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When it comes to the probability of something coming into fruition, a number is calculated based upon the future. The probability of a dice landing on 6 means that if one were to roll a dice in the future, it has a 1/6 chance of landing on 6.

But what about eternal posited beings such as god? What is their probability? Should it be undefined since they’ve always existed or defined? The problem I’m having with the idea of an eternal thing having an undefined probability is that any proposed eternal thing would then have an undefined probability. Both an eternal atom vs. an eternal all powerful god would have undefined probabilities. Yet intuitively, the former seems more simpler and perhaps…more probable?

If probability is undefined in these cases, how does one compare something happening by chance vs by an eternal being if the latter is undefined? When faced between something that is possible by chance vs. something that is potentially created by a posited eternal being, how does one choose?

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  • Even given the variety of kinds/theories of probability, we can make some headway when it comes to relatively specific definitions of things like deities. Perfect/maximal being theology, for example, does not countenance a deity as more probable except in the vacuous sense that such a deity, if it exists, necessarily exists. And Kant inveighed against the kind of "averaged probabilities" arguments for metaphysical claims: either an a priori argument fully confirms a metaphysical thesis, or it does not. But so weaker/less metaphysical deities might figure in other calculations. Jun 1, 2023 at 0:01
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    the probability for the given outcome of a dice roll to be 1/6 is just an axiom. It is to say, everybody agrees that it's reasonnable to posit that it is actually the case. In fact it might not be, but there is no way to verify that (one could toss a given dice a million times and see the statisitical outcome tends to 1/6, but that wouldn't be a demonstration, just further establish the axiom as reasonable). Also there is no such thing as an eternal atom.
    – armand
    Jun 1, 2023 at 0:28
  • But what about eternal posited beings such as god? What is their probability? God either exists or not. Two states. With no further information, it's like a coin: 50/50.
    – user64314
    Jun 1, 2023 at 2:22
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    See Pascal's wager. Jun 1, 2023 at 8:05

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On a Bayesian understanding of probability, the role of probability is to quantify uncertainty. We are uncertain of the future, but we can be uncertain of other things too, including things in the present and the past and even eternal things. So, it is not undefined to speak of the probability of the existence of gods, in the sense of the appropriate degree of uncertainty that attaches to such a proposition. The problem is that such probabilities are imponderable: there is just no good way to put a value on them. It is difficult even to say what counts as evidence for the existence of gods.

Richard Swinburne (The Existence of God, 2nd edition, 2004) presents a Bayesian argument for the existence of God. Starting from a prior probability of 0.5, he attempts to show that it is probable that God exists, given our total empirical experience. But the project is beset with difficulties. Why should we start from a prior of 0.5? There are after all lots of different gods that people believe in. What alternative hypotheses are there? What is the space of possibilities and how is it structured?

More specifically, how do we assess the conditional probability of some feature of our experience assuming a deity and assuming not? We cannot observe what the universe would be like if there was a god and if there wasn't: we can only speculate about such things. Nor can we perform experiments that have different results depending on whether a god exists or not. Or if we try to do so, there will always be difficulties in interpreting the results.

The upshot is that the question of the existence of gods is just one to which there is no definite answer. We can only ask whether in the big picture it seems more plausible to suppose there are or that there aren't, and different people have different views of the matter. The important thing is not to fight about it.

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  • About Swinburne's argument - Bayesian probability does require a prior value as a starting-point to its process. But the standard prior is 0.
    – Ludwig V
    Jun 1, 2023 at 12:35
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    You cannot use a prior of 0 or 1, otherwise it would be impossible to update it through Bayesian conditioning. A prior of 0.5 may be justifiable in some circumstances, in line with the principle of indifference, but in practice it is difficult to use the principle of indifference without additional knowledge of the possibility space.
    – Bumble
    Jun 2, 2023 at 3:28
  • Thanks for putting me straight. Perhaps I misunderstood something I read, which, to be accurate, described the standard prior as the null hypothesis - i.e. that the proposed evidence would have no effect on credence. Perhaps it all depends on the possibility space. (And, by the way, you've just clarified for me the relationship between probability and possibility. More thanks for that.)
    – Ludwig V
    Jun 2, 2023 at 10:25
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The probability of an event can be estimated or calculated only, if there is prior knowledge about similar events and the mechanisms leading to them.

We have no prior knowledge about any gods appearing or any mechanism leading to their appearance.

Therefore we cannot estimate or calculate the probability of such an event.

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When it comes to the probability of something coming into fruition, a number is calculated based upon the future.

This is wrong. Probabilities are based on past events or a complete knowledge of all possible states. This is used to make a prediction of a future event. When discussing the existence of God using probabilities, what constitutes a "God exists" or "God does not exist event"? How many of these events are required to calculate a robust probability for use in predicting the next "God event"?

God exists and God does not exist are the only two possible states. So a 50/50 probability is a fine starting point until "God events" have been defined and counted.

Is finding a potato that looks exactly like Jesus a "God exists" event?

