Argument

This article is about the word as it is used in logic. For other uses, see Argument (disambiguation).

An argument is a claim or set of claims supported, if successful, by one or more defensible reason(s). In strict terms, an argument is defined as either (a) a set of one or more meaningful declarative sentences in a natural language known as the premises along with another sentence known as the conclusion; or (b) a non-empty collection of formulas in a formal language, one of which is designated to be the conclusion. An argument in a formal language shows the logical form of the natural language arguments obtained by its interpretations.

The standards of justification for a standard deductive argument (and therefore the basis on which it is to be defended) normally rest on its validity and soundness. The criteria for evaluating other types of arguments may rest on different criteria, such as the persuasiveness of so-called "indispensability claims" or the disclosure of new possibilities for understanding (see fallibilism).

Some authors refer to the premises and conclusion of an argument in a natural language using the terms declarative sentence, statement, proposition, sentence, or even indicative utterance. The reason for the variety is concern about the ontological significance of the terms, proposition in particular.

Formal and informal arguments

Further information: Informal logic and Formal logic

Informal arguments are studied in informal logic, are presented in ordinary language and are intended for everyday discourse. Conversely, 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 may be said to emphasize the study of argumentation, whereas formal logic emphasizes implication and inference. Informal arguments are sometimes implicit. That is, the logical structure –the relationship of claims, premises, warrants, relations of implication, and conclusion –is not always spelled out and immediately visible and must sometimes be made explicit by analysis.

Standard argument types

There are several kinds of arguments in logic, the best-known of which are "deductive" and "inductive." These are sometimes referred to broadly as "truth-preserving" arguments, because they assert something about the truth of a particular claim. A deductive argument asserts that the truth of the conclusion is a logical consequence of the premises. An inductive argument, on the other hand, asserts that the truth of the conclusion is supported by the premises. Each premise and the conclusion are truth bearers or "truth-candidates", capable of being either true or false (and not both). While statements in an argument are referred to as being either true or false, arguments are referred to as being valid or invalid (see logical truth). A deductive argument is valid if and only if the truth of the conclusion is entailed by (is a logical consequence) of the premises, and its corresponding conditional is therefore a logical truth. A sound argument is a valid argument with true premises; a valid argument may well have false premises.

Deductive arguments

Main article: Deductive argument

A deductive argument is one which, if valid, has a conclusion that is entailed by its premises. In other words, the truth of the conclusion is a logical consequence of the premises—if the premises are true, then 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.

Validity

Main article: Validity

Deductive arguments may be either valid or invalid. If an argument is valid, and its premises are true, the conclusion must be true: a valid argument cannot have true premises and a false conclusion.

The validity of an argument depends, however, not on the actual truth or falsity of its premises and conclusions, but solely on whether or not 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 and a false conclusion.

Logic seeks to discover the valid forms, the forms that make arguments valid arguments. An argument form is valid if and only if all arguments of that form are valid. Since the validity of an argument depends on its form, an argument can be shown to be invalid by showing that its form is invalid, and this can be done by giving another argument of the same form that has true premises but a false conclusion. In informal logic this is called a counter argument.

The form of 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 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. The conclusion of a valid argument need not be a necessary truth: if it were so, it would be so independently of the premises.

For example:

Some Greeks are logicians; therefore, some logicians are Greeks. Valid argument; it would be self-contradictory to admit that some Greeks are logicians but deny that some (any) logicians are Greeks.

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. (Remember that this does not mean the conclusion has to be true; it is only true if the premises are true, which they may not be!)

Premise 1: Some men are hawkers. Premise 2: Some hawkers are rich. Conclusion: Some men are rich.

This argument is invalid. There is a way where you can determine whether an argument is valid, give a counter-example with the same argument form.

Counter-Example: Premise 1: Some people are herbivores. Premise 2: Some herbivores are zebras. Conclusion: Some people are zebras. (This is obviously false!)

Note that the counter-example follows the P1. Some x are y. P2. Some y are z. C. Some x are z. format. We can now conclude that the hawker argument is invalid.

