An argument is one or more premises—sentences, statements, or propositions—directed towards arriving at a logical conclusion. The purpose of an argument is to give reasons for one's thinking and understanding via justification, explanation, or persuasion. As a series of logical steps, arguments are intended to determine or show the degree of truth or acceptability of a logical conclusion.Ralph H. Johnson, Manifest Rationality: A pragmatic theory of argument (New Jersey: Laurence Erlbaum, 2000), 46–49.This is called "argument-as-product", distinguished from "argument-as-process" and "argument-as-procedure." Wenzel, J. W. (1987). The rhetorical perspective on argument. In F. H. van Eemeren, R. Grootendorst, J. A. Blair, & C. A. Willard (Eds.), Argumentation. Across the lines of discipline. Proceedings of the conference on argumentation 1986 (pp. 101–109). Dordrecht-Providence: Foris.
The process of crafting or delivering arguments, argumentation, can be studied from three main perspectives: through the logical, the dialectical, and the rhetorical perspective.
In logic, an argument is usually expressed not in natural language but in a symbolic formal language, and it can be defined as any group of propositions of which one is claimed to follow from the others through deductively valid inferences that preserve truth from the premises to the conclusion. This logical perspective on argument is relevant for scientific fields such as mathematics and computer science. Logic is the study of the forms of reasoning in arguments and the development of standards and criteria to evaluate arguments. Deductive arguments can be valid, and the valid ones can be sound: in a valid argument, premises necessitate the conclusion, even if one or more of the premises is false and the conclusion is false; in a sound argument, true premises necessitate a true conclusion. Inductive arguments, by contrast, can have different degrees of logical strength: the stronger or more cogent the argument, the greater the probability that the conclusion is true, the weaker the argument, the lesser that probability."Deductive and Inductive Arguments", Internet Encyclopedia of Philosophy. The standards for evaluating non-deductive arguments may rest on different or additional criteria than truth—for example, the persuasiveness of so-called "indispensability claims" in transcendental arguments,Charles Taylor, "The Validity of Transcendental Arguments", Philosophical Arguments (Harvard, 1995), 20–33. "[Transcendental] arguments consist of a string of what one could call indispensability claims. They move from their starting points to their conclusions by showing that the condition stated in the conclusion is indispensable to the feature identified at the start ... Thus we could spell out Kant's transcendental deduction in the first edition in three stages: experience must have an object, that is, be of something; for this, it must be coherent; and to be coherent it must be shaped by the understanding through the categories." the quality of hypotheses in retroduction, or even the disclosure of new possibilities for thinking and acting.
In dialectics, and also in a more colloquial sense, an argument can be conceived as a social and verbal means of trying to resolve, or at least contend with, a conflict or difference of opinion that has arisen or exists between two or more parties. For the rhetorical perspective, the argument is constitutively linked with the context, in particular with the time and place in which the argument is located. From this perspective, the argument is evaluated not just by two parties (as in a dialectical approach) but also by an audience. In both dialectic and rhetoric, arguments are used not through formal but through natural language. Since classical antiquity, philosophers and rhetoricians have developed lists of argument types in which premises and conclusions are connected in informal and defeasible ways.
Etymology The Latin root arguere (to make bright, enlighten, make known, prove, etc.) is from Proto-Indo-European *argu-yo-, suffixed form of *arg- (to shine; white).
Formal and informal
Informal arguments as studied in informal logic, are presented in ordinary language and are intended for everyday discourse. Formal arguments are studied in formal logic (historically called symbolic logic, more commonly referred to as mathematical logic today) and are expressed in a formal language. Informal logic emphasizes the study of argumentation; formal logic emphasizes implication and inference. Informal arguments are sometimes implicit. The rational structure—the relationship of claims, premises, warrants, relations of implication, and conclusion—is not always spelled out and immediately visible and must be made explicit by analysis.
Standard logical account of argument types
There are several kinds of arguments in logic, the best known of which are "deductive" and "inductive." An argument has one or more premises but only one conclusion. Each premise and the conclusion are truth bearers or "truth-candidates", each capable of being either true or false (but not both). These truth values bear on the terminology used with arguments.
Deductive arguments
A deductive argument asserts that the truth of the conclusion is a logical consequence of the premises: if the premises are true, the conclusion must be true. It would be self-contradictory to assert the premises and deny the conclusion because the negation of the conclusion is contradictory to the truth of the premises. Based on the premises, the conclusion follows necessarily (with certainty). Given premises that A=B and B=C, then the conclusion follows necessarily that A=C. Deductive arguments are sometimes referred to as "truth-preserving" arguments. For example, consider the argument that because bats can fly (premise=true), and all flying creatures are birds (premise=false), therefore bats are birds (conclusion=false). If we assume the premises are true, the conclusion follows necessarily, and it is a valid argument.
