In his quest to disprove skepticism, Descartes first endeavoured to prove that he existed, then that God existed, and then that others existed through his cogito. Many arguments surrounding the assumption of a deity are similar. Most base themselves on the proposition that I, myself exist, and then go on to show that infinite other people exist, so also must a God. However, atheism often dismisses this line of reasoning as oblivious, yet fails to provide a comprehensive account of reality without a deity.

Atheism is one thing: a lack of belief in gods. It is the affirmative belief that there is 100% no deity that exists within our universe. Atheists claim to know this to be true due to the lack of empirical evidence for a God. However, most have never questioned the probability side of a theist’s argument, which posits that the existence of a deity is more likely than not.

Believers often argue that the complexity and order of the universe suggests the presence of a higher intelligence. They point to the fine-tuning of physical constants, the emergence of life, and the intricate development of our consciousness as prime evidence. But, just how realistic is this viewpoint?

Using Bayes’ theorem, we can try to understand this argument and search for any realism. This equation, based on the calculation of conditional probability takes prior probability, likelihood and marginal likelihood to find the posterior probability of a proposition being true.

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To illustrate this, consider the following analogy.

Imagine you are a wildlife researcher studying a rare species of bird in a large forest. You have developed a highly reliable bird call detector that can identify the call of this rare bird 99% of the time when it hears it, and it correctly identifies 99% of the sounds that are not from this bird. You know from prior surveys that only 1% of the sounds in the forest come from this rare bird.

Now, if the detector indicates it has heard the rare bird, what are the chances it is actually the bird’s call? Intuitively you might say 99%, but the correct answer is about 50%. Let me explain.

Bayes’ theorem helps us understand the relationship between what we know (the probability of the detector identifying a sound as the rare bird’s call given it is the bird’s call, p(H∣E)), and what we want to know (the probability the sound is the bird’s call given the detector indicated a positive result, p(H+)). Bayes’ theorem essentially combines the likelihood of a positive detection given the bird’s call with the prior probability of the bird’s call to determine the posterior probability of the bird’s call given positive detection.

To visualise this, let’s say the forest has 10,000 sounds. According to prior information (p(h)=0.01), we know that 1% of the sounds are from the rare bird, while the other 99% are from other sources. When the detector scans the forest, it correctly identifies 99 of the 100 bird calls (due to its 99% reliability). However, because of the 1% error rate, it also incorrectly identifies 99 out sounds as bird calls.

Thus, if the detector indicates a positive detection, there will be 198 positive results: 99 actual bird calls and 99 false positives. Therefore, despite positive detection, there is only a 50% chance that the sound actually comes from this rare bird.

Now, let’s imagine you move to another forest where the rare bird is even scarcer, with only 0.5% of the sounds coming from this bird (1 in every 200). In this forest, if the detector indicates a positive detection, it is more likely that the sound is from another source than from the rare bird, to find a precise probability, you would need to update the prior probability considering the lower prevalence of the bird’s call. Due to the scarcity, the likelihood that the sound comes from this rare bird drops to 33.2%:

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• p(H) (the prior probability that a sound is from the rare bird) = 0.005.

• p(¬H) (the probability that a sound is from another source) = 1 – 0.005 = 0.995.

• p(+∣E) (the probability that the detector correctly identifies the rare bird’s call) = 0.99.

• p(+∣H) (the probability that the detector incorrectly identifies another sound as the rare bird’s call) = 0.01.

p(+)=(0.99⋅0.005)+(0.01⋅0.995) = 0.332

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Now, moving this back to a theists’ argument for probability. We can employ Bayes’ theorem to calculate the probability of God given our experiences (such as the existence of evil or religious experiences) and assign likelihoods of these facts based on the existence or nonexistence of God, as well as the prior belief in God’s existence. One such person to do this was Richard Swinburne.

Where:

• p(H∣E) is the probability of the hypothesis H (God’s existence) given the evidence E.

• p(E∣H) is the probability of the evidence E given that H is true.

