In a typical deductive argument, the premises are meant to provide a guarantee of the truth of the conclusion, while in an inductive argument, they are thought to provide reasons supporting the conclusion's probable truth. 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, the quality of hypotheses in retroduction, or even the disclosure of new possibilities for thinking and acting.
The standards and criteria used in evaluating arguments and their forms of reasoning are studied in logic. Ways of formulating arguments effectively are studied in rhetoric (see also: argumentation theory). An argument in a formal language shows the logical form of the symbolically represented or natural language arguments obtained by its interpretations.
- 1 Formal and informal
- 2 Standard types
- 3 Deductive
- 4 Inductive
- 5 Defeasible arguments and argumentation schemes
- 6 By analogy
- 7 Other kinds
- 8 Explanations
- 9 Fallacies and nonarguments
- 10 See also
- 11 Notes
- 12 References
- 13 Further reading
- 14 External links
Formal and informalordinary 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 rational 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 typesThere are several kinds of arguments in logic, the best-known of which are "deductive" and "inductive." Deductive arguments are sometimes referred to as "truth-preserving" arguments, because the truth of the conclusion follows given that of the premises. 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 otherwise 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 under a given interpretation, however, the truth value of a conclusion cannot be determined by an unsound argument.
An argument is formally valid if and only if the denial of the conclusion is incompatible with accepting all the premises.
The validity of an argument depends, however, not on the actual truth or falsity of its premises and conclusion, 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. Under a given interpretation, 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 either true or false.
Logic seeks to discover the valid forms, 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 solely on its form, an argument can be shown to be invalid by showing that its form is invalid. This can be done by giving 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 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. If the conclusion, itself, just so happens to be a necessary truth, it is so without regard to the premises.
- 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!)
- Some men are hawkers. Some hawkers are rich. Therefore, some men are rich. Invalid argument. This can be easier 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.
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).
Defeasible arguments and argumentation schemesIn modern argumentation theories, arguments are regarded as defeasible passages from premises to a conclusion. Defeasibility means that when additional information (new evidence or contrary arguments) is provided, the premises may be no longer lead to the conclusion (non-monotonic reasoning). This type of reasoning is referred to as defeasible reasoning. For instance we consider the famous Tweedy example:
- Tweedy is a bird.
- Birds generally fly.
- Therefore, Tweedy (probably) flies.
|Major Premise:||Source E is an expert in subject domain S containing proposition A.|
|Minor Premise:||E asserts that proposition A is true (false).|
|Conclusion:||A is true (false).|
|CQ1:||Expertise Question. How credible is E as an expert source?|
|CQ2:||Field Question. Is E an expert in the field that A is in?|
|CQ3:||Opinion Question. What did E assert that implies A?|
|CQ4:||Trustworthiness Question. Is E personally reliable as a source?|
|CQ5:||Consistency Question. Is A consistent with what other experts assert?|
|CQ6:||Backup Evidence Question. Is E's assertion based on evidence?|
By analogyArgument 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.
Other kindsOther 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.
In informal logicArgument is an informal calculus, relating an effort to be performed or sum to be spent, to possible future gain, either economic or moral. In informal logic, an argument is a connexion between
- an individual action
- through which a generally accepted good is obtained.
- You should marry Jane (individual action, individual decision)
- 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).
- You should not smoke (individual action, individual decision)
- because smoking is harmful (generally accepted wisdom that health is good).
Logical statusArgument does not belong to logic, because it is connected to a real person, a real event, and a real effort to be made.
- If you, John, will buy this stock, it will become twice as valuable in a year.
- If you, Mary, study dance, you will become a famous ballet dancer.
Both the above argument and explanation require knowing the generalities that a) fleas often cause itching, and b) that one often scratches to relieve itching. The difference is in the intent: an argument attempts to settle whether or not some claim is true, and an explanation attempts to provide understanding of the event. Note, that by subsuming the specific event (of Fred's cat scratching) as an instance of the general rule that "animals scratch themselves when they have fleas", Joe will no longer wonder why Fred's cat is scratching itself. Arguments address problems of believe, explanations address problems of understanding. Also note that in the argument above, the statement, "Fred's cat has fleas" is up for debate (i.e. is a claim), but in the explanation, the statement, "Fred's cat has fleas" is assumed to be true (unquestioned at this time) and just needs explaining.
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.
