An argument is an attempt to demonstrate the truth of an assertion called a conclusion, based on the truth of a set of assertions called premises. If the argument is successful, the conclusion is said to be proved. This article classifies arguments as either deductive or inductive. An argument always assumes a certain kind of dialogue, with one person presenting the argument, attempting to persuade an interlocutor. An argument could be part of a written text, a speech, or a conversation.
In an argument, some statements are put forward as giving evidence for another statement. For example, the following is an argument:
Here the conclusion is “she probably likes kumquats.” The statements offered in support are “she likes citrus fruit” and “kumquats are citrus fruits.” These premises are asserted, without any additional argument or support. These premises may or may not be true. A statement is argued for if it is given other statements as support; it is asserted if it has no such support.
Sometimes the premises actually provide no support for the conclusion. Consider this argument:
The conclusion of this argument is “the next flip will probably come up tails.” The statement provided as evidence for this gives no support at all. The previous flips have no bearing on the next flip. Yet this is an argument because the premises were offered as evidence for the conclusion.
Some collections of statements may look like arguments without being arguments. For example, if one’s purpose is to explain or clarify a statement, one is not giving an argument:
If my purpose in saying this is to explain why I liked the movie, I am not arguing. The second sentence is not given as evidence for or in support of the first sentence, but is meant to explain why I liked the movie. These same sentences may be used in an argument for the conclusion; if I’m trying to convince you that the movie was good, I might offer the quality of the writing, acting, and filming as evidence of the movie’s quality.
A deductive argument uses the laws of logic to attempt to prove its conclusion. A deductive argument may be valid or invalid. If it is valid, it is logically impossible for the premises to be true and the conclusion false. In a valid argument, the premises are said to imply the conclusion. In some ways this is a very strong requirement (much stronger than the ordinary use of the word imply would suggest). It is irrational to accept the premises of a deductive argument and not accept the conclusion. One is not merely invited to accept the conclusion as plausible if one accepts the premises, rather, one is compelled to accept it as true.
At the same time, it is in some ways a very weak requirement. Consider the following argument:
This argument is valid since the conclusion follows logically from the premises. If the premises were true, the conclusion would be true as well. But the premises are not true, so the argument is not entirely successful. If an argument is valid and has true premises, it is called sound.
A valid argument may be unsound even if it has a true conclusion. The following argument expressed this point:
The conclusion is probably true, but at least some of the premises are certainly false. The first and third premises together prove that babies are despised, and this is surely false. If all babies are illogical (which is probably true), then at least some illogical persons are not despised. So the third premise is false (and perhaps the second premises too), but the conclusion is true.
Thus, a valid argument can have a true conclusion but untrue premises. At the same time, it can never be the vice versa. Faced with a valid argument, if you don’t believe the conclusion you must reject one of the premises. For example:
Here the conclusion is false: the platypus is a mammal. Here the false premise is the first. Some mammals (specifically, the platypus and the echidna) do lay eggs.
In a sense, logic is the study of validity. A system of logic, such as syllogism, will give rules to allow one to deduce a conclusion from premises. If a system of logic is adequate, its rules are exactly the ones needed to prove every valid argument it can express without proving any invalid arguments.
Strictly speaking, inductive arguments prove conclusions from premises that give special cases. For example:
There are many other kinds of inductive arguments as well. For example, an argument by analogy, in which the conclusion is argued for by presenting an example of something held to be similar, is not strictly an inductive argument, but for many purposes can be treated as one. In the preceding example, the general argument could be converted into an argument by analogy simply by changing the word ‘any’ to ‘our’, so the conclusion becomes this: “if our city adopts a measure like this, it will likely face similar failure.” Abductive argument, or reasoning to the best explanation, is another kind of non-deductive argument that is some ways similar to induction. Abductive arguments set out specific examples and then a general fact or principle that explains these examples.
Notice that the conclusion is not guaranteed by the premises. Hence, this argument is technically invalid. But if the comparisons are apt (if the measure being proposed by this city is relevantly similar, if the city is relevantly similar to the other cities, and so on), the argument is quite compelling. Thus, validity is the wrong measure for inductive arguments. Instead, an inductive argument is said to be compelling or cogent. An argument that is compelling or cogent is able to rationally persuade the interlocutor of the conclusion.
This standard of rational persuasion is not as well-defined as it in the case of deductive arguments. In many cases it is clear that an argument has gone wrong. The persuasive power of many arguments is emotional or in some other way not rational. Such an argument is fallacious, and there are many common fallacies, which, once seen, lose their ability to deceive. It is not so easy to explain the standards of cogency, to explain how an argument goes right.
The conclusion of a valid deductive argument is true if its premises are, so if one believes the premises of an argument, one must rationally believe the conclusion. Often arguments are between parties with different initial assumptions. In these cases, one party will present an argument whose premises he or she does not present as true, but as acceptable to the other party. The other party will counter with an argument from premises he or she thinks the other person believes to be true.
For example, a theodicy might have different premises if its intended audience consisted of believing Christians than if its intended audience consisted of agnostics, atheists, or Buddhists. An argument’s strength often depends on selecting the right premises for the intended audience.
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