In logic, an argument is a set of one or more declarative sentences (or "propositions") known as the premises along with another declarative sentence (or "proposition") known as the conclusion. Logic is the study of the principles of valid demonstration and Inference. In Linguistics, a sentence is a grammatical unit of one or more words bearing minimal syntactic relation to the words that precede or follow it often preceded and followed In Logic and Philosophy, proposition refers to either (a the content or Meaning of a meaningful Declarative sentence In Discourse and Logic, a premise is a claim that is a reason (or element of a set of reasons for or objection against some other claim A deductive argument asserts that the truth of the conclusion is a logical consequence of the premises; an inductive argument asserts that the truth of the conclusion is supported by the premises. A conclusion is a Proposition, which is arrived at after the consideration of Evidence, Arguments or Premises Logic "Therefore" redirects here For the symbol see Therefore sign. Induction or inductive reasoning, sometimes called inductive logic, is the process of Reasoning in which the premises of an argument are believed The meaning of the word truth extends from Honesty, Good faith, and Sincerity in general to agreement with Fact or Reality
Each premise and the conclusion are only either true or false, not ambiguous. Ambiguity (Am-big-u-i-ty is the property of being ambiguous, where a Word, term notation sign Symbol, Phrase, sentence, or any 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. In Logic and Philosophy, proposition refers to either (a the content or Meaning of a meaningful Declarative sentence Whichever term is used, each premise and the conclusion must be capable of being true or false and nothing else: they are truthbearers. Truthbearer is a term used by philosophers and linguists to designate entities that are either True or False and nothing else
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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. Informal logic (or occasionally non-formal logic) is the study of arguments as presented in ordinary language as contrasted with the presentations of arguments in Mathematical logic is a subfield of Logic and Mathematics with close connections to Computer science and Philosophical logic. Discourse (L discursus, "running to and from" means either "written or spoken communication or debate" or "a formal discussion Formal arguments are studied in formal logic (historically called symbolic logic, more commonly referred to as mathematical logic today) are expressed in a formal language. A formal language is a set of words, ie finite strings of letters, or symbols. Informal logic may be said to emphasize the study of argumentation, whereas formal logic emphasizes implication and inference. Argumentation theory, or argumentation, embraces the arts and sciences of civil debate Dialogue, conversation and persuasion studying rules of Inference Inference is the act or process of deriving a Conclusion based solely on what one already knows
Deductive arguments
A deductive argument is one which, if valid, has a conclusion which is entailed by its premises. Deductive reasoning is Reasoning which uses deductive Arguments to move from given statements ( Premises to Conclusions which must be true if the 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.
A deductive argument is often described as the type of argument that proceeds from general principles to derive particular claims. However, Some Greeks are men therefore some men are Greeks and The Morning Star is the Evening Star , The Evening Star is Venus therefore The Morning Star is Venus are valid deductive arguments which do not fit this description.
Validity
Arguments may be either valid or invalid. The term validity (also called logical truth, analytic truth, or necessary truth) as it occurs in Logic refers generally to a property of 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. In Logic, the argument form or test form of an Argument results from replacing the different words or sentences that make up the argument with letters 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. The term validity (also called logical truth, analytic truth, or necessary truth) as it occurs in Logic refers generally to a property of 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. In Logic an interpretation gives meaning to an artificial or Formal language or to a sentence of such a language by assigning a denotation (extension 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. In Logic, and in particular Proof theory, a proof procedure for a given logic is a systematic method for producing proofs in some Proof calculus
The corresponding conditional, of a valid argument is a necessary truth (true in all possible worlds) and so we might say that 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) logicans 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 logician are tiresome therefore some Greeks are tiresome. Invalid argument: the tiresome logicians might all be Romans!
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 does not mean the conclusion has to be true, only if the premisses are true, and perhaps they are not, perhaps some people are saved and some people are doomed, and perhaps some neither saved nor doomed!)
