6.3: Proving Your Conclusion

When the reasons do establish the conclusion, the argument is called a proof. Because the line between when the reasons establish the conclusion and when they don’t can be a fuzzy one, the term proof is vague, except in the case of mathematical proofs. Mathematical proofs are not a matter of degree; they are either correct or incorrect, but the kind of proofs we have in ordinary life and in science are a matter of degree; they make their case more or less strongly.

Some things are harder to prove than others, as we all know. You may have heard someone say, "It's impossible to prove a negative." This statement is an exaggeration, but it contains a valuable kernel of truth. It is an exaggeration, because it is easy to prove this negative: my car keys are not in my pocket. But it is much more difficult to prove the following negative: There is no telepathy.

Unlike a search of my pocket, the place to be searched for telepathy is not well defined because a psychic could say that just because you haven’t found any telepathy so far doesn’t mean you won’t find telepathy in other situations you haven’t yet investigated. Also, there is so much uncertainty about what counts as being an actual case of telepathy; for example, a psychic says that some event is a sign of telepathy, but a skeptic disagrees and says the psychic is jumping to conclusions.

Even though it is difficult to prove that there is no telepathy, it has been proved. First, given what else we know about nature, especially what else we know about brain physiology, telepathy is highly improbable, so not only is the burden of proof on anyone who says telepathy does exist, but the burden is a heavy one in the sense that it will have to be an extraordinarily good proof. Systematic searches for telepathy by qualified scientists have turned up no solid evidence. These two reasons prove there is no telepathy. They do not make it 100% certain there is no telepathy, but still it is enough to feel confident.

The above reasoning applies a special method of reasoning: hold off believing that something exists until you get the evidence in favor of it. Science is both a body of knowledge and a way of getting knowledge. Science involves a skeptical attitude that says, "I won't believe you until you show me the solid evidence."

When is evidence solid evidence? For most of us, the most solid form of evidence we have are the reports of experts we trust plus our knowledge that the experts agree with each other. But among the experts themselves, it often does take an expert to decide what counts as solid evidence. Usually, though, solid evidence must be reproducible. For example, if one researcher says, "I tested the subject and found her to be a psychic," other researchers will need to be satisfied that she can actually perform as well when the testing is repeated by themselves or by some other researcher they trust. The truth will be able to stand up to repeated tests, but falsehood will eventually be exposed.

People sometimes ask, "Why can't scientists give poorly supported suggestions the benefit of the doubt and simply accept them? Why the obsessional preoccupation with matters of validation?" The answer is that this liberal attitude leads to a contradiction. Suppose you have poor support for some suggestion S, and you also have poor support for its negation, Not-S. The liberal attitude above would have us accept both S and Not-S, which is absurd. Besides, the track record of accepting unsupported hypotheses is quite poor; they turn out to be unhelpful for creating good explanations and making accurate predictions, which are the two main goals of science.

When you argue that some conclusion should be drawn from the evidence you present, be careful not to defend a stronger conclusion than what the evidence justifies. Here is an example that illustrates the point. Two Italian-speaking men suffered strokes that damaged their brains, but not in the usual ways. According to a report in the well-respected British science journal Nature, examination of the first man two weeks after his stroke revealed that he omitted all vowels when writing about himself, his town, or common objects. He would leave blank spaces for the vowels. For example, he spelled the name of his town, Bologna, as “B lgn.” He was aware of the fact that he had misspelled the words, but he could not correct his errors. The second man also had a vowel-specific disturbance. He could write vowels, but he misspelled many words, and most of the misspellings involved errors with vowels and not consonants. Both men had no such difficulties before their strokes. The experimental psychologist who reported these two astonishing cases said that they may indicate the brain contains two different mechanisms, one for identifying and generating vowels and one for identifying and generating consonants. But notice that the evidence of these two cases is not a proof of this; it does no more than "indicate" this, as the researcher was careful to note. If, instead, the researcher had said that the evidence of these two cases "proves" there is a cerebral vowel organizer, then the researcher would have drawn too strong a conclusion and likely would have been told by the journal editor to tone down the conclusion before the article would be published.

Exercise \(\PageIndex{1}\)

What is the error in the following sentence?

In good scientific reasoning, the scientific reasoner should be cautious and never claim that something is known or proved unless it can be shown that from the evidence acquired that it would be absolutely impossible for the claim to be false.

Answer

This statement is making it too difficult for scientific reasoning to establish its claims. A proof of a claim is simply a strong, convincing argument; it need not be an argument so strong that "it would be absolutely impossible for the claim to be false."