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For example, say there is a lottery with 10 million people. Only one of them is a Christian. The Christian wins.

The P(Christian winning | chance) is 1 in 10 million.

The P(Christian winning | Christian God existing) seems unknown. However, can one say that P(Christian winning | Christian God existing) is above P (Muslim winning | Christian God existing). The second statement seems true intuitively but something about it feels off as well since ultimately there’s no independent evidence the supposed Christian God (if he exists) would do that or meddle around with lotteries in the first place.

My general question is this: if there is no direct evidence for something, can we speculate it’s likelihood based on other characteristics we know about the hypothesis? For example, can we say that the Christian god is more likely to hit an atheist with a lightning bolt than a Christian?

When the question is framed with another example, the answer seems even more unclear. For example, suppose we know that Alex is a human being and gives gifts. From this, can we say that P (Alex giving his father a gift) > P (Alex giving a stranger a gift)? Intuitively, it seems yes, since given our background knowledge of human beings (i.e. closeness to their father), it would make sense that Alex is more likely to give his father a gift than a stranger. But what if this was some new proposed being? Like the Christian God? In this case, it seems like we have no background information, but we do have other information ABOUT the christian God that might suggest he do some actions that would favor Christians over others. I fail to see how those actions would be "ad hoc" either.

For example, if I was to reason that a Christian god is more likely to strike an atheist with lightning than a Christian, I would be reasoning this based off of the knowledge that the Christian god loves people who believe in him more than people who don't. This reasoning doesn't seem like a speculation invented from thin air.

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  • Islam is descended from Christianity, and say their God is the God of the old testament, so it's dubious to say they worship a different God. Anyway, you didn't say how many Muslims there are in your lottery, so we can't say much about P(Muslim winning | Christianity is correct). If there are nine Muslims and one Christian in the lottery, and no one else, then P(Muslim winning | Christianity is correct) is probably about 0.9, if we assume God rarely intervenes.
    – causative ♦
    Commented Oct 10, 2022 at 20:24
  • Let’s assume the rest are Muslim. Although I’m not sure how this is relevant to the question I’m asking. My general question is this: if there is no direct evidence for something, can we speculate? For example, can we say that the Christian god is more likely to hit an atheist with a lightning bolt than a Christian?
    – user62907
    Commented Oct 10, 2022 at 20:29
  • Which of the several questions you asked is your question?
    – BillOnne
    Commented Oct 11, 2022 at 1:37
  • I would try and reframe this question around examples that had actually happened. For example, Isaak Newton was rather confident in the existence of gravity, even though it was not experimentally confirmed until more than 100 years later.
    – Yuri Zavorotny
    Commented Oct 11, 2022 at 4:19
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    All these are singular events unrepeatable, thus a probability as frequency of occurence is uncomputable a priori. If one takes the subjective view of probability one can prove any probability simply by making appropriate assumptions, even if ungrounded
    – Nikos M.
    Commented Oct 13, 2022 at 9:41

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For example, can we say that the Christian god is more likely to hit an atheist with a lightning bolt than a Christian?

If the Christian God chooses a random individual to electrocute, than it is more likely a Christian will be the victim since Christians significantly outnumber atheists.

If the Christian God hates atheists and targets them whenever possible, then an atheist is the likely victim.

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  • All these are singular events unrepeatable, thus a probability as frequency of occurence is uncomputable a priori. If one takes the subjective view of probability one can prove any probability simply by making appropriate assumptions, even if ungrounded
    – Nikos M.
    Commented Oct 13, 2022 at 9:42
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For example, if I was to reason that a Christian god is more likely to strike an atheist with lightning than a Christian,

The probability that God does anything at all is premised on the probability that God exists to begin with, but the probability that God exists is infinitely close to zero since we have no information. Given this, the probability that God does anything at all is infinitely close to zero.

I would be reasoning this based off of the knowledge that the Christian god loves people who believe in him more than people who don't.

This is obviously not knowledge at all. This is an imagined reality without any empirical data to support it.

This reasoning doesn't seem like a speculation invented from thin air.

Whatever the value of the reasoning might be, it is premised on an assumption which we have no good reason to regard as true.

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  • When considering the likelihood of God doing anything, it must necessarily presume His existence, no? Even if the likelihood of Him doing something was 1 for something extraordinary, such as the Bible saying that X event will happen on X date with the event being improbable, that would also be hinged upon the assumption that God exists correct? But noone would say that's not adequate evidence?
    – user62907
    Commented Oct 11, 2022 at 19:46
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    @thinkingman "When considering the likelihood of God doing anything, it must necessarily presume His existence, no?" It? Not "it", no, you: if YOU consider the likelihood of God doing anything, YOU presume its existence. And since the probability of God's existence is infinitely close to zero, so the probability of God doing anything is infinitely close to zero. 2. "But noone would say that's not adequate evidence?" Where is the "adequate evidence" here? You are not going to convince anyone ever if you don't bother to articulate your ideas.
    – Speakpigeon
    Commented Oct 12, 2022 at 10:25
  • How does no information equal probability close to zero?! Wouldn't that instead mean a probability we can't quantify? Like we can assume a-priori probabilities that are low or high depending on our beliefs about the world, but can't get an a-posteriori probability without information, right?
    – kutschkem
    Commented Oct 12, 2022 at 13:16
  • @kutschkem "How does no information equal probability close to zero?" Not anything I said. Before throwing a die, you may know for example it has six sides, but you have no data making any side more probable, so the six sides are equally probable, until you get some information, that for example the die is loaded, or you do throw the die and get the data that it is a 3. Any idea of God is just one in a potentially infinite number of ideas of God since we know nothing about it except that it is an idea of God. This makes all ideas of God equally probable.
    – Speakpigeon
    Commented Oct 12, 2022 at 16:32

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