An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the

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. *

Argumentation and the Social Grounds of Knowledge

1982.

The Controversy Manual

' (Sparsnäs, Sweden: Irene Publishing, 2014).

logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premi ...

al, the dialectical and the rhetoric
Rhetoric () is the art of persuasion, which along with grammar and logic (or dialectic), is one of the three ancient arts of discourse. Rhetoric aims to study the techniques writers or speakers utilize to inform, persuade, or motivate par ...

al perspective.
In logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premi ...

, an argument is usually expressed not in natural language
In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation. Natural languages ...

but in a symbolic formal language
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules.
The alphabet of a formal language consists of symb ...

, and it can be defined as any group of proposition
In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...

s of which one is claimed to follow from the others through deductively valid inference
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word ''infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in ...

s that preserve truth from the premises to the conclusion. This logical perspective on argument is relevant for scientific fields such as mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includ ...

. Logic is the study of the forms of reason
Reason is the capacity of consciously applying logic by drawing conclusions from new or existing information, with the aim of seeking the truth. It is closely associated with such characteristically human activities as philosophy, science, lang ...

ing in arguments and the development of standards and criteria to evaluate arguments. Deductive arguments can be valid, and the valid ones can be sound
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by ...

: in a valid argument, premisses necessitate the conclusion, even if one or more of the premises is false and the conclusion is false; in a sound argument, true premises necessitate a true conclusion. Inductive arguments, by contrast, can have different degrees of logical strength: the stronger or more cogent the argument, the greater the probability that the conclusion is true, the weaker the argument, the lesser that probability. 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
Disclosure may refer to:
Arts and media
* ''Disclosure'' (The Gathering album), 2012
*Disclosure (band), a UK-based garage/electronic duo
* ''Disclosure'' (novel), 1994 novel written by Michael Crichton
** ''Disclosure'' (1994 film), an American ...

of new possibilities for thinking and acting.
In dialectics, and also in a more colloquial sense, an argument can be conceived as a social and verbal means of trying to resolve, or at least contend with, a conflict or difference of opinion that has arisen or exists between two or more parties. For the rhetoric
Rhetoric () is the art of persuasion, which along with grammar and logic (or dialectic), is one of the three ancient arts of discourse. Rhetoric aims to study the techniques writers or speakers utilize to inform, persuade, or motivate par ...

al perspective, the argument is constitutively linked with the context, in particular with the time and place in which the argument is located. From this perspective, the argument is evaluated not just by two parties (as in a dialectical approach) but also by an audience. In both dialectic and rhetoric, arguments are used not through a formal but through natural language. Since classical antiquity, philosophers and rhetoricians have developed lists of argument types in which premises and conclusions are connected in informal and defeasible ways.
Etymology

The Latin root ''arguere'' (to make bright, enlighten, make known, prove, etc.) is from Proto-Indo-European ''argu-yo-'', suffixed form of ''arg-'' (to shine; white).Formal and informal

Informal arguments as studied in ''informal logic'', are presented in ordinary language and are intended for everydaydiscourse
Discourse is a generalization of the notion of a conversation to any form of communication. Discourse is a major topic in social theory, with work spanning fields such as sociology, anthropology, continental philosophy, and discourse analysis. F ...

. 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
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules.
The alphabet of a formal language consists of symb ...

. Informal logic emphasizes the study of argumentation
Argumentation theory, or argumentation, is the interdisciplinary study of how conclusions can be supported or undermined by premises through logical reasoning. With historical origins in logic, dialectic, and rhetoric, argumentation theory, includ ...

; formal logic emphasizes implication and inference
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word ''infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in ...