Arguments can be invalid for a variety of reasons. There are well-established patterns of reasoning that render arguments that follow them invalid; these patterns are known as logical fallacies.

Soundness

Main article: Soundness

A sound argument is a valid argument with true premises. A sound argument, being both valid and having true premises, must have a true conclusion. Some authors (especially in earlier literature) use the term sound as synonymous with valid.

Inductive arguments

Main article: Inductive 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 problem of induction is the philosophical question of whether inductive reasoning is valid.

Defeasible arguments

An argument is defeasible when additional information (such as new counterreasons) can have the effect that it no longer justifies its conclusion. The term "defeasibility" goes back to the legal theorist H.L.A. Hart, although he focused on concepts instead of arguments. Stephen Toulmin's influential argument model includes the possibility of counterreasons that is characteristic of defeasible arguments, but he did not discuss the evaluation of defeasible arguments. Defeasible arguments give rise to defeasible reasoning.

Argument by analogy

Argument by analogy may be thought of as argument from the particular to particular. An argument by analogy may use a particular truth in a premise to argue towards a similar particular truth in the conclusion. For example, if A. Plato was mortal, and B. Socrates was like Plato in other respects, then asserting that C. Socrates was mortal is an example of argument by analogy because the reasoning employed in it proceeds from a particular truth in a premise (Plato was mortal) to a similar particular truth in the conclusion, namely that Socrates was mortal.

Transitional arguments

In epistemology, transitional arguments attempt to show that a particular explanation is better than another because it is able to make sense of a transition from old to new. That is, if explanation b can account for the problems that existed with explanation a, but not vice versa, then b is regarded to be the more reasonable explanation. A common example in the history of science is the transition from pre-Galilean to Galilean understandings of physical motion.

Other kinds of arguments

Other kinds of arguments may have different or additional standards of validity or justification. For example, Charles Taylor writes that so-called transcendental arguments are made up of a "chain of indispensability claims" that attempt to show why something is necessarily true based on its connection to our experience, while Nikolas Kompridis has suggested that there are two types of "fallible" arguments: one based on truth claims, and the other based on the time-responsive disclosure of possibility (see world disclosure). The late French philosopher Michel Foucault is said to have been a prominent advocate of this latter form of philosophical argument.

Argument in fuzzy logic

Argument is a reference to possible future gain, either economic or moral, if an individual action is performed. In informal logic, an argument is a connexion between a) an individual action b) through which a generally accepted good is obtained. Ex :

1. a) You should marry Jane (individual action, individual decision)

b) because she has the same temper as you. (generally accepted wisdom that marriage is good in itself, and it is generally accepted that people with the same character get along well).

1. a) You should not smoke (individual action, individual decision)

b) because smoking is harmful (generally accepted wisdom that health is good). The argument is neither a) advice nor b) moral or economical judgement, but the connection between the two. An argument uses always the connective because. An argument is not an explanation. It does not connect two events, cause and effect, who already took place, but a possible individual action and it's beneficial outcome. An argument is not a proof. A proof is logical and cognitive concept; an argument is a praxeologic concept. A proof changes our knowledge ; an argument determines us to act.

World-disclosing arguments

Main article: world disclosure

World-disclosing arguments are a group of philosophical arguments that are said to employ a disclosive approach, to reveal features of a wider ontological or cultural-linguistic understanding – a "world," in a specifically ontological sense – in order to clarify or transform the background of meaning and "logical space" on which an argument implicitly depends.

Explanations and arguments

Main article: Explanation

While arguments attempt to show that something is, will be, or should be the case, explanations try to show why or how something is or will be. If Fred and Joe address the issue of whether or not Fred's cat has fleas, Joe may state: "Fred, your cat has fleas. Observe the cat is scratching right now." Joe has made an argument that the cat has fleas. However, if Fred and Joe agree on the fact that the cat has fleas, they may further question why this is so and put forth an explanation: "The reason the cat has fleas is that the weather has been damp." The difference is that the attempt is not to settle whether or not some claim is true, it is to show why it is true.

