Argument

• 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.

Arguments are commonly used in philosophy and other disciplines when a logical approach is required. A discussion of the types of arguments used in philosophy may be considered meta-philosophy.

In mathematics, an argument can be formalized using symbolic logic of discrete mathematics. In that case, an argument is seen as an ordered list of statements, each one of which is either one of the premises or derivable from the combination of some subset of the preceding statements and one or more axiom. The last statement in the list is the conclusion.

Often, however, arguments are less formal. The logical relationship between the premises and the conclusion may not be explicitly stated, and sometimes the conclusion itself is left to the reader to supply.

In recent decades one of the more influential discussions of philosophical arguments is that by the prolific University of Pittsburgh philosophy professor Nicholas Rescher in his book The Strife of Systems. Rescher models philosophical problems on what he calls aporia or an aporetic cluster: a set of statements, each of which has initial plausibility but which are jointly inconsistent. The only way to solve the problem, then, is to reject one of the statements. If this is correct, it constrains how philosophical arguments are formulated.

Arguments vs. explanations

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 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.

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.

Referenced By