As an aspiring scientist, I hold the Truth above all. As Hodgell once said, "That which can be destroyed by the truth should be." But what if the thing that is holding our pursuit of the Truth back is our own system? I will share an example of an argument I overheard between a theist and an atheist once - showing an instance where human intuition might fail us.
*General Transcript*
Atheist: Prove to me that God exists!
Theist: He obviously exists – can’t you see that plants growing, humans thinking, [insert laundry list here], is all His work?
Atheist: Those can easily be explained by evolutionary mechanisms!
Theist: Well prove to me that God doesn’t exist!
Atheist: I don’t have to! There may be an invisible pink unicorn baby flying around my head, there is probably not. I can’t prove that there is no unicorn, that doesn’t mean it exists!
Theist: That’s just complete reductio ad ridiculo, you could do infrared, polaroid, uv, vacuum scans, and if nothing appears it is statistically unlikely that the unicorn exists! But God is something metaphysical, you can’t do that with Him!
Atheist: Well Nietzsche killed metaphysics when he killed God. God is dead!
Theist: That is just words without argument. Can you actually…..
As one can see, the biggest problem is determining burden of proof. Statistically speaking, this is much like the problem of defining the null hypothesis.
A theist would define: H0 : God exists. Ha: God does not exist.
An atheist would define: H0: God does not exist. Ha God does exist.
Both conclude that there is no significant evidence hinting at Ha over H0. Furthermore, and this is key, they both accept the null hypothesis. The correct statistical term for the proper conclusion if insignificant evidence exists for the acceptance of the alternate hypothesis is that one fails to reject the null hypothesis. However, human intuition fails to grasp this concept, and think in black and white, and instead we tend to accept the null hypothesis.
This is not so much a problem with statistics as it is with human intuition. Statistics usually take this form because simultaneous 100+ hypothesis considerations are taxing on the human brain. Therefore, we think of hypotheses to be defended or attacked, but not considered neutrally.
Considered a Bayesian outlook on this problem.
There are two possible outcomes: At least one deity exists(D). No deities exist(N).
Let us consider the natural evidence (Let’s call this E) before us.
P(D+N) = 1. P[(D+N)|E] = 1. P(D|E) + P(N|E) = 1. P(D|E) = 1- P(N|E).
Although the calculation of the prior probability of the probability of god existing is rather strange, and seems to reek of bias, I still argue that this is a better system of analysis than just the classical H0 and Ha, because it effectively compares the probability of D and N with no bias inherent in the brain’s perception of the system.
Example such as these, I believe, show the flaws that result from faulty interpretations of the classical system. If instead we introduced a Bayesian perspective – the faulty interpretation would vanish.
This is a case for the expanded introduction of Bayesian probability theory. Even if cannot be applied correctly to every problem, even if it is apparently more complicated than the standard method they teach in statistics class ( I disagree here), it teaches people to analyze situations from a more objective perspective.
And if we can avoid Truth-seekers going awry due to simple biases such as those mentioned above, won’t we be that much closer to finding Truth?
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Conditional probabilities are allowed to be 100%, because they are probability ratios. In particular, P(A|A) is 100% by definition.
But P(E|D) is not 100% by any definition. Conditional probabilities are only 100% if
D-->E. And if that was true, why does this argument exist?