In logic Logic is the study of reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, and computer science. Logic examines general forms which arguments may take, which forms are valid, and which are fallacies. It is one kind of critical thinking. In philosophy, the study of logic, an argument is a set of one or more meaningful declarative sentences In the field of linguistics, a sentence is an expression in natural language, often defined to indicate a grammatical and lexical unit consisting of one or more words that represent distinct concepts. A sentence can include words grouped meaningfully to express a statement, question, exclamation, request or command (or "propositions" A proposition is a sentence expressing something true or false. In philosophy, particularly in logic, a proposition is identified ontologically as an idea, concept, or abstraction whose token instances are patterns of symbols, marks, sounds, or strings of words. Propositions are considered to be syntactic entities and also truthbearers) known as the premises In logic, an argument is a set of one or more declarative sentences known as the premises along with another declarative sentence (or "proposition") known as the conclusion. Aristotle held that any logical argument could be reduced to two premises and a conclusion. Premises are sometimes left unstated in which case they are called along with another meaningful declarative sentence (or "proposition") known as the conclusion, is asserted. A deductive argument asserts that the truth of the conclusion is a logical consequence Logical consequence is a fundamental concept in logic. It is the relation that holds between a set of sentences and a sentence (proposition) when the former "entails" the latter. For example, 'Kermit is green' is said to be a logical consequence of 'All frogs are green' and 'Kermit is a frog', because it would be "self-contradictory& of the premises; an inductive argument Inductive reasoning, also known as induction or inductive logic, is a type of reasoning that involves moving from a set of specific facts to a general conclusion. It uses premises from objects that have been examined to establish a conclusion about an object that has not been examined. It can also be seen as a form of theory-building, in which asserts that the truth Truth can have a variety of meanings, from the state of being the case, being in accord with a particular fact or reality, being in accord with the body of real things, events, actuality, or fidelity to an original or to a standard, truth "behind" everything, the ontological truth. In archaic usage it could be fidelity, constancy or of the conclusion is supported by the premises. Deductive arguments are valid or invalid, and sound or not sound. An argument is valid if and only if the truth of the conclusion is a logical consequence Logical consequence is a fundamental concept in logic. It is the relation that holds between a set of sentences and a sentence (proposition) when the former "entails" the latter. For example, 'Kermit is green' is said to be a logical consequence of 'All frogs are green' and 'Kermit is a frog', because it would be "self-contradictory& of the premises and (consequently) its corresponding conditional is a necessary truth. A sound argument is a valid argument with true premises.

Each premise and the conclusion are only either true or false, i.e. are truth bearers Truthbearer is a term used to designate entities that are either true or false and nothing else. The acceptance that some things are true while others are false raises the question of the nature of such things. Since there is no agreement on the matter, the term truthbearer is used to be neutral among the various theories. Candidates truthbearers. The sentences composing an argument are referred to as being either true or false, not as being valid or invalid; deductive 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 Truthbearer is a term used to designate entities that are either true or false and nothing else. The acceptance that some things are true while others are false raises the question of the nature of such things. Since there is no agreement on the matter, the term truthbearer is used to be neutral among the various theories. Candidates truthbearers.

Formal and informal arguments

Informal arguments are studied in informal logic, are presented in ordinary language The phrase ordinary language is often used in philosophy and logic to distinguish between ordinary, unsurprising uses of terms and their more specialized uses in theorizing, or jargon. For example, the statements "I find that class of person very annoying" and "Birds fall into a different class from bees" might be said to and are intended for everyday discourse Discourse means either "written or spoken communication or debate" or "a formal discussion of debate." The term is often used in semantics and discourse analysis. 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 A formal language is a set of words, i.e. finite strings of letters, symbols, or tokens. The set from which these letters are taken is called the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar ; accordingly, words that belong to a formal language are sometimes called well-formed words (. Informal logic may be said to emphasize the study of argumentation Argumentation theory, or argumentation, is the interdisciplinary study of how humans should, can, and do reach conclusions through logical reasoning, that is, claims based, soundly or not, on premises. It includes the arts and sciences of civil debate, dialogue, conversation, and persuasion. It studies rules of inference, logic, and procedural, whereas formal logic emphasizes implication and inference Inference is the process of drawing a conclusion by applying heuristics to observations or hypotheses; or by interpolating the next logical step in an intuited pattern. The conclusion drawn is also called an inference. The laws of valid inference are studied in the field of logic. 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.

Deductive arguments

A deductive argument is one which, if valid, has a conclusion that is entailed In logic, entailment is a relation between sets of sentences and a sentence. Typically entailment is defined in terms of necessary truth preservation: some set T of sentences entails a sentence A if and only if it is necessary that A be true whenever each member of T is true 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

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 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, along the lines of algebra; the letters represent logical variables. This is of importance since the validity of an argument is determined solely by its form. The sentence forms which classify. 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 In logic, the corresponding conditional of an argument is a material conditional whose antecedent is the conjunction of the argument's (or derivation's) premises and whose consequent is the argument's conclusion. An argument is valid if and only if its corresponding conditional is a logical truth. It follows that an argument is valid if and only, and an argument form is valid if and only its corresponding conditional is a logical truth Logical truth is one of the most fundamental concepts in logic, and there are different theories on its nature. A logical truth is a statement which is true and remains true under all reinterpretations of its components other than its logical constants. It is a type of analytic statement. 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 An interpretation is an assignment of meaning to the symbols of a language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal. A statement form can be shown to be a logical truth by either (a) showing that it is a tautology In logic, a tautology is a formula which is true in every possible interpretation. The philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921; it had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternate sense today 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 of statements.

