Question

Hooper reviews both the origin and the purpose of Bayes' theorem which involves examining probability theory with full control of predictive outcomes as opposed to probability theory with some predictive outcomes outside the realm of individual control. Consider, then, the juxtaposition of Bayes' theorem with cognitive comprehension. To what extent does this juxtaposition relate to one's understanding of God? Explain.

Answer 1

Hooper reviews both the origin and the purpose of Bayes' theorem which involves examining probability theory with full control of predictive outcomes as opposed to probability theory with some predictive outcomes outside the realm of individual control. Consider, then, the juxtaposition of Bayes' theorem with cognitive comprehension. To what extent does this juxtaposition relate to one's understanding of God? Explain.

Bayes' Theorem:

By definition, Bayes’ theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. It involves taking into account all possible causes and reasons prior to arriving at a conclusion. The mathematical representation has been defined as follows:

P (A|B) = [P(B|A) P(A)] / P(B)

Where P(A|B) is the probability of event A occurring given B is true

P(B|A) is the probability of event B occurring given A is true

P(A), P(B) are the probabilities of A & B occurring independently of each other.

Bayes' theorem has essentially helped us arrive at conclusions about problems that might have required more investigation if not for the Bayes' hypothesis. It has made things simple, with the example of 'cancer' detection most widely being used to illustrate it. What Bayes' theorem essentially outlines are the following:

It talks at great length about how tests are just tests and are flawed. They give us an idea of possibilities but not the possibilities itself.

Also, Bayes' theorem concentrates more on numbers and helps at arriving at the real possibilities by correcting measurement errors.

It takes into account any 'false positives' and helps us handle it as mentioned above.

Juxtapositioning Bayes' theorem and Cognitive Comprehension

From a biblical standpoint, an application of Bayes' theorem to the happenings in the Bible helps us arrive at an idea of the probability of the said events of having happened.

Scenarios that could be considered:

1. The possibility of an arc with a single pair of all species of animals to survive when others were getting washed away in a devastating flood
2. The possibility of parting the red sea
3. The possibility of multiplying bread loaves and fish

Similar test cases:

1. Number of evil occurrences in a person's life
2. Number of good occurrences in a person's life
3. The probability of redemption in criminals due to religious sermons

Each of these above scenarios can be considered as A, with the alternative scenarios associated with A, being B. The probability of each of these occurrences are calculated and the mathematical explanations are applied. Depending upon the difference in the probability of each of these occurrences, the likelihood of the scenarios from happening can be drawn off. The chances of the scenario happening against all the explanations for it, helps us come to a conclusion about whether or not the event might have occurred. And if the event itself has not occurred then the persons explained in the event are also assumed to be hypothetical since there is a lot of evidence of people lying and making things up, more often than not. Classic examples of the application Bayes' theorem to whether or not God exists has been employed by Stephen Unwin and Richard Carrier. The same Bayes' theorem has been used by both of them in order to prove that God exists and that God does not exist, respectively. Both the books make a good read in making Bayes' theorem easy to understand with respect to the possibility of God's existence.