• p(H) is the prior probability of the hypothesis H (the initial probability assigned before considering the evidence).

• p(E) is the total probability of the evidence E.

Starting with the prior probability (p(H)), Swinburne assigned it 0.5 (50%) for his existence as there are only two possibilities: God exists or God does not exist. Without any evidence, he considers these to be equally likely, hence 0.5.

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Now, taking the likelihoods (p(E/H) and p(E/¬H)), we evaluate various pieces of evidence that might support or contradict the existence of God, such as:

• E1: the existence of the universe

  • p(E/H): the probability the universe exists if God exists

  • p(E/¬H):: the probability that the universe exists if God does not exist

• E2: the presence of order and fine-tuning in the universe

  • p(E/H): The probability that the universe is fine-tuned for life if God exists

  • p(E/¬H):: The probability that the universe is fine-tuned for life if God does not exist

• E3: the existence of conscious beings

  • p(E/H): The probability that conscious beings exist if God exists

  • p(E/¬H): The probability that conscious beings exist if God does not exist

• E4: the occurrence of religious experiences

  • p(E/H): The probability that religious experiences occur if God exists

  • p(E/¬H):: The probability that religious experiences occur if God does not exist

• E5: the occurrence of moral conscience

  • p(E/H): If God exists, it is likely that humans would have a moral conscience, as God would instil a sense of right or wrong in its creations

  • p(E/¬H):: If God does not exist, the existence of a universal moral conscience is less likely, though it could still arise from evolutionary or social processes

• E6: historical evidence of religious figures

  • p(E/H): If God exists, the existence and impact of these figures could be part of a divine plan to guide humanity

  • p(E/¬H):: If God does not exist, these figures could still exist and have an impact due to social, political, and cultural factors

• E7: the presence of altruism and selfless behaviour in humans and animals

  • p(E/H): If God exists, altruism and selflessness could be encouraged or designed by God as moral virtues

  • p(E/¬H):: If God does not exist, altruism and selflessness might be explained by evolutionary advantages or social conditioning

• E8: sense of purpose

  • p(E/H): If God exists, it is likely that humans would feel a sense of purpose and meaning

  • p(E/¬H): If God does not exist, this sense of purpose and being could stem from biological processes, but we still cannot explain it through evolutionary history

• E9: problem of evil

  • p(E/H): If God exists, it is likely that he would create a universe without evil

  • p(E/¬H): If God does not exist, evil would exist either by chance or action

• E10: argument from nonbelief

  • p(E/H): If God exists, it would desire that people believe in him

  • p(E/¬H): If God does not exist, there would be no reason to believe in it

• E11: incoherence of divine attributes

  • p(E/H): If God exists, it must not contain all divine attributes due to paradoxes

  • p(E/¬H): If God does not exist, no paradoxes would exist due to no deity to implement them on

For each piece of evidence, we assess how likely it is to occur if God exists (p(E/H)) and how likely it is to occur if God does not exist (p(E/¬H)).

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Next, we use the prior probability (0.5) and the likelihoods to apply Bayes’ theorem to calculate the posterior probability of God’s existence given the evidence:

E1:

• p(E/H) ≈ 0.8

  • The probability that the universe exists if God exists is nearly certain. This is because God, as an omnipotent, omniscient and omnibenevolent being, would have the power, knowledge, and motivation to create a universe for humanity.

• p(E/¬H) ≈ 0.1

  • The probability that the universe exists if God does not exist is very low. The idea is that without an intentional creator, the emergence of a universe from nothing, apart from unexplained so-called random processes is extremely unlikely.

E2:

• p(E/H) ≈ 0.9

  • Given the existence of God, the probability that the universe is ordered and fine-tuned for humanity is high. God, being rational and good, would create a universe with order, strict morality, and complex structure, including life.

• p(E/¬H) ≈ 0.1

  • The probability that the universe is ordered and fine-tuned if God does not exist is almost nil. The specific conditions for humanity and life to thrive without the rational being creating order are extremely unlikely to occur by chance.

