Friday, July 28, 2017

Fact-Checking the Torah -- DH's Conjunction Fallacy

The steps in DH that get to JE are all required and that makes this description a conjunction. The idea that DH is true is based on the Conjunction Fallacy. You might know about this fallacy if you know about the Linda problem, which you can find all over the web. The most common description is this:
“Linda is 31 years old, yadda yadda yadda. Which is more probable?
1. Linda is a bank teller.
2. Linda is a bank teller and is active in the feminist movement.”
Most people pick the wrong answer, #2, the conjunction. Why is it wrong?
There are two terms in answer 2; let’s call them “bank teller” and “feminist”. Each of them has a probability of being true, let’s say X and Y.
Nothing in the description has probative value for either term, that’s why I “yadda’d” it. Since there’s no evidence either way, X and Y are between 0 and 1.
The probability of answer 1 which has only term “bank teller” is therefore X. But the probability of answer 2 is X times Y. Because  X and Y are both between 0 and 1, their product is lower than either one. Also, whichever of X or Y is less, the probability of answer 2 is less than that.
The subject doesn’t have to be Linda; it can be sports, foreign affairs, or anything else under the sun. In every case, most people pick the conjunction as more probable, and they are wrong. The only way to make them pick the other choice, is basically to give them a course in probability calculations, and even then some of them will pick the conjunction.
Most disciplines consist of conjunctions. Why are they not conjunction fallacies? Because their descriptions always contain evidence of the truth of their claims. They use observations, experiments, and mathematics to demonstrate the probability that their conclusions are true.
They don’t make guesses, they calculate what statements are more accurate to make. They make predictions that are borne out in experiment or observation. If not, people are forced to rethink things, sometimes leading to new discoveries. As new information turns up or new concepts appear, they refine their statements to be more accurate.
They tend to support each other, either around the edges or because information from one can be directly inserted into another. Use of radioactive decay known from physics, to provide dates for archaeology, is an example of the first situation; chemistry incorporating the findings of quantum mechanics in physics is an example of the latter.
And their results have turned out to be useful, time after time. The physics that tells geologists that the world is about 4.5 billion years old, helps doctors save the lives of cancer patients. The chemistry that shows how DNA is the fuel of evolution, also helps correct genetic diseases.
I’m about to show you what the difference is between the conjunctions that are the sciences, and the conjunction fallacy that is DH.
For my special invitees, you have studied DH and know where the fallacies and bad facts lie. I’d be flattered if you stuck around for more of my offbeat perspective, or at least checked in at the end of each month to see what else I posted since your last visit.
For the rest of you, have a blast! I did.
(I had to use Jan Gullberg’s book Mathematics to work out the math of the probabilities; I also used Gary Curtis’ Fallacy Files website. If I have messed this up, don’t blame them; it’s completely my fault.)
© Patricia Jo Heil, 2013-2018 All Rights  Reserved

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