. Informal arguments are sometimes implicit. The rational structure—the relationship of claims, premises, warrants, relations of implication, and conclusion—is not always spelled out and immediately visible and must be made explicit by analysis.
Standard logical account of argument types

There are several kinds of arguments in logic, the best-known of which are "deductive" and "inductive." An argument has one or more premises but only one conclusion. Each premise and the conclusion are truth bearers or "truth-candidates", each capable of being either true or false (but not both). These truth values bear on the terminology used with arguments.Deductive arguments

A ''deductive argument'' asserts that thetruth
Truth is the property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth 2005 In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, ...

of the conclusion is a logical consequence of the premises: if the premises are true, the conclusion must be true. It would be self-contradictory to assert the premises and deny the conclusion, because negation of the conclusion is contradictory to the truth of the premises. Based on the premises, the conclusion follows necessarily (with certainty). Given premises that A=B and B=C, then the conclusion follows necessarily that A=C. Deductive arguments are sometimes referred to as "truth-preserving" arguments. For example, consider the argument that because bats can fly (premise=true), and all flying creatures are birds (premise=false), therefore bats are birds (conclusion=false). If we assume the premises are true, the conclusion follows necessarily, and it is a valid argument.
Validity

Deductive arguments may be either valid or invalid. If valid, it has a conclusion that is entailed by its premises; if its premises are true, the conclusion must be true. An argument is formally validif and only if
In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false.
The connective is bicond ...

the denial of the conclusion is incompatible with accepting all the premises.
The validity of an argument depends not on the actual truth or falsity of its premises and conclusion, but on whether 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 that render it inconclusive: the conclusion of a valid argument with one or more false premises may be true or false.
Logic seeks to discover 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 on its form, an argument can be shown invalid by showing that its form is invalid. This can be done by 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 an 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 if 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, is a necessary truth, it is without regard to the premises.
Some examples:
* ''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. (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.''
In the above second to last case (Some men are hawkers ...), the counter-example follows the same logical form as the previous argument, (Premise 1: "Some ''X'' are ''Y''." Premise 2: "Some ''Y'' are ''Z''." Conclusion: "Some ''X'' are ''Z''.") in order to demonstrate that whatever hawkers may be, they may or may not be rich, in consideration of the premises as such. (See also: Existential import
A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. ...

).
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 In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (; Latin for " tdoes not follow") is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic sy ...

and Informal fallacy
Informal fallacies are a type of incorrect argument in natural language. The source of the error is not just due to the ''form'' of the argument, as is the case for formal fallacies, but can also be due to their ''content'' and ''context''. Fallac ...

).
Soundness

A sound argument is a valid argument whose conclusion follows from its premise(s), and the premise(s) of which is/are true.Inductive arguments

An inductive argument asserts that the truth of the conclusion is supported by the probability of the premises. For example, given that themilitary budget of the United States
The military budget is the largest portion of the discretionary United States federal budget allocated to the Department of Defense, or more broadly, the portion of the budget that goes to any military-related expenditures. The military budg ...

is the largest in the world (premise=true), then it is probable that it will remain so for the next 10 years (conclusion=true). Arguments that involve predictions are inductive since the future is uncertain. An inductive argument is said to be strong or weak. If the premises of an inductive argument are assumed true, is it probable the conclusion is also true? If yes, the argument is strong. If no, it is weak. A strong argument is said to be cogent if it has all true premises. Otherwise, the argument is uncogent. The military budget argument example is a strong, cogent 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 A statistical syllogism (or proportional syllogism or direct inference) is a non-deductive syllogism. It argues, using inductive reasoning, from a generalization true for the most part to a particular case.
Introduction
Statistical syllogisms may ...

, 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
Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if it is impossible for the premises to be true and the conclusion to be fals ...

's "soundness
In logic or, more precisely, deductive reasoning, an argument is sound if it is both valid in form and its premises are true. Soundness also has a related meaning in mathematical logic, wherein logical systems are sound if and only if every form ...