E3:

• p(E/H) ≈ 0.9

  • The probability that conscious beings exist if God exists is high because beings can experience and appreciate the goodness of the world, engage in relationships, and have a capacity for moral development, all of which align with the intentions of a benevolent deity.

• p(E/¬H) ≈ 0.2

  • The probability that conscious beings exist if God does not exist is almost nil because we have no explanation. This stems from the assumption that we have a physical consciousness, one which we have not yet located, and even if it does exist, was created without any intentional design.

E4:

• p(E/H) ≈ 0.4

  • If God exists, then God would allow people to have religious experiences. These experiences could serve as a means for God to communicate with humans and for humans to develop a relationship with it. However, the probability of this occurring is average due to the difficulty of explaining neurological/spiritual experiences.

• p(E/¬H) ≈ 0.5

  • If there is no God, the occurrence of religious experiences is unlikely. Such experiences could still happen due to psychological or neurological factors, the specific content and the widespread nature of these experiences would be hard to account for without invoking a divine source.

E5:

• p(E/H) ≈ 0.9

  • If God exists, then it would instil a moral conscience in humans to guide their behaviours and help them discern right from wrong. This would serve as a means to communicate moral truths and foster ethical living

• p(E/¬H) ≈ 0.3

  • If there is no God, the occurrence of moral consciences can be explained through evolutionary and social mechanisms. However, the universality and depth of moral conscience are harder to account for without a divine source

E6:

• p(E/H) ≈ 0.8

  • If God exists, then the appearance and influence of religious figures could be expected, as God might choose to reveal itself through prophets and incarnations. Also, the cross-referencing throughout religious texts, and across religions suggests correlations.

• p(E/¬H) ≈ 0.4

  • If there is no God, historical evidence and religious figures could be seen as a result of cultural evolution and myth-making processes. While such figures could exist, their influences and religious experiences become more challenging to explain.

E7:

• p(E/H) ≈ 0.7

  • If God exists, altruism and selflessness could be designed as moral virtues. These behaviours align with the moral framework an omnibenevolent God might promote

• p(E/¬H) ≈ 0.6

  • If God does not exist, altruism and selflessness might be explained by evolutionary advantages or social conditioning. This moderate probability reflects the potential for these behaviours to arise from natural selection and societal development, even without divine influence

E8:

• p(E/H) ≈ 0.8

  • If God exists, it is likely that humans would feel a sense of purpose and meaning. A high probability indicates that a purposeful existence would be expected from a divine creator intending for humans to have meaningful lives

• p(E/¬H) ≈ 0.5

  • If God does not exist, this sense of purpose and meaning could stem from biological processes, but we still can’t fully explain it through evolutionary history, hence the lower probability.

E9:

• p(E/H) ≈ 0.4

  • If God exists, it is likely he would create a universe without evil. This lower-end probability reflects that an omnibenevolent God would prevent natural evil, yet its presence still exists. Challenging this probability is the free will rebuttal.

• p(E/¬H) ≈ 0.5

  • If God does not exist, evil would exist either by chance or action, aligning that without divine moral order, its presence is more easily explained by natural or random processes.

E10:

• p(E/H) ≈ 0.2

  • If God exists, it would desire that people believe in it. The widespread nonbelief is unexpected for a God who may desire it, therefore, leading to a lower probability.

• p(E/¬H) ≈ 0.8

  • If God does not exist, there would be no reason to believe in it. The nonbelief would occur naturally and is expected in the absence of a deity.

E11:

• p(E/H) ≈ 0.3

  • If God exists, he must not contain all divine attributes due to paradoxes such as the one of the stone. This is reflected in the low probability as it is difficult to reconcile a paradoxical divine attribute within a coherent concept of God.

• p(E/¬H) ≈ 0.8

  • If God does not exist, no paradoxes would exist due to the absence of the proposition, leading to a higher probability.

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Given the piece of evidence (E1, E2, E3, E4) we can now calculate the posterior probability of God’s existence. For simplicity, we first calculate the combined likelihood of all this evidence.

