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Argument
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Attempt to persuade or to determine the truth of a conclusion
This article is about the subject as it is studied in logic and
philosophy. For other uses, see Argument (disambiguation).
An argument is a statement or group of statements called premises
intended to determine the degree of truth or acceptability of another
statement called a conclusion.^[1]^[2] Arguments can be studied from
three main perspectives: the logical, the dialectical and the
rhetorical perspective.^[3]
In logic, an argument is usually expressed not in natural language but
in a symbolic formal language, and it can be defined as any group of
propositions 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. Logic is
the study of the forms of reasoning in arguments and the development of
standards and criteria to evaluate arguments.^[4] Deductive arguments
can be valid, and the valid ones can be sound: 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.^[5] 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,^[6] the quality of hypotheses in
retroduction, or even the disclosure of new possibilities for thinking
and acting.^[7]
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.^[8] 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.^[9] 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.^[10]
[ ]
Contents
* 1 Etymology
* 2 Formal and informal
* 3 Standard logical account of argument types
+ 3.1 Deductive arguments
o 3.1.1 Validity
o 3.1.2 Soundness
+ 3.2 Inductive arguments
* 4 Defeasible arguments and argumentation schemes
* 5 By analogy
* 6 Other kinds
+ 6.1 World-disclosing
* 7 Explanations
* 8 Fallacies and non-arguments
* 9 Elliptical or ethymematic arguments
* 10 Argument mining
* 11 See also
* 12 Notes
* 13 References
* 14 Further reading
* 15 External links
Etymology[edit]
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).^[11]
Formal and informal[edit]
Further information: Informal logic and Formal logic
Informal arguments as studied in informal logic, are presented in
ordinary language and are intended for everyday discourse. Formal
arguments are studied in formal logic (historically called symbolic
logic, more commonly referred to as mathematical logic today) and are
expressed in a formal language. 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[edit]
Argument terminology
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[edit]
Main article: Deductive argument
A deductive argument asserts that the truth 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[edit]
Main article: Validity (logic)
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 valid if and only
if 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).
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 and Informal fallacy).
Soundness[edit]
Main article: 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[edit]
Main article: Inductive reasoning
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 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, 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's "soundness". Despite its name, mathematical induction
is not a form of inductive reasoning. The lack of deductive validity is
known as the problem of induction.
Defeasible arguments and argumentation schemes[edit]
Main article: Argumentation scheme
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). 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.^[12] A typical example is the
argument from expert opinion, shown below, which has two premises and a
conclusion.^[13]
CAPTION: Argument from expert opinion
Major Premise: Source E is an expert in subject domain S containing
proposition A.
Minor Premise: E asserts that proposition A is true (false).
Conclusion: A is true (false).
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[edit]
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[edit]
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,^[14] while
Nikolas Kompridis 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).^[15]
Kompridis said that the French philosopher Michel Foucault was a
prominent advocate of this latter form of philosophical argument.^[16]
World-disclosing[edit]
Main article: World disclosure
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 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.^[17]
Explanations[edit]
Main article: Explanation
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.^[18]
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.^[19]
* Likewise, "... arguments are essential to the process of justifying
the validity of any explanation as there are often multiple
explanations for any given phenomenon."^[18]
Explanations and arguments are often studied in the field of
information systems to help explain user acceptance of knowledge-based
systems. Certain argument types may fit better with personality traits
to enhance acceptance by individuals.^[20]
Fallacies and non-arguments[edit]
Main article: Fallacy
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[edit]
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
Enthymeme S: Syllogism with an unstated premise). 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[edit]
Main article: 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.^[21] 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.^[22]^[23]
See also[edit]
Philosophy portal
* Abductive reasoning
* Argument map
* Argumentation theory
* Bayes' theorem
* Belief bias
* Boolean logic
* Cosmological argument
* Critical thinking
* Dialectic
* Evidence
* Evidence-based policy
* Inquiry
* Logical reasoning
* Practical arguments
* Proof (truth)
* Soundness theorem
* Syllogism
Notes[edit]
1. ^ Ralph H. Johnson, Manifest Rationality: A pragmatic theory of
argument (New Jersey: Laurence Erlbaum, 2000), 46-49.
2. ^ This is called "argument-as-product", distinguished from
"argument-as-process" and "argument-as-procedure." Wenzel, J. W.
(1987). The rhetorical perspective on argument. In F. H. van
Eemeren, R. Grootendorst, J. A. Blair, & C. A. Willard (Eds.),
Argumentation. Across the lines of discipline. Proceedings of the
conference on argumentation 1986 (pp. 101-109).
Dordrecht-Providence: Foris.
3. ^ Wagemans, Jean H. M. (2 December 2021), Stalmaszczyk, Piotr
(ed.), "The Philosophy of Argument", The Cambridge Handbook of the
Philosophy of Language (1 ed.), Cambridge University Press,
pp. 571-589, doi:10.1017/9781108698283.032, ISBN 978-1-108-69828-3,
S2CID 244088211, retrieved 2 May 2022
4. ^ Copi, Irving M.; Cohen, Carl; McMahon, Kenneth (9 September
2016). Introduction to Logic. doi:10.4324/9781315510897.
