An argument is a statement or group of statements called
premise
A premise or premiss is a true or false statement that helps form the body of an argument, which logically leads to a true or false conclusion. A premise makes a declarative statement about its subject matter which enables a reader to either agre ...
s intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the
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 premise ...
al, the
dialectical and the
rhetorical 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 premise ...
, an argument is usually expressed not in
natural language 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 sy ...
, 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 inferences that preserve truth from the premises to the conclusion. This logical perspective on argument is relevant for scientific fields such as
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 (includi ...
. 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, ...
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'' b ...
: 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 A transcendental argument is a deductive philosophical argument which takes a manifest feature of experience as granted, and articulates what must be the case so that such experiences are possible.Transcendental-arguments and Scepticism; Answering ...
, the quality of hypotheses in
retroduction
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 century ...
, 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
rhetorical 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
Proto-Indo-European (PIE) is the reconstructed common ancestor of the Indo-European language family. Its proposed features have been derived by linguistic reconstruction from documented Indo-European languages. No direct record of Proto-Indo- ...
''argu-yo-'', suffixed form of ''arg-'' (to shine; white).
Formal and informal
Informal arguments as studied in ''informal logic'', are presented in
ordinary language
Ordinary language philosophy (OLP) is a philosophical methodology that sees traditional philosophical problems as rooted in misunderstandings philosophers develop by distorting or forgetting how words are ordinarily used to convey meaning in ...
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) 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 sy ...
. Informal logic emphasizes the study of
argumentation; formal logic emphasizes
implication and
inference. 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
![Argument terminology used in logic (en)](https://upload.wikimedia.org/wikipedia/commons/a/a4/Argument_terminology_used_in_logic_%28en%29.svg)
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 the
truth
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 belie ...
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
In English common law, fee tail or entail is a form of trust established by deed or settlement which restricts the sale or inheritance of an estate in real property and prevents the property from being sold, devised by will, or otherwise alien ...
by its premises; if its premises are true, the conclusion must be true. An argument is formally valid
if 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 b ...
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
In logic, logical form of a statement is a precisely-specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguou ...
. 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
In reasoning and argument mapping, a counterargument is an objection to an objection. A counterargument can be used to rebut an objection to a premise, a main contention or a lemma. Synonyms of counterargument may include rebuttal, reply, count ...
.
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
In logic, the corresponding conditional of an argument (or derivation) 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 v ...
, and an argument form is valid if and only if its corresponding conditional is a
logical truth
Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement whic ...
. 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 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 (provable) statements.
Types of proof calculi used
There are several types of proof calculi. The mo ...
.
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
Inductive reasoning is a method of reasoning in which a general principle is derived from a body of observations. It consists of making broad generalizations based on specific observations. Inductive reasoning is distinct from ''deductive'' rea ...
, 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 syst ...
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''. Fall ...
).
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 the
military 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 budget ...
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
Induction, Inducible or Inductive may refer to:
Biology and medicine
* Labor induction (birth/pregnancy)
* Induction chemotherapy, in medicine
* Induced stem cells, stem cells derived from somatic, reproductive, pluripotent or other cell t ...
, 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 is a method of reasoning in which a general principle is derived from a body of observations. It consists of making broad generalizations based on specific observations. Inductive reasoning is distinct from ''deductive'' rea ...
'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 formu ...
". 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.
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 re ...
). This type of reasoning is referred to as
defeasible reasoning
In philosophical logic, defeasible reasoning is a kind of reasoning that is rationally compelling, though not deductive reasoning, deductively valid. It usually occurs when a rule is given, but there may be specific exceptions to the rule, or su ...
. 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 scheme
In argumentation theory, an argumentation scheme or argument scheme is a template that represents a common type of argument used in ordinary conversation. Many different argumentation schemes have been identified. Each one has a name (for example, ...
s 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 by
analogy may be thought of as argument from the particular to particular. An argument by analogy may use a particular truth in a premise to argue towards a similar particular truth in the conclusion. For example, if A. Plato was mortal, and B. Socrates was like Plato in other respects, then asserting that C. Socrates was mortal is an example of argument by analogy because the reasoning employed in it proceeds from a particular truth in a premise (Plato was mortal) to a similar particular truth in the conclusion, namely that Socrates was mortal.
Other 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 A transcendental argument is a deductive philosophical argument which takes a manifest feature of experience as granted, and articulates what must be the case so that such experiences are possible.Transcendental-arguments and Scepticism; Answering ...
are made up of a "chain of indispensability claims" that attempt to show why something is necessarily true based on its connection to our experience, while
Nikolas Kompridis
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 ...
has suggested that there are two types of "
fallible
Originally, fallibilism (from Medieval Latin: ''fallibilis'', "liable to err") is the philosophical principle that propositions can be accepted even though they cannot be conclusively proven or justified,Haack, Susan (1979)"Fallibilism and Nece ...
