Argument

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In philosophy, an argument is a compelling, rigorous demonstration of the truth of a conclusion, based on the truth of any number of premises. If the argument is valid, the premises together entail or imply the conclusion.

Also:

• In mathematics, argument is used in two senses:
  • Informally, the term is sometimes used instead of parameter or independent variable for a value on which the value of a function depends. So if f(x) is the value of a function, x is the argument.
  • In complex analysis, the argument or complex argument of a complex number is one component of the mod-arg form of that number. See complex number.
• In computer science, an argument is an informal term for actual parameter, which can be variable or value passed into a function, subroutine, or computer program. The usage is analogous to that in mathematics.

In The ways in which philosophical arguments go wrong fall into certain patterns, called logical fallacies, meaning false notation of logic. Arguments can be formalized using symbolic logic, mathematical logic, and discrete mathematics. In these cases, arguments are ordered lists of statements, each one a premise, or derivable from the combination of subsets of preceding statements, and one or more axioms. The last statement in the list is the conclusion.

Often, however, arguments are much more informal. Often the 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. The arguments used in philosophy are therefore of a very interesting character, studied in many various ways by many philosophers in their writings, constituting a meta-philosophy and meta-logic.

Argument vs Explanation

There are other sets of statements beside 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, but an explanation, that of James explaining why there are tides. He is not trying to convince anyone that there are tides, or that tides follow from a set of facts. It is already agreed that there are tides.

On the other hand, suppose the response to James was "I don't believe you, everybody knows that tides are caused by Poseidon". He could respond by collecting information, such as the position of the moon and sun and the height of the tide and using this to show why he is more likely correct. Then he will have produced an argument, irrespective of whether he manages to convince anybody. Then James has constructed an argument.

So, the function or purpose of an argument is to convince people who might doubt the conclusion. The function or purpose of an explanation is to describe some phenomenon which we observe or relate from others. Frustrations between people discussing a topic can often be traced back to this distinction, and whether or not one participant is using it or not.

References

• Adapted from the Wikipedia article, "Argument" http://en.wikipedia.org/wiki/Argument, used under the GNU Free Documentation License