". Despite its name, mathematical induction
Mathematical induction is a method for proving that a statement ''P''(''n'') is true for every natural number ''n'', that is, that the infinitely many cases ''P''(0), ''P''(1), ''P''(2), ''P''(3), ... all hold. Informal metaphors help ...

is not a form of inductive reasoning. The lack of deductive validity is known as the problem of induction
First formulated by David Hume, the problem of induction questions our reasons for believing that the future will resemble the past, or more broadly it questions predictions about unobserved things based on previous observations. This inferen ...

.
Defeasible arguments and argumentation schemes

In 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
A non-monotonic logic is a formal logic whose conclusion relation is not monotonic. In other words, non-monotonic logics are devised to capture and represent defeasible inferences (cf. defeasible reasoning), i.e., a kind of inference in which ...

). This type of reasoning is referred to as defeasible reasoning. For instance we consider the famous Tweety example:
:: Tweety is a bird.
:: Birds generally fly.
:: Therefore, Tweety (probably) flies.
This argument is reasonable and the premises support the conclusion unless additional information indicating that the case is an exception comes in. If Tweety is a penguin, the inference is no longer justified by the premise. Defeasible arguments are based on generalizations that hold only in the majority of cases, but are subject to exceptions and defaults.
In order to represent and assess defeasible reasoning, it is necessary to combine the logical rules (governing the acceptance of a conclusion based on the acceptance of its premises) with rules of material inference, governing how a premise can support a given conclusion (whether it is reasonable or not to draw a specific conclusion from a specific description of a state of affairs).
Argumentation schemes have been developed to describe and assess the acceptability or the fallaciousness of defeasible arguments. Argumentation schemes are stereotypical patterns of inference, combining semantic-ontological relations with types of reasoning and logical axioms and representing the abstract structure of the most common types of natural arguments. A typical example is the argument from expert opinion, shown below, which has two premises and a conclusion.
Each scheme may be associated with a set of critical questions, namely criteria for assessing dialectically the reasonableness and acceptability of an argument. The matching critical questions are the standard ways of casting the argument into doubt.
By analogy

Argument byanalogy
Analogy (from Greek ''analogia'', "proportion", from ''ana-'' "upon, according to" lso "against", "anew"+ ''logos'' "ratio" lso "word, speech, reckoning" is a cognitive process of transferring information or meaning from a particular subject ( ...

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 kinds

Other kinds of arguments may have different or additional standards of validity or justification. For example, philosopher Charles Taylor said 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, whileNikolas Kompridis
Nikolas Kompridis (; born 1953) is a Canadian philosopher and political theorist. His major published work addresses the direction and orientation of Frankfurt School critical theory; the legacy of philosophical romanticism; and the aesthetic d ...

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 (world disclosure World disclosure (german: Erschlossenheit, literally "development, comprehension") refers to how things become intelligible and meaningfully relevant to human beings, by virtue of being part of an ontological ''world'' – i.e., a pre-interpreted a ...

). Kompridis said that the French philosopher Michel Foucault
Paul-Michel Foucault (, ; ; 15 October 192625 June 1984) was a French philosopher, historian of ideas, writer, political activist, and literary critic. Foucault's theories primarily address the relationship between power and knowledge, and how ...

was a prominent advocate of this latter form of philosophical argument.
World-disclosing

World-disclosing arguments are a group of philosophical arguments that according to Nikolas Kompridis employ a disclosive approach, to reveal features of a widerontological
In metaphysics, ontology is the philosophical study of being, as well as related concepts such as existence, becoming, and reality.
Ontology addresses questions like how entities are grouped into categories and which of these entities exis ...

or cultural-linguistic understanding—a "world", in a specifically ontological sense—in order to clarify or transform the background of meaning ( tacit knowledge) and what Kompridis has called the "logical space" on which an argument implicitly depends.
Explanations

While arguments attempt to show that something was, 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 Joe asks Fred, "Why is your cat scratching itself?" the explanation, "... because it has fleas." provides understanding. 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 belief, 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 inrhetoric
Rhetoric () is the art of persuasion, which along with grammar and logic (or dialectic), is one of the three ancient arts of discourse. Rhetoric aims to study the techniques writers or speakers utilize to inform, persuade, or motivate par ...