" 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 an ...
). Kompridis said that the French philosopher
Michel Foucault 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 wider
ontological
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 exi ...
or cultural-linguistic understanding—a "world", in a specifically ontological sense—in order to clarify or transform the background of meaning (
tacit knowledge
Tacit knowledge or implicit knowledge—as opposed to formal, codified or explicit knowledge—is knowledge that is difficult to express or extract, and thus more difficult to transfer to others by means of writing it down or verbalizing it. This ...
) 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 in
rhetorical use. This is the cause of much difficulty in
thinking critically about claims. There are several reasons for this difficulty.
* People often are not themselves clear on whether they are arguing for or explaining something.
* The same types of words and phrases are used in presenting explanations and arguments.
* The terms 'explain' or 'explanation,' et cetera are frequently used in arguments.
* Explanations are often used within arguments and presented so as to serve ''as arguments''.
* Likewise, "... arguments are essential to the process of justifying the validity of any explanation as there are often multiple explanations for any given phenomenon."
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, people ...
to help explain user acceptance of
knowledge-based systems
A knowledge-based system (KBS) is a computer program that reasons and uses a knowledge base to solve complex problems. The term is broad and refers to many different kinds of systems. The one common theme that unites all knowledge based systems i ...
. 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 from
natural language text with the aid of computer programs. Such argumentative structures include the premise, conclusions, the
argument scheme
In argumentation theory, an argumentation scheme or argument scheme is a template that represents a common type of argument used in ordinary conversation. Many different argumentation schemes have been identified. Each one has a name (for example, ...
and the relationship between the main and subsidiary argument, or the main and counter-argument within discourse.
See also
*
Abductive reasoning
*
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
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, incl ...
*
Bayes' theorem
*
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
*
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 ...
*
Critical thinking
*
Dialectic
*
Evidence
*
Evidence-based policy
Evidence-based policy is an idea in public policy proposing that policy decisions should be based on, or informed by, rigorously established objective evidence. The implied contrast is with policymaking based on ideology, 'common sense,' anecd ...
*
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
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 formul ...
*
Syllogism
Notes
References
*
*
Robert Audi
Robert N. Audi (born November 1941) is an American philosopher whose major work has focused on epistemology, ethics (especially on ethical intuitionism), rationality and the theory of action. He is O'Brien Professor of Philosophy at the Universi ...
, ''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
John Langshaw Austin (26 March 1911 – 8 February 1960) was a British philosopher of language and leading proponent of ordinary language philosophy, perhaps best known for developing the theory of speech acts.
Austin pointed out that we u ...
'', Oxford University Press, 1976.
* H. P. Grice, ''Logic and Conversation'' in ''The Logic of Grammar'', Dickenson, 1975.
*
Vincent F. Hendricks
Vincent Fella Rune Møller Hendricks (born 6 March 1970) is a Danish philosopher and logician. He holds a doctoral degree (PhD) and a habilitation (dr.phil) in philosophy and is Professor of Formal Philosophy and Director of the Center for Informa ...
, ''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
Yuri Ivanovich Manin (russian: Ю́рий Ива́нович Ма́нин; born 16 February 1937) is a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logi ...
, ''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
Sir Karl Raimund Popper (28 July 1902 – 17 September 1994) was an Austrian-British philosopher, academic and social commentator. One of the 20th century's most influential philosophers of science, Popper is known for his rejection of the c ...
''Objective Knowledge; An Evolutionary Approach'', Oxford: Clarendon Press, 1972.
*
L. S. Stebbing
Lizzie Susan Stebbing (2 December 1885 – 11 September 1943) was a British philosopher. She belonged to the 1930s generation of analytic philosophy, and was a founder in 1933 of the journal ''Analysis.'' Stebbing was the first woman to hold a p ...
, ''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
Douglas Neil Walton (2 June 1942 – 3 January 2020) was a Canadian academic and author, known for his books and papers on argumentation, logical fallacies and informal logic. He was a Distinguished Research Fellow of the Centre for Research in ...
, ''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
Ronald Prescott Loui is an American computer scientist, currently working as a professor of computer science at Case Western Reserve University. He is known for having supplied first-hand biographical information on Barack Obama about his time in H ...
, ''Logical Models of Argument'', ACM Computing Surveys, vol. 32, num. 4, pp. 337–383, 2000.
*
T. Edward Damer. ''
Attacking Faulty Reasoning
''Attacking Faulty Reasoning'' is a textbook on logical fallacies by T. Edward Damer that has been used for many years in a number of college courses on logic, critical thinking, argumentation, and philosophy. It explains 60 of the most commonl ...
'', 5th Edition, Wadsworth, 2005.
* 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).
*
Martin, Brian.
The Controversy Manual' (Sparsnäs, Sweden: Irene Publishing, 2014).
External links
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{{Authority control
Critical thinking skills
Logical consequence
Reasoning