguing semantics here. When I say that Islam is false, I don't (for the sake of argument) deny that the truths you mentioned are false. I only mean that there is no Allah. In other words, I mean that the *disputed* aspects (i.e. Allah being the one and only God, Muhammad being the messenger of Allah etc.) of Islam are false. – tryingtobeastoic May 18 '23 at 16:52
  • Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/146110/discussion-between-j-d-and-tryingtobeastoic). – J D May 18 '23 at 16:53
  • @thinkingman More on my previous comment: if you do not believe me, I can cite you Richard Swinburne's work. In his book "The Existence of God", he calculated, using Bayes' theorem, the probability of Christianity being true to be [more than 0.5](https://en.wikipedia.org/wiki/The_Existence_of_God_(book)#Probability_of_God_according_to_theism_using_Bayes'_theorem) So, the probability need not to be a dicrete 0 or a discrete 1. – tryingtobeastoic May 18 '23 at 17:01
  • @tryingtobeastoic: Suppose that I have a bag containing a red ball, and I ask the machine what is the probability that the ball is red. What answer does it give? Does it magically know that the ball is in fact red, and report 100%? If so, then it should also say either 0% or 100% for Islam. Or does it apply Bayesian reasoning, making its best guess based on whatever it does know? If so, then it's misleading to say that it "accurately" gives probabilities; maybe you meant to say "honestly"? – ruakh May 19 '23 at 01:03
  • Ya should read *Parmenides* who, to Karl Popper, is *Albert Einstein*, who, to me, is E = mc². – Agent Smith May 21 '23 at 00:44
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It depends on subjective criteria. For example, you may decide that a difference of 0.2% is not significant to you, and conclude "do nothing". Or you might use a Pascal wager type argument. Or you can look at the utilities of each choice in some other way. The probability values alone are not enough to decide, you need to supply some decision function that will probably include some amount of subjectivity.

Frank
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I object to the grounds of your question. It is impossible to calculate a probability for the truth of a religion. Even if you could allocate a probability, a probability alone is no basis for decision making. You need to take into account all of the applicable pros and cons associated with the choices you are presented with, weighing them against each other in terms of their importance to you and their likelihood.

Marco Ocram
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Say I obtained from that machine that the probability of Islam being true is 50.1%, and that the probability of Islam being false is 49.9%.

I would say that the machine has determined that, with all the available information, there is a 50-50 chance of Islam being true.

My first question is; What information was used by the machine to arrive at these probabilities? I want to determine for myself whether the methodology and use is appropriate.

If no flaw can be found, then this leaves you with two choices:

  1. Find a fair coin, flip it, and make your choice or a random number generator that spits out numbers from 1 to 1000. Any number 499 or less and the choice is Islam is false. Otherwise, Islam is true.

  2. Read the Koran, the Bible, and all other religions and make a choice.

The coin flip is MUCH easier.

Edit for umbrella and 40% chance of rain.

  1. Get a random number generator that randomly spits out integers from 1 to 10.

  2. Any number of 4 or less: Carry the umbrella. Otherwise go umbrella free.

The other choice is to use the probability information as basis for further analysis: A forty percent chance of rain may lead to checking current weather satellite information to determine whether this general probability for rain applies to my specific region.

Decisions based solely on probability are a last resort to be used when there is no ability to get further information necessary to give the decision more certainty.

A common method to deal with rain probabilities is to buy an inexpensive 6 pack of collapsible umbrellas and keep one in each vehicle, one at work, etc. That way there is no math involved in keeping dry.

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Decision Analysis

Decision Analysis is a formal method for assigning probabilities to outcomes in the context of making decisions. Another search term would be decision-making with probabilities.

The idea is to compute the expected value or expected payoff for each course of action then take the decision based on the prospect of gain or loss. Then the expected values are mapped to a decision tree. I cannot find a good reference via simple keyword search.

Surfing, Stock Trading, Risk Adventures

In a surfing competition the surfer must intuitively decide whether to ride a breaking wave or pass up that wave for a better wave that might arrive soon. If the surfer does not catch the wave properly then she can "kick out" which means to abort the ride and wait for another wave. There is a time limit on the competition and the surfer wants to optimize the points scored by judges for taking their best rides in the limited time. This is a type of decision analysis that does not involve formal estimates of probability but rather the surfer is intuitively deciding expected payoffs and taking action in real time.

Some experts argue that no one can time or beat the stock market because all information is priced into the decisions unless insiders or others have some strategic advantage. However, stocks trade with price action and there do seem to be traders who are better than the others at making money from price action. I compare this to how surfers decide to ride or not ride a wave, and when to enter a trade, and when to kick out to cut a loss short, and when to hold a winning trade to let profits run on the price trend. The point is that human skill is a factor in decision making which influences the expected payoffs.

When negotiating contracts, the skill and know-how of an expert making a bid is part of the expected payoff or expected outcome. Hunters and fisherman would assess each other's skill at finding game or fish and go with the most skilled hunters or fisherman to earn their living if possible. Probability theory is a tool to perhaps help improve outcomes based on decisions. But it cannot replace intuition and skill in a rich model of human decisions.

SystemTheory
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