Validity
In terms of validity, deductive arguments may be either valid or invalid. An argument is valid, if and only if (iff) it is impossible in all possible worlds for the premises to be true and the conclusion false; validity is about what is possible; it is concerned with how the premises and conclusion relate and what is possible. An argument is formally valid if and only if the denial of the conclusion is incompatible with accepting all the premises.
In formal logic, the validity of an argument depends not on the actual truth or falsity of its premises and conclusion, but on whether the argument has a valid logical form. The validity of an argument is not a guarantee of the truth of its conclusion. A valid argument may have false premises that render it inconclusive: the conclusion of a valid argument with one or more false premises may be true or false.
Logic seeks to discover the forms that make arguments valid. A form of argument is valid if and only if the conclusion is true under all interpretations of that argument in which the premises are true. Since the validity of an argument depends on its form, an argument can be shown invalid by showing that its form is invalid. This can be done by a counter example of the same form of argument with premises that are true under a given interpretation, but a conclusion that is false under that interpretation. In informal logic this is called a counter argument.
The form of an argument can be shown by the use of symbols. For each argument form, there is a corresponding statement form, called a corresponding conditional, and an argument form is valid if and only if its corresponding conditional is a logical truth. A statement form which is logically true is also said to be a valid statement form. A statement form is a logical truth if it is true under all interpretations. A statement form can be shown to be a logical truth by either (a) showing that it is a tautology or (b) by means of a proof procedure.
The corresponding conditional of a valid argument is a necessary truth (true in all possible worlds) and so the conclusion necessarily follows from the premises, or follows of logical necessity. The conclusion of a valid argument is not necessarily true, it depends on whether the premises are true. If the conclusion, itself, is a necessary truth, it is without regard to the premises.
Some examples: All Greeks are human and all humans are mortal; therefore, all Greeks are mortal. : Valid argument; if the premises are true the conclusion must be true. Some Greeks are logicians and some logicians are tiresome; therefore, some Greeks are tiresome. Invalid argument: the tiresome logicians might all be Romans (for example). Either we are all doomed or we are all saved; we are not all saved; therefore, we are all doomed. Valid argument; the premises entail the conclusion. (This does not mean the conclusion has to be true; it is only true if the premises are true, which they may not be!) Some men are hawkers. Some hawkers are rich. Therefore, some men are rich. Invalid argument. This can be more easily seen by giving a counter-example with the same argument form: Some people are herbivores. Some herbivores are zebras. Therefore, some people are zebras. Invalid argument, as it is possible that the premises be true and the conclusion false.
In the above second to last case (Some men are hawkers ...), the counter-example follows the same logical form as the previous argument, (Premise 1: "Some X are Y." Premise 2: "Some Y are Z." Conclusion: "Some X are Z.") in order to demonstrate that whatever hawkers may be, they may or may not be rich, in consideration of the premises as such. (See also: Existential import).
The forms of argument that render deductions valid are well-established, however some invalid arguments can also be persuasive depending on their construction (inductive arguments, for example). (See also: Formal fallacy and Informal fallacy).
Soundness
An argument is sound when the argument is valid and argument's premise(s) is/are true, therefore the conclusion is true.
Inductive arguments
An inductive argument asserts that the truth of the conclusion is supported by the probability of the premises. For example, given that the military budget of the United States is the largest in the world (premise=true), then it is probable that it will remain so for the next 10 years (conclusion=true). Arguments that involve predictions are inductive since the future is uncertain. An inductive argument is said to be strong or weak. If the premises of an inductive argument are assumed true, is it probable the conclusion is also true? If yes, the argument is strong. If no, it is weak. A strong argument is said to be cogent if it has all true premises. Otherwise, the argument is uncogent. The military budget argument example is a strong, cogent argument.
Non-deductive logic is reasoning using arguments in which the premises support the conclusion but do not entail it. Forms of non-deductive logic include the statistical syllogism, which argues from generalizations true for the most part, and induction, a form of reasoning that makes generalizations based on individual instances. An inductive argument is said to be cogent if and only if the truth of the argument's premises would render the truth of the conclusion probable (i.e., the argument is strong), and the argument's premises are, in fact, true. Cogency can be considered inductive logic's analogue to deductive logic's "soundness". Despite its name, mathematical induction is not a form of inductive reasoning. The lack of deductive validity is known as the problem of induction.
Defeasible arguments and argumentation schemes