al 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."
Explanations and arguments are often studied in the field of information systems
An information system (IS) is a formal, sociotechnical, organizational system designed to collect, process, store, and distribute information. From a sociotechnical perspective, information systems are composed by four components: task, peopl ...

to help explain user acceptance of knowledge-based systems. Certain argument types may fit better with personality traits to enhance acceptance by individuals.
Fallacies and non-arguments

Fallacies are types of argument or expressions which are held to be of an invalid form or contain errors in reasoning. One type of fallacy occurs when a word frequently used to indicate a conclusion is used as a transition (conjunctive adverb) between independent clauses. In English the words ''therefore'', ''so'', ''because'' and ''hence'' typically separate the premises from the conclusion of an argument. Thus: ''Socrates is a man, all men are mortal therefore Socrates is mortal'' is an argument because the assertion ''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 or ethymematic arguments

Often an argument is invalid or weak because there is a missing premise—the supply of which would make it valid or strong. This is referred to as an elliptical or enthymematic argument (see also ). Speakers and writers will often leave out a necessary premise in their reasoning 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.'' The missing premise is: ''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.'' The hidden assumptions are: (1) the milkman was not the murderer and (2) the murderer has left (3) by a door and (4) not by e.g. a window or through ''an 'ole in 't roof'' and (5) there are no other doors than the front or back door.Argument mining

The goal of argument mining is the automatic extraction and identification of argumentative structures fromnatural language
In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation. Natural languages ...

text with the aid of computer programs. Such argumentative structures include the premise, conclusions, the argument scheme and the relationship between the main and subsidiary argument, or the main and counter-argument within discourse.
See also

*Abductive reasoning
Abductive reasoning (also called abduction,For example: abductive inference, or retroduction) is a form of logical inference formulated and advanced by American philosopher Charles Sanders Peirce beginning in the last third of the 19th centu ...

* Argument map
An argument map or argument diagram is a visual representation of the structure of an argument. An argument map typically includes the key components of the argument, traditionally called the '' conclusion'' and the ''premises'', also called ''con ...

* Argumentation theory
* Bayes' theorem
In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For examp ...

* Belief bias
Belief bias is the tendency to judge the strength of arguments based on the plausibility of their conclusion rather than how strongly they support that conclusion. A person is more likely to accept an argument that supports a conclusion that alig ...

* Boolean logic
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in e ...

* Cosmological argument
A cosmological argument, in natural theology, is an argument which claims that the existence of God can be inferred from facts concerning causation, explanation, change, motion, contingency, dependency, or finitude with respect to the universe o ...

* Critical thinking
Critical thinking is the analysis of available facts, evidence, observations, and arguments to form a judgement. The subject is complex; several different definitions exist, which generally include the rational, skeptical, and unbiased analysis ...

* Dialectic
* Evidence
Evidence for a proposition is what supports this proposition. It is usually understood as an indication that the supported proposition is true. What role evidence plays and how it is conceived varies from field to field.
In epistemology, eviden ...

* Evidence-based policy
* Inquiry
* Logical reasoning
Two kinds of logical reasoning are often distinguished in addition to formal deduction: induction and abduction. Given a precondition or ''premise'', a conclusion or ''logical consequence'' and a rule or ''material conditional'' that implies the ...

* Practical arguments
* Proof (truth)
* Soundness theorem
* Syllogism
Notes

References

* * 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, * 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
Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...

, ''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 N. 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.
* Charles Arthur Willard, A Theory of Argumentation. 1989.
* Charles Arthur WillardArgumentation 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). * Martin, Brian.The Controversy Manual

' (Sparsnäs, Sweden: Irene Publishing, 2014).

External links

* * * * {{Authority control Critical thinking skills Logical consequence Reasoning