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. A fallacy is a component of an Argument which being demonstrably flawed in its Logic or form renders the argument invalid in whole
Soundness
A sound argument is a valid argument with true premises. In Mathematical logic, a Logical system has the soundness property If and only if its Inference rules prove only formulas that are 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
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 or inductive reasoning, sometimes called inductive logic, is the process of Reasoning in which the premises of an argument are believed 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. Mathematical induction is a method of Mathematical proof typically used to establish that a given statement is true of all Natural numbers It is done by proving that (See Problem of induction. The problem of induction is the philosophical question of whether inductive reasoning is valid ) In spite of the name, mathematical induction is a form of deductive reasoning and is fully rigorous.
Cogent arguments
An argument is cogent if and only if the truth of the argument's premises would render the truth of the conclusion probable (i. 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. Induction or inductive reasoning, sometimes called inductive logic, is the process of Reasoning in which the premises of an argument are believed Deductive reasoning is Reasoning which uses deductive Arguments to move from given statements ( Premises to Conclusions which must be true if the In Mathematical logic, a Logical system has the soundness property If and only if its Inference rules prove only formulas that are "
Fallacies and non arguments
A fallacy is an invalid argument that appears valid, or a valid argument with disguised assumptions. A fallacy is a component of an Argument which being demonstrably flawed in its Logic or form renders the argument invalid in whole 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.
- 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: 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).
Rhetoric, dialectic, and argumentative dialogue
- 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. See also Argument Whereas formal arguments are static such as one might find in a textbook or research article argumentative dialogue is dynamic In classical Philosophy, dialectic (διαλεκτική is controversy the exchange of arguments and counter-arguments respectively advocating Propositions Rhetoric has had many definitions no simple definition can do it justice It serves as a published record of justification for an assertion. Arguments can also be interactive, with the proposer and the interlocutor having a 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]
Argumentation theory
- Further information: Argumentation theory
Argumentation theory, (or argumentation) embraces the arts and sciences of civil debate, dialogue, conversation, and persuasion. Argumentation theory, or argumentation, embraces the arts and sciences of civil debate Dialogue, conversation and persuasion studying rules of Inference A dialogue (sometimes spelled dialog) is a reciprocal Conversation between two or more entities. It studies rules of inference, logic, and procedural rules in both artificial and real world settings. Inference is the act or process of deriving a Conclusion based solely on what one already knows Logic is the study of the principles of valid demonstration and Inference. Argumentation is concerned primarily with reaching conclusions through logical reasoning, that is, claims based on premises. Reasoning is the cognitive process of looking for Reasons for beliefs conclusions actions or feelings In Discourse and Logic, a premise is a claim that is a reason (or element of a set of reasons for or objection against some other claim
Arguments in various disciplines
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.
Mathematical arguments
The basis of mathematical truth has been the subject of long debate. The philosophy of mathematics is the branch of Philosophy that studies the philosophical assumptions foundations and implications of Mathematics. 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. Friedrich Ludwig Gottlob Frege ( 8 November 1848, Wismar, Grand Duchy of Mecklenburg-Schwerin &ndash 26 July 1925 The philosophy of mathematics is the branch of Philosophy that studies the philosophical assumptions foundations and implications of Mathematics. 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 Arithemetic using Peano axioms. In Mathematical logic, the Peano axioms, also known as the Dedekind-Peano axioms or the Peano postulates, are a set of Axioms for the Natural 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.
Scientific arguments
Legal arguments
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. Philosophy of science is the study of assumptions foundations and implications of Science. Oral arguments are spoken presentations to a Judge or Appellate court by a Lawyer (or parties when representing themselves of the legal reasons A closing argument, summation, or summing up is the concluding statement of each party's Counsel (often called an attorney in the United States reiterating A judge, or justice, is an Official who presides over a Court of law Court of Appeal, Court of Appeals, and Appellate Division redirect here for a list of specific courts using those titles see Court of Appeal A lawyer, according to Black's Law Dictionary, is "a person learned in the law as an attorney, Counsel or Solicitor; a person Law is a system of rules enforced through a set of Institutions used as an instrument to underpin civil obedience politics economics and society Oral argument at the appellate level accompanies written briefs, which also advance the argument of each party in the legal dispute. A brief (Latin " brevis " short or factum (Latin for "act" or "deed" is a written legal document used in various legal 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 counsel or a counsellor gives advice more particularly in legal matters A trier of fact (or finder of fact) is a person who determines facts in a legal proceeding A legal case is a dispute between opposing parties resolved by a Court, or by some equivalent legal process A closing argument occurs after the presentation of evidence. The Law of evidence governs the use of Testimony (eg oral or written statements such as an Affidavit) and exhibits (e
Political arguments
A political argument is an instance of a logical argument applied to politics. See also Argument political argument is an instance of a Logical argument applied to Politics. Politics Politics is the process by which groups of people make decisions Political arguments are used by academics, media pundits, candidates for political office and government officials. A pundit is someone who offers to mass-media his/her opinion or commentary on a particular subject area (most typically political analysis, the Social sciences Political arguments are also used by citizens in ordinary interactions to comment about and understand political events.