- Likewise, "...arguments are essential to the process of justifying the validity of any explanation as there are often multiple explanations for any given phenomenon."
Fallacies and nonarguments
In Logic types of fallacy are firmly described thus: First the premises and the conclusion must be statements, capable of being true or 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
- Abductive reasoning
- Argument map
- Argumentation theory
- Argumentative dialogue
- Belief bias
- Boolean logic
- Deductive reasoning
- Defeasible reasoning
- Evidence-based policy
- Formal fallacy
- Inductive reasoning
- Informal fallacy
- Practical arguments
- Soundness theorem
- "Argument", Internet Encyclopedia of Philosophy." "In everyday life, we often use the word "argument" to mean a verbal dispute or disagreement. This is not the way this word is usually used in philosophy. However, the two uses are related. Normally, when two people verbally disagree with each other, each person attempts to convince the other that his/her viewpoint is the right one. Unless he or she merely results to name calling or threats, he or she typically presents an argument for his or her position, in the sense described above. In philosophy, "arguments" are those statements a person makes in the attempt to convince someone of something, or present reasons for accepting a given conclusion."
- Ralph H. Johnson, Manifest Rationality: A pragmatic theory of argument (New Jersey: Laurence Erlbaum, 2000), 46-49.
- Ralph H. Johnson, Manifest Rationality: A pragmatic theory of argument (New Jersey: Laurence Erlbaum, 2000), 46.
- The Cambridge Dictionary of Philosophy, 2nd Ed. CUM, 1995 "Argument: a sequence of statements such that some of them (the premises) purport to give reason to accept another of them, the conclusion"
- Stanford Enc. Phil., Classical Logic
- "Deductive and Inductive Arguments," Internet Encyclopedia of Philosophy.
- hCharles 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."
- Kompridis, Nikolas (2006). "World Disclosing Arguments?". Critique and Disclosure. Cambridge: MIT Press. pp. 116–124. ISBN 0262277425.
- "Argument", Internet Encyclopedia of Philosophy."
- Macagno, Fabrizio; Walton, Douglas (2015). "Classifying the patterns of natural arguments". Philosophy & Rhetoric . 48 (1): 26–53.
- Walton, Douglas; Reed, Chris; Macagno, Fabrizio (2008). Argumentation Schemes. New York: Cambridge University Press. p. 310.
- Shaw 1922: p. 74.
- Charles Taylor, "The Validity of Transcendental Arguments", Philosophical Arguments (Harvard, 1995), 20-33.
- Nikolas Kompridis, "Two Kinds of Fallibilism", Critique and Disclosure (Cambridge: MIT Press, 2006), 180-183.
- In addition, Foucault said of his own approach that "My role ... is to show people that they are much freer than they feel, that people accept as truth, as evidence, some themes which have been built up at a certain moment during history, and that this so-called evidence can be criticized and destroyed." He also wrote that he was engaged in "the process of putting historico-critical reflection to the test of concrete practices… I continue to think that this task requires work on our limits, that is, a patient labor giving form to our impatience for liberty." (emphasis added) Hubert Dreyfus, "Being and Power: Heidegger and Foucault" and Michel Foucault, "What is Enlightenment?"
- Nikolas Kompridis, "World Disclosing Arguments?" in Critique and Disclosure, Cambridge:MIT Press (2006), 118-121.
- JONATHAN F. OSBORNE, ALEXIS PATTERSON School of Education, Stanford University, Stanford, CA 94305, USA Received 27 August 2010; revised 22 November 2010; accepted 29 November 2010 DOI 10.1002/sce.20438 Published online 23 May 2011 in Wiley Online Library (wileyonlinelibrary.com)
- Critical Thinking, Parker and Moore
- Justin Scott Giboney, Susan Brown, and Jay F. Nunamaker Jr. (2012). "User Acceptance of Knowledge-Based System Recommendations: Explanations, Arguments, and Fit" 45th Annual Hawaii International Conference on System Sciences, Hawaii, January 5–8.
- 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.
- Walton, Douglas; Christopher Reed; Fabrizio Macagno, Argumentation Schemes, New York: Cambridge University Press, 2008.
- 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.
- 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).
- Martin, Brian. The Controversy Manual (Sparsnäs, Sweden: Irene Publishing, 2014).
- Argument at PhilPapers
- Argument at the Indiana Philosophy Ontology Project
- Argument entry in the Internet Encyclopedia of Philosophy