Let’s define the combined likelihood for the existence of God, p(E/H), and for the non-existence of God, p(E/¬H). Assuming the evidences are independent (which may not be entirely accurate but simplifies the calculation), we can multiply the individual likelihoods.

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Combined Likelihoods:

p(E∣H)=p(E1∣H)×p(E2∣H)×p(E3∣H)×p(E4∣H)×p(E5∣H)×p(E6∣H)×p(E7∣H)×p(E8∣H)×p(E9∣H)×p(E10∣H)×p(E11∣H)

p(E∣¬H)=p(E1∣¬H)×p(E2∣¬H)×p(E3∣¬H)×p(E4∣¬H)x p(E5∣¬H)× p(E6∣¬H)×p(E7∣¬H)×p(E8∣¬H)×p(E9∣¬H)×p(E10∣¬H)×p(E11∣¬H)

Taking the combined likelihoods, the equation would look like this:

p(E∣H) = 0.8 x 0.9 x 0.9 x 0.4 x 0.9 x 0.8 x 0.7 x 0.8 x 0.4 x 0.2 x 0.3 = 0.002508

p(E∣¬H) = 0.1 x 0.1 x 0.2 x 0.5 x 0.3 x 0.4 x 0.6 x 0.5 x 0.5 x 0.8 x 0.8 = 0.00001152

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Now, applying Bayes’ theorem to update the prior probability with the combined likelihood of the evidence:

p(H∣E)=(p(E∣H) x p(H))/p(E)

Where p(E) is the total probability of the evidence, calculated as:

p(E) = p(E∣H) x p(H) + P(E∣¬H) x p(¬H)

Given the prior probability p(H) = 0.5 and p(¬H) = 0.5

p(E) = 0.002508 x 0.5 + 0.00001152 x 0.5 ≈ 0.001259

Therefore the posterior probability is:

p(H∣E) = (0.002508 x 0.5)/0.001259 = 0.996

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Thus, given the combined evidence, the posterior probability of God’s existence, p(H∣E), is approximately 0.996, or 99.6%.

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The application of Bayes’ theorem to the question of God’s existence provides a rigorous probabilistic framework to assess the strength of various arguments and evidence. Swinburne’s analysis, alongside opinions of my own, suggests that, given the considered arguments, the probability of God’s existence is extremely high. However, to put these arguments into a singular number up to 1 can be extremely over-simplistic. But, for a probability equation, a specific number had to be chosen. For this reason, each E has an explanation below for my numerical allocation.

Also, reducing the numbers slightly would minimally reduce the probability of a deity’s existence. For example, reducing all of the positive E’s for its existence by 1 would be still create an approx posterior probability of 97.3%.

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Atheism, which asserts the nonexistence of deities, often challenges theistic arguments on different grounds, such as the problem of evil, or lack of empirical evidence for supernatural beings. Theistic arguments, fortified by probabilistic reasoning like Bayes’ theorem, offer a counterpoint that emphasises the coherence and explanatory power of a theistic worldview.

Now, I am not saying that God, in the way we describe it, is likely to exist. No. I am suggesting that a deity, whether this be from a different religion, or a completely different idea altogether, is likely to exist. Therefore, basing your whole worldview on the idea that no supernatural being exists, is to me, naive.

Ultimately, I understand that these calculations are completely up for debate, and this definitely doesn’t even scratch the surface of the arguments between theists and atheists. However, the probability for a deity to exist is far more likely than the opposite, leading me to question anyone’s logic to enter a worldview of ignorance and dismiss the potential for the supernatural entirely.

To reject outright the possibility of any supernatural being is to ignore the depth and complexity of our existence, the universe and the unexplained. While atheism provides a materialistic view, it fails to address the philosophical and existential questions that arise from our very existence.

In conclusion, the question of why there’s something rather than nothing will continue to provoke thought and debate until the question is answered or humanity ends (whichever comes first).

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