References
- ^ Ayer, A. J. , & O'Grady, J. (1992). A dictionary of philosophical quotations. Oxford, UK: Blackwell Publishers. Page 484.
- ^ McTaggart, J. M. E. (1964). A commentary on Hegel's logic. New York: Russell & Russell. Page 11
- Robert Audi, Epistemology, Routledge, 1998. Robert Audi (born November 1941 is a philosopher whose major work has focused on epistemology Ethics —especially on Ethical intuitionism, and the theory of action 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. John Langshaw Austin ( March 26, 1911 – February 8, 1960) was a British philosopher of language, born in Lancaster and
- 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. Vincent F Hendricks ( March 6, 1970) is a distinguished philosopher and logician 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. Yuri Ivanovitch Manin (Юрий Иванович Манин born 1937 Simferopol) is a Russian / German mathematician known for work in Algebraic 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. Chaïm Perelman ( May 20, 1912 &ndash January 22, 1984) was a Polish-born philosopher of law, who studied taught and lived most of 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. Jules Henri Poincaré ( 29 April 1854 &ndash 17 July 1912) (ˈʒyl ɑ̃ˈʁi pwɛ̃kaˈʁe was a French Mathematician
- K. R. Popper Objective Knowledge; An Evolutionary Approach, Oxford: Clarendon Press, 1972. Sir Karl Raimund Popper ( July 28 1902 &ndash September 17 1994) was an Austrian and British Philosopher and a professor
- L. S. Stebbing, A Modern Introduction to Logic, Methuen and Co. L (Lizzie Susan Stebbing (1885-1943 was a British philosopher , 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. Douglas Neil Walton is a Canadian academic and author well known for his many widely published books and papers on Argumentation, logical Fallacies and 32, num. 4, pp. 337-383, 2000.
- T. Edward Damer. Attacking Faulty Reasoning, 5th Edition, Wadsworth, 2005. Attacking Faulty Reasoning is a textbook on Logical fallacies by T ISBN 0-534-60516-8
Further reading
More on Arguments:
Wesley C Salmon, Logic, Prentice-Hall, New Jersey 1963 (Library of Congress Catalog Card no. 63-10528)
More on Logic:
Aristotle, Prior and Posterior Analytics, ed. and trans. John Warrington, Dent: London (everyman Library) 1964
Benson Mates, Elementary Logic, OUP, New York 1
972 (Library of Congress Catalog Card no. 74-166004)
Elliot Mendelson, Introduction to Mathematical Logic,, Van Nostran Reinholds Company, New York 1964
More on Logic and Maths:
1884. Die Grundlagen der Arithmetik: eine logisch-mathematische Untersuchung über den Begriff der Zahl. Breslau: W. Koebner. Translation: J. L. Austin, 1974. The Foundations of Arithmetic: A logico-mathematical enquiry into the concept of number, 2nd ed. Blackwell. Gottlob Frege, The Foundations of Arithmetic: A logico-mathematical enquiry into the concept of number, 1884, trans Jacquette, Pearson Longman, 2007
See also
Dictionary
argument
-noun
- A fact or statement used to support a proposition; a reason:
- A verbal dispute; a quarrel.
- A process of reasoning.
- (philosophy, logic) A series of statements organized so that the final statement is a conclusion which is intended to follow logically from the preceding statements, which function as premises.
- (mathematics) The independent variable of a function.
- (programming) A value, or reference to a value, passed to a function.
- (programming) A parameter in a function definition; a formal argument.
- A summary or short statement of the plot or chief points of a book.
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