Chapter 4: Deduction and Logic
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“The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding, can lead to them.” [Einstein, 1879-1955]
“'From a drop of water,' said [Sherlock Holmes], 'a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other. So all life is a great chain, the nature of which is known whenever we are shown a single link of it. Like all other arts, the Science of Deduction and Analysis is one which can only be acquired by long and patient study, nor is life long enough to allow any mortal to attain the highest possible perfection in it.” [Doyle, 1893b]
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Scientific deduction bears little similarity to the mythical conception conveyed by Sherlock Holmes. In science, obvious deductions are ubiquitous, insightful deductions are sporadic, and neither is infallible. We wield our logic with confidence, not noticing our occasional deductive errors. Before declaring that you are immune to such errors and skipping to the next chapter, please take ten minutes to attack the following problem:
Imagine that four 3"x5" cards are on the table. You can see that each card has a single letter or number on its top: one has the letter ‘A’, one has ‘B’, one has the number ‘4’, and one has the number ‘7’. You may assume that each card contains a single letter on one side and a single numeral on the other side. What cards is it necessary to turn over, to evaluate the validity of this rule: ‘If a card has an A on one side, then it has a 4 on the other side’?
This problem, posed by Wason [1966], is considered by many to be a good example of the type of deductive decision-making that scientists face. Only 10% of college students answer the card problem correctly [Kuhn et al., 1988]. I suspect that you, like I, spent only a minute or two on the problem and got the wrong answer. Before proceeding, please consider the problem once more, this time actually using some props such as post-its, sheets of paper, or pencil and pad. Imagine that each card flip will be a major, time-consuming experiment. Will each experiment really be crucial to testing the hypothesis?
