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The word argument has a number of senses. Here are two:

  1. (Logic) An argument is a set of statements, one of which (the conclusion), it is said or implied, follows from the others (the premises).
  2. (Mathematics and computer science) An argument is a variable or value passed into a function, subroutine, or an application program. An argument passed to an application program is referred to as a command line argument.

The rest of this article concerns "argument" in the first sense.

To give an argument is to give evidence, and then draw a conclusion from it; it is to give reasons to believe something, and then to state the belief. The statements that give expression to the evidence, or the reasons, are all called the premises; the thing one argues for is called the conclusion; and if the argument is successful, the premises together entail or imply the conclusion. One can think of a whole argument as a set of statements, comprising premise or premises, the conclusion, and the fact (or supposed fact) that the premises entail the conclusion. But usually the latter logical relationship between the premises and the conclusion is not explicitly stated, and sometimes the conclusion itself is not stated either, but left to the reader to supply.

There are other kinds of sets of statements besides arguments, such as explanations. Logic does not, except in its applications, concern itself with explanations. For example, suppose James offers an explanation for why there are tides: he talks about the gravitational effect of the moon and the sun on the oceans, and so on. That is not an argument; it is an explanation. In that case, James explains why there are tides. He is not trying to convince anyone that there are tides. It is already agreed that there are tides. The question the explanation answers is why there are.

On the other hand, suppose James argue for the following claim: "God exists." In that case James is not explaining why there is a God. If he tried to explain why there is a God, he would be assuming that there is a God. But if what he is doing is arguing for the existence of God, then he is not assuming that he exists; rather, he is trying to convince someone that God exists.

The difference between an argument and an explanation should be clear. On the one hand, the function or purpose of an argument is to convince people who might be doubting the conclusion. On the other hand, the function or purpose of an explanation is to give the cause of some phenomenon which we observe, or are willing to assume actually occurs. To put it even more briefly, the purpose of an argument is to persuade, while the purpose of an explanation is to explain.

There are good arguments and bad. No doubt there are a lot more bad arguments in the world than good ones. The ways in which arguments go wrong fall into certain patterns, called logical fallacies.