A deductive argument begins with premises and logically infers a conclusion. In order to be sound, the premises of an argument must be true. In order to be valid, the two premises must prove the conclusion. A deductive argument that stands as both sound and valid is factually true and therefore cogently strong. In juxtaposition, an inductive argument begins with a conclusion and then seeks to logically infer a relationship between the conclusion and the premises. Inductive arguments are not valid; that is, by its nature, an inductive argument cannot deductively prove that a relationship between its premises and its conclusion. Resultantly, although inductive arguments may strongly suggest a link between the premise and conclusion, it cannot be said to have the same cogent strength that a deductive argument has. Consider the following example of a deductive argument:
1. John is a fireman.
2. All fireman have blonde hair.
3. Therefore: John has blonde hair.
This argument is valid but not sound. If we accept the premises as true, then it does in fact follow logically that John has blonde hair. However, all fireman do not have blonde hair. Because the premise of the argument is false, the argument cannot be considered sound. The strength of a deductive argument lies in its ability to clearly and definitively reveal whether its argument is true or false. Consider the following example of a valid and sound argument:
1. John is a fireman.
2. Firemen put out fires.
3. Therefore: John puts out fires.
Both the premises are true. The conclusion follows logically from the two premises. Thus the argument is both valid and sound. With an absolute degree of certainty we know that John puts out fires: it is logical and therefore a very strong argument.
Deductive reasoning is used largely in philosophy and science to establish a causal relationship between different premises. For example, imagine a scientist is trying to test to see if a new toothpaste cures all cavities. Like any good scientist, he isolates his test variable (the toothpaste); perhaps he forbids his participants from using any other toothpaste for 24 hours prior to his experiment. Then he checks all the participants’ teeth to see how many cavities each has. He then has the participants apply the toothpaste to their teeth. After they are done, he tests their teeth for cavities. In this case all the cavities are gone. It can thus be logically inferred that the toothpaste cured the cavities. The argument in this case is simple. All variables except the toothpaste were isolated. The participant had cavities. After the toothpaste was applied, the cavities were gone. Thus, the toothpaste removed the cavities. Assuming that all the facts presented are true, this argument is both sound and valid. The weakness in deductive argument lies in its rigidity. While deductive arguments are strong at testing predictions, they are incapable of making predictions.
In contrast to this, inductive arguments are used largely to make predictions. Whereas a deductive argument seeks to prove a fact, inductive argument attempts to make best guesses. Although these arguments can vary from the absurdly weak to the convincingly strong, they can never be considered technically valid. Consider the following example:
1. Jeff’s wife said Jeff cheated.
2. Therefore, Jeff cheated.
This argument could be true, but it is impossible to know. One could make the argument stronger by saying:
1. Jeff’s wife said Jeff cheated.
2. Another woman claims to have had an affair with Jeff.
3. Jeff confessed to cheating.
4. Therefore, Jeff cheated.
Although the second argument is convincing enough, it is not logically valid. There is no solid referential relationship between the premises and the conclusion. Jeff’s wife claimed he cheated, as did another woman, on top of that Jeff confessed to it, so it seems reasonable to infer that Jeff in fact cheated. But consider that there are other explanations. Maybe it is one