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) 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!)

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 deductive fallacy, or logical fallacy, is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion. Thus, a deductive fallacy is a fallacy where deduction goes wrong, and is no longer a logical process.

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

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 Around 1960, Ray Solomonoff founded the theory of universal inductive inference, the theory of prediction based on observations; for example, predicting the next symbol based upon a given series of symbols. Solomonoff's theory attempts to be mathematically rigorous, 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 Inductive reasoning, also known as induction or inductive logic, is a type of reasoning that involves moving from a set of specific facts to a general conclusion. It uses premises from objects that have been examined to establish a conclusion about an object that has not been examined It can also be seen as a form of theory-building, in which's analogue to deductive logic Deductive reasoning, also called Deductive logic, is reasoning which constructs or evaluates deductive arguments. In logic, an argument is deductive when its conclusion is a logical consequence of the premises. Deductive arguments are valid or invalid, never true or false. A deductive argument is valid if and only if the conclusion does follow's "soundness In mathematical logic, a logical system has the soundness property if and only if its inference rules prove only formulas that are valid with respect to its semantics. In most cases, this comes down to its rules having the property of preserving truth, but this is not the case in general. The word derives from the Germanic 'Sund' as in Gesundheit,." Despite its name, mathematical induction 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 the first statement in the infinite sequence of statements is true, and then proving that if any one statement in the infinite sequence of statements is true, then so is the next one is not a form of inductive reasoning. The problem of induction The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge. That is, what is the justification for either: 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 Herbert Lionel Adolphus Hart was an influential legal philosopher of the 20th century. He was Professor of Jurisprudence at Oxford University. He authored The Concept of Law and made major contributions to political philosophy, although he focused on concepts instead of arguments. Stephen Toulmin Stephen Edelston Toulmin was a British philosopher, author, and educator. Influenced by the Austrian born British philosopher Ludwig Wittgenstein, Toulmin devoted his works to the analysis of moral reasoning. Throughout his writings, he sought to develop practical arguments which can be used effectively in evaluating the ethics behind moral issues'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 Defeasible reasoning is a kind of reasoning that is based on reasons that are defeasible, as opposed to the indefeasible reasons of deductive logic. Defeasible reasoning is a particular kind of non-demonstrative reasoning, where the reasoning does not produce a full, complete, or final demonstration of a claim, i.e., where fallibility and.

Argument by analogy

Argument by analogy may be thought of as argument from the particular to particular.^[1] An argument by analogy may use a particular truth in a premise to argue towards a similar particular truth in the conclusion.^[1] For example, if A. Plato was mortal, and B. Plato was just like Socrates, 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.^[2]

Explanations and arguments

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 A proposition is a sentence expressing something true or false. In philosophy, particularly in logic, a proposition is identified ontologically as an idea, concept, or abstraction whose token instances are patterns of symbols, marks, sounds, or strings of words. Propositions are considered to be syntactic entities and also truthbearers is true, it is to show why it is true.

Arguments and explanations largely resemble each other in rhetorical Rhetoric is the art of using language to communicate effectively. It involves three audience appeals: logos, pathos, and ethos, as well as the five canons of rhetoric: invention or discovery, arrangement, style, memory, and delivery. Along with grammar and logic or dialectic, rhetoric is one of the three ancient arts of discourse. From ancient use. This is the cause of much difficulty in thinking critically Critical thinking, in its broadest sense, has been described as "purposeful reflective judgment concerning what to believe or what to do." The list of core critical thinking skills, as identified by Ennis, Swartz, Paul, Halpern, Fisher, Wade, Scriven, Boyd, Chafee, Gittens, Moore, Browne, Parker, White, Keely, Facione an many others about claims A proposition is a sentence expressing something true or false. In philosophy, particularly in logic, a proposition is identified ontologically as an idea, concept, or abstraction whose token instances are patterns of symbols, marks, sounds, or strings of words. Propositions are considered to be syntactic entities and also truthbearers. 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.^[3]

Fallacies and non arguments

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 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

Notes

1. ^ ^{a b} Shaw 1922: p. 74.
2. ^ Shaw 1922: p. 75.
3. ^ Critical Thinking, Parker and Moore

References

• Shaw, Warren Choate (1922). The Art of Debate. Allyn and Bacon. http://books.google.com/books?id=WgtKAAAAIAAJ&pg=PA74&dq=%22argument+by+analogy%22&as_brr=0#PPA74,M1. Retrieved 4 December 2008.
• 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).

External links

• BadArguments.org
• Yerpl | Get your argument on!

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