Argument

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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 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.

Deductive Arguments

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, 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:

All dogs are blue.
Nothing is blue except fish.
Therefore, all dogs are fish.

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.

An valid argument may be unsound even if it has a true conclusion. The following argument is due to Lewis Carroll:

All babies are illogical.
Nobody is despised who can manage a crocodile.
Illogical persons are despised.
Therefore, no baby can manage a crocodile.

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 premise, too), but the conclusion is true.

Thus, a valid argument can have a true conclusion but untrue premises. But 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,

Mammals do not lay eggs.
The platypus lays eggs.
Therefore, the platypus is not a mammal.

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.

Inductive Arguments

Strictly speaking, inductive arguments prove conclusions from premises that give special cases. For example:

Every major city that has adopted similar measures has ultimately repealed them after losing millions of dollars. If any city adopts a measure like this, it will likely face similar failure. We are not immune.

But many other kinds of arguments are also called inductive. 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 indictive argument, but for many purposes can be treated as one. (The above 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 in 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.

Dialectic

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 theses cases, one party will present an argument whose premises he does not present as true, but as acceptable to the other party. The other party will counter with an argument from premises she thinks he 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.

References
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  • Rober Audi, Epistemology, Routledge, 1998. Particularly relevant is Chapter 6, which explores the relationship between knowledge, inference and argument.
  • J. L. Austin How to Do things with Words, Oxford University Press, 1976.
  • H. P. Grice, Logic and Conversation in The Logic of Grammar, Dickenson, 1975.
  • Henri Poincaré, Science and Hypothesis, Dover Publications, 1952
  • Frans van Eemeren and Rob Grootendorst, Speech Acts in Argumentative Discussions, Foris Publications, 1984.
  • K. R. Popper Objective Knowledge; An Evolutionary Approach, Oxford: Clarendon Press, 1972.
  • L. S. Stebbing, A Modern Introduction to Logic, Methuen and Co., 1948. An account of logic that covers the classic topics of logic and argument while carefully considering modern developments in logic.
  • Douglas Walton, Informal Logic: A Handbook for Critical Argumentation, Cambridge, 1998
  • Carlos Chesñevar, Ana Maguitman and Ronald Loui, Logical Models of Argument, ACM Computing Surveys, vol. 32, num. 4, pp.337-383, 2000.

See also

  • Logical fallacy
  • Nonargument

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