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You are right about the problem. Probability theory requires a future event (on the assumption that the outcome is uncertain), because if the event has already happened or not, its probability is 1 or 0. But if the outcome is not known, even if it is in the past, one can calculate a probability for it. One could articulate a probability for a past event, provided one uses the past tense - "the probability was x (at the time in question), so that you can then say the outcome (at a later time) was . Of course, one needs also to ignore the fact that the outcome is known. The question would be something like "If we didn't know what the outcome was, what probability would we assign to it."

The bottom line is that a probability requires a change.

Pascal's wager illustrates the way round this. Pascal proposes we consider the event of our death and our prospects after death. The probability of my going to heaven or hell satisfies the requirement.

But probability requires more than that. It requires a list of possible outcomes. Coin-tossing and similar games satisfy this. Empirical questions are more difficult. The process there is to rely on past experience (statistical evidence) and a "confidence interval", with further complications around infinitely variable outcomes like temperature.

We could ask what the probability is that we will discover that God exists, or that there is no such entity or that we will never discover whether there is such an entity or not. But those would be meaningless, since there's no time limit. So we need to impose one, such as "in the next ten years" or "before I die".

But it is still a one-off event, so there is no alternative to Bayesian probability which works on assigning a level of "credence" to an event. (I think it probably (!) still needs a time limit.)

There is, however, another requirement for probability. Probability can only be assigned to an empirical proposition that might be true or might be false. But I think that God exists is a hinge proposition - roughly an idea that governs the way that evidence is interpreted. If one accepts it, one interprets all the evidence one way. If one does not accept it, one interprets the evidence in another way. One could not assign a probability to it. That's an over-simplification, but I think it works in this case.

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Probability theory is a branch of mathematics that deals with the analysis of random phenomena. It is used to model systems that are subject to chance or uncertainty. Probability theory does not require a beginning and can apply to eternal things like God. However, the application of probability theory to God is a topic of philosophical debate and has been discussed by many philosophers.

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If probability is undefined in these cases, how does one compare something happening by chance vs by an eternal being if the latter is undefined?

In other words, when I win a lottery, how to choose whether to attribute this event to coincidence vs. non-coincidence. Non-coincidence includes supernatural possibilities (Karma, Prayers etc.) but also unknowable natural ones (cheating, a conspiracy by the government to make me rich).

Philosophy has as goal to remain as truthful and rational as possible, but that duty is not formally a duty outside philosophy. Outside philosophy we know of white lies, cognitive dissonance, political statements, advertizing, diplomacy which all allow for deviation from the perfect truth.

In philosophy, there is no straightforward solution for how to compare mutually exclusive claims with regard to credibility if any of them has no defined probability, but there are related topics:

  • Occams razor helps to choose a theory if 2 theories can be compared in terms of simplicity of number of assumptions
  • Carl Sagan popularized the saying "Extraordinary claims require extraordinary evidence.", which can help when defining the supernatural as extraordinary
  • Pascals Wager suggests to make a choice based on the best utility rather than highest credibility
  • "How many angels can dance on the head of a pin?" is a phrase explaining that irrelevant speculation about the unknowable supernatural is futile
  • Shaping and recognizing multiple different paradigms can help making such choices and understanding why such choices are made differently by different people

Paradigms in particular might serve to prevent useless debates about such questions as whether events might be caused by supernatural influence. Physicalism and naturalism as an example simply reject any such claims (until such a day when extraordinary evidence would refute the paradigm). Religious paradigms such as by Christianity would be strongly biased in explaining every event as potentially influenced by supernatural agents (gods, devils, angels, demons).

How to choose a paradigm just moves the problem to a different level, but once a person chose their paradigm, they can quickly decide about many uncertain claims within their paradigm.

Philosophers can be asked about their stance regarding various paradigms, and so surveys exist as this 2013 one (David Bourget and David J. Chalmers, What do philosophers believe? https://philpapers.org/archive/BOUWDP).

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This might furnish a path forward in dealing with the question:

Fourier analysis and Fourier transforms are an integral part of the mathematics of probability, and so will be embedded in statistical descriptions of the world.

The Fourier transform of a signal that is continuous (i.e., has always existed and has no beginning at some time t) is mathematically distinct from the transform of a signal that began at some time t. This distinction is vitally important in information theory because all real-world signals (containing information) have a beginning time, and their transforms necessarily bear this imprint.

Your challenge now is to somehow mathematically express the signal of interest as the existence of god. If god has always existed, then the transform of the signal will not be the same as the transform of god's existence in the case where god's existence had a beginning.

Then you need to know how to back out the probability of god's existence from the two transforms, and thereby assess the probability of the eternal existence of god compared to the probability of the event of god's birth at some time t.

That said, I do not know how to express the signal, nor how to solve for either of these transforms, nor how to back-calculate the probabilities from them.

This is the midterm exam, and counts for half of your final grade. Points will be deducted for incorrect answers, so do not guess! Oh yes- and show your work.

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