Arguments and explanations largely resemble each other in rhetorical use. This is the cause of much difficulty in thinking critically about claims. There are several reasons for this difficulty.

• People often are not themselves clear on whether they are arguing for or explaining something.
• The same types of words and phrases are used in presenting explanations and arguments.
• The terms 'explain' or 'explanation,' et cetera are frequently used in arguments.
• Explanations are often used within arguments and presented so as to serve as arguments.

Fallacies and non arguments

Main article: Logical fallacy

A fallacy is an invalid argument that appears valid, or a valid argument with disguised assumptions. First the premises and the conclusion must be statements, capable of being true and false. Secondly it must be asserted that the conclusion follows from the premises. In English the words therefore, so, because and hence typically separate the premises from the conclusion of an argument, but this is not necessarily so. Thus: Socrates is a man, all men are mortal therefore Socrates is mortal is clearly an argument (a valid one at that), because it is clear it is asserted that Socrates is mortal follows from the preceding statements. However I was thirsty and therefore I drank is NOT an argument, despite its appearance. It is not being claimed that I drank is logically entailed by I was thirsty. The therefore in this sentence indicates for that reason not it follows that.

• Elliptical arguments

Often an argument is invalid because there is a missing premise the supply of which would make it valid. Speakers and writers will often leave out a strictly necessary premise in their reasonings if it is widely accepted and the writer does not wish to state the blindingly obvious. Example: All metals expand when heated, therefore iron will expand when heated. (Missing premise: iron is a metal). On the other hand a seemingly valid argument may be found to lack a premise – a ‘hidden assumption’ – which if highlighted can show a fault in reasoning. Example: A witness reasoned: Nobody came out the front door except the milkman therefore the murderer must have left by the back door. (Hidden assumption- the milkman was not the murderer).

See also

• Abductive reasoning
• Analogy
• Argument map
• Argumentation theory
• Argumentative dialogue
• Belief bias
• Boolean logic
• Deductive reasoning
• Defeasible reasoning
• Fallacy

• Dialectic
• Formal fallacy
• Inductive reasoning
• Informal fallacy
• Inquiry
• Practical arguments
• Soundness theorem
• Soundness
• Truth
• Validity

References

• Shaw, Warren Choate (1922). The Art of Debate. Allyn and Bacon. p. 74.
• Robert 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.
• Vincent F. Hendricks, Thought 2 Talk: A Crash Course in Reflection and Expression, New York: Automatic Press / VIP, 2005, ISBN 87-991013-7-8
• R. A. DeMillo, R. J. Lipton and A. J. Perlis, Social Processes and Proofs of Theorems and Programs, Communications of the ACM, Vol. 22, No. 5, 1979. A classic article on the social process of acceptance of proofs in mathematics.
• Yu. Manin, A Course in Mathematical Logic, Springer Verlag, 1977. A mathematical view of logic. This book is different from most books on mathematical logic in that it emphasizes the mathematics of logic, as opposed to the formal structure of logic.
• Ch. Perelman and L. Olbrechts-Tyteca, The New Rhetoric, Notre Dame, 1970. This classic was originally published in French in 1958.
• 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.
• T. Edward Damer. Attacking Faulty Reasoning, 5th Edition, Wadsworth, 2005. ISBN 0-534-60516-8
• Charles Arthur Willard, A Theory of Argumentation. 1989.
• Charles Arthur Willard, Argumentation and the Social Grounds of Knowledge. 1982.

Further reading

• Salmon, Wesley C. Logic. New Jersey: Prentice-Hall (1963). Library of Congress Catalog Card no. 63-10528.
• Aristotle, Prior and Posterior Analytics. Ed. and trans. John Warrington. London: Dent (1964)
• Mates, Benson. Elementary Logic. New York: OUP (1972). Library of Congress Catalog Card no. 74-166004.
• Mendelson, Elliot. Introduction to Mathematical Logic. New York: Van Nostran Reinholds Company (1964).
• Frege, Gottlob. The Foundations of Arithmetic. Evanston, IL: Northwestern University Press (1980).