The Bohr-Einstein Debate
Reductio Ad Absurdum Arguments
The Double-Slit Experiment
Bell's Argument (Experimental Metaphysics)
Preliminary Example: Identical twins are separated in two rooms and each is asked two out of four questions:
A: Do you like apples?
M: Do you like milk?
P: Do you like pears?
Y: Do you like yogurt?
Suppose that 1,000 pairs of twins are tested in the following way: The left twin is asked questions A and Y, and the right twin is asked questions M and P.
Fact 1: Twins always give the same answers to the fruit questions.
Fact 2: Twins give the same answers to the dairy questions.
Question: If 250 out of 1,000 twins answer 'yes' to A and 'yes' to M, how many twins answer 'yes' to P and 'yes' to Y?
Reasoning: (yes, yes) answers are given to Y and P if and only if (yes, yes) answers are given to A and M.
"Bell" Example: Same as before, except that there 4,000 pairs of twins, and each twin is asked only one question. There are four possible question combinations that could be asked: (A, P), (Y, M), (A, P) and (Y, P). So, the 4,000 pairs are randomly divided into four groups with 1,000 in each group, and each group is given a different pair of questions. They have no prior information about what questions will be asked, and they are asked the questions simultaneously in different rooms separated a large distance from each other.
Group 1: Left twin is asked A and right twin is asked P.
Group 2: Left twin is asked Y and right twin is asked M.
Results 1 and 2: These results accord with facts 1 and 2 abovein each group, about ½ of the twin pairs answer 'yes' to both questions and about ½ answer 'no' to both questions. No twins give different answers.
Explanation: The principle of common cause says that to suppose that the correlation between the answers is too improbable to have arisen by chance. So, we need to explain it by introducing a common cause. There is, we suppose, two genetic factors. One that determines a like for fruit, and a second that determines a like for dairy products. Call these genes F and D respectively. Our explanation says that twins have the same genes. This explains our results.
Group 3: Left twin is asked A and right twin is asked M.
Result 3: About ¼ respond (yes, yes), ¼ answer (yes, no), ¼ answer (no, yes) and ¼ answer (no, no). The explanation for this is that there is a random distribution of these genes in the population.
Group 4: Left twin is asked Y and right twin is asked P.
Prediction: About ¼ will answer (yes, yes).
Result 4: The prediction is false. No twins answer (yes, yes) when Y and P are asked.
Argument: The prediction is made by a valid argument from the common cause explanation. If the conclusion of a valid argument is false, then at least one premise is false. The only premise that could be wrong is the common cause explanation.
Therefore the common cause explanation is wrong.
The Philosophical Lessons