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In logic, an argument is a set of one or more declarative sentences known as the premises, along with another declarative sentence known as the conclusion, which asserts that the truth of the conclusion is a logical consequence of the premisses.
Each premise and the conclusion are only either true or false, not ambiguous. The sentences comprising an argument are referred to as being either "true" or "false", not as being "valid" or "invalid"; arguments are referred to as being "valid" or "invalid", not as being "true" or "false".
Some authors refer to the premises and conclusion 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. Whichever term is used, each premise and the conclusion must be capable of being true or false and nothing else: they are ‘truthbearers’.
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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. Formal arguments are studied in formal logic (historically called symbolic logic, more commonly referred to as mathematical logic today) expressed in a formal language. Informal logic may be said to emphasize the study of argumentation, whereas formal logic emphasizes implication and inference.
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Main article: Deductive argument |
A deductive argument is one in which it is intended that the conclusion necessarily follows from the premise. It is more commonly understood as the type of reasoning that proceeds from general principles or premises to derive particular information.
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Main article: Validity |
Arguments may be either valid or invalid. The validity of an argument depends on whether or not the argument follows valid logical forms, not on the truth or falsity of its premises and conclusions. The validity of an argument is not a guarantee of the truth of its conclusion, a valid argument may have false premises rendering the argument unsound. Only a valid argument with true premises has a true conclusion.
Logic seeks to discover the forms of valid arguments. Since a valid argument is one such that if the premises are true then the conclusion must necessarily be true it follows that a valid argument cannot have true premises and a false conclusion. 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 because other arguments of the same form have true premises and false conclusions. In informal logic this is called a counter argument.
A valid argument is one in which the premises cannot be true and the conclusion false. It has been long recognised that the validity of an argument depends solely on its form. The form of argument can be shown by the use of symbols. An argument-form is valid if and only if all arguments of its form are valid. For each argument-form, there is a corresponding statement-form, 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 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.
Some authors describe a sound argument as a valid argument with true premises; a sound argument being both valid and having true premises must have a true conclusion; other authors (especially in earlier literature) use the term sound as synonymous with valid.
Arguments can be invalid for a variety of reasons. There are well-established patterns of reasoning that arguments may follow which render them invalid; these patterns are known as logical fallacies.
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Main article: Soundness |
A sound argument is a valid argument with true premises.
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Main article: Inductive argument |
Inductive logic, is the process of reasoning in which the premises of an argument are believed to support the conclusion but do not entail it. Induction is a form of reasoning that makes generalizations based on individual instances.
Mathematical induction should not be misconstrued as a form of inductive reasoning, which is considered non-rigorous in mathematics. (See Problem of induction.) In spite of the name, mathematical induction is a form of deductive reasoning and is fully rigorous.
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Main article: Cogency |
An argument is 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."
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Main article: Logical fallacy |
A fallacy is an invalid argument that appear 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 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.
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: Iron is a metal therefore it will expand when heated. (Missing premise: all metals expand when heated). 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).
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Further information: Argumentative dialogue, Dialectic, and Rhetoric |
Whereas formal arguments are static, such as one might find in a textbook or research article argumentative dialogue is dynamic. It serves as a published record of justification for an assertion. Arguments can also be interactive, in which the proposer and the interlocutor have a more symmetrical relationship. The premises are discussed, as well the validity of the intermediate inferences.
Dialectic is controversy, that is, the exchange of arguments and counter-arguments respectively advocating propositions. The outcome of the exercise might not simply be the refutation of one of the relevant points of view, but a synthesis or combination of the opposing assertions, or at least a qualitative transformation in the direction of the dialogue.[1][2]
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Further information: Argumentation theory |
Argumentation theory, (or argumentation) embraces the arts and sciences of civil debate, dialogue, conversation, and persuasion. It studies rules of inference, logic, and procedural rules in both artificial and real world settings. Argumentation is concerned primarily with reaching conclusions through logical reasoning, that is, claims based on premises.
Statements are put forward as arguments in all disciplines and all walks of life. Logic is concerned with what consititutes an argument and what are the forms of valid arguments in all interpretations and hence in all disciplines, the subject matter being irrelevant. There are not different valid forms of argument in different subjects.
Arguments as they appear in science and mathematics (and other subjects) do not usually follow strict proof precedures; typically they are elliptical arguments (q.v.) and the rules of inference are implicit rather than explicit. An argument can be loosely said to be valid if it can be shown that, with the supply of the missing premises it has a valid argument form and demonstrateable by an accepted proof procedure.
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Main article: Philosophy of mathematics |
The basis of mathematical truth has been the subject of long debate. Frege in particular sought to demonstrate (see Gottlob Frege, The Foundations of Arithemetic, 1884, and Logicism in Philosophy of mathematics) that that arithmetical truths can be derived from purely logical axioms and therefore are, in the end, logical truths. The project was developed by Russell and Whitehead in their Principia Mathematica. If an argument can be cast in the form of sentences in Symbolic Logic, then it can be tested by the application of accepted proof procedures. This has been carried out for Arithemetics using Peano axioms. Be that as it may, an argument in Mathematics, as in any other discipline, can be considered valid just in case it can be shown to be of a form such that it cannot have true premises and a false conclusion.
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Main article: Philosophy of Science |
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Main articles: Oral argument and closing argument |
Legal arguments (or oral arguments) are spoken presentations to a judge or appellate court by a lawyer (or parties when representing themselves) of the legal reasons why they should prevail. Oral argument at the appellate level accompanies written briefs, which also advance the argument of each party in the legal dispute. A closing argument (or summation) is the concluding statement of each party's counsel (often called an attorney in the United States) reiterating the important arguments for the trier of fact, often the jury, in a court case. A closing argument occurs after the presentation of evidence.