ISBN 9781315510880.
5. ^ "Deductive and Inductive Arguments", Internet Encyclopedia of
Philosophy.
6. ^ Charles Taylor, "The Validity of Transcendental Arguments",
Philosophical Arguments (Harvard, 1995), 20-33. "[Transcendental]
arguments consist of a string of what one could call
indispensability claims. They move from their starting points to
their conclusions by showing that the condition stated in the
conclusion is indispensable to the feature identified at the
start ... Thus we could spell out Kant's transcendental deduction
in the first edition in three stages: experience must have an
object, that is, be of something; for this it must be coherent; and
to be coherent it must be shaped by the understanding through the
categories."
7. ^ Kompridis, Nikolas (2006). "World Disclosing Arguments?".
Critique and Disclosure. Cambridge: MIT Press. pp. 116-124.
ISBN 0262277425.
8. ^ Walton, Douglas N. (August 1990). "What is Reasoning? What Is an
Argument?". The Journal of Philosophy. 87 (8): 399-419.
doi:10.2307/2026735. JSTOR 2026735.^[permanent dead link]
9. ^ van Eemeren, Frans H.; Garssen, Bart; Krabbe, Erik C. W.; Snoeck
Henkemans, A. Francisca; Verheij, Bart; Wagemans, Jean H. M.
(2021), van Eemeren, Frans H.; Garssen, Bart; Verheij, Bart;
Krabbe, Erik C. W. (eds.), "Informal Logic", Handbook of
Argumentation Theory, Dordrecht: Springer Netherlands, pp. 1-45,
doi:10.1007/978-94-007-6883-3_7-1, ISBN 978-94-007-6883-3,
retrieved 2 May 2022
10. ^ Wagemans, Jean H.M. (2016). "Constructing a Periodic Table of
Arguments". SSRN Electronic Journal. doi:10.2139/ssrn.2769833.
ISSN 1556-5068.
11. ^ Harper, Douglas. "Argue". Online Etymology Dictionary.
MaoningTech. Retrieved 15 June 2018.
12. ^ Macagno, Fabrizio; Walton, Douglas (2015). "Classifying the
patterns of natural arguments". Philosophy & Rhetoric. 48 (1):
26-53. doi:10.5325/philrhet.48.1.0026.
13. ^ Walton, Douglas; Reed, Chris; Macagno, Fabrizio (2008).
Argumentation Schemes. New York: Cambridge University Press.
p. 310.
14. ^ Charles Taylor, "The Validity of Transcendental Arguments",
Philosophical Arguments (Harvard, 1995), 20-33.
15. ^ Nikolas Kompridis, "Two Kinds of Fallibilism", Critique and
Disclosure (Cambridge: MIT Press, 2006), 180-183.
16. ^ Nikolas Kompridis, "Disclosure as (Intimate) Critique", Critique
and Disclosure (Cambridge: MIT Press, 2006), 254. In addition,
Foucault said of his own approach that "My role ... is to show
people that they are much freer than they feel, that people accept
as truth, as evidence, some themes which have been built up at a
certain moment during history, and that this so-called evidence can
be criticized and destroyed." He also wrote that he was engaged in
"the process of putting historico-critical reflection to the test
of concrete practices ... I continue to think that this task
requires work on our limits, that is, a patient labor giving form
to our impatience for liberty." (emphasis added) Hubert Dreyfus,
"Being and Power: Heidegger and Foucault" and Michel Foucault,
"What is Enlightenment?"
17. ^ Nikolas Kompridis, "World Disclosing Arguments?" in Critique and
Disclosure, Cambridge: MIT Press (2006), 118-121.
18. ^ ^a ^b Osborne, Jonathan F.; Patterson, Alexis (23 May 2011).
"Scientific argument and explanation: A necessary distinction?".
Science Education. Wiley Online Library. 95 (4): 627-638.
Bibcode:2011SciEd..95..627O. doi:10.1002/sce.20438.
19. ^ Critical Thinking, Parker and Moore
20. ^ Justin Scott Giboney, Susan Brown, and Jay F. Nunamaker Jr.
(2012). "User Acceptance of Knowledge-Based System Recommendations:
Explanations, Arguments, and Fit" 45th Annual Hawaii International
Conference on System Sciences, Hawaii, January 5-8.
21. ^ Lippi, Marco; Torroni, Paolo (20 April 2016). "Argumentation
Mining: State of the Art and Emerging Trends". ACM Transactions on
Internet Technology. 16 (2): 1-25. doi:10.1145/2850417.
hdl:11585/523460. ISSN 1533-5399. S2CID 9561587.
22. ^ "Argument Mining - IJCAI2016 Tutorial". www.i3s.unice.fr.
Archived from the original on 18 April 2021. Retrieved 9 March
2021.
23. ^ "NLP Approaches to Computational Argumentation - ACL 2016,
Berlin". Retrieved 9 March 2021.
References[edit]
*
Shaw, Warren Choate (1922). The Art of Debate. Allyn and Bacon. p. 74.
"argument by analogy."
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 Poincare, 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 Chesnevar, 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[edit]
* 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 (Sparsnaes, Sweden: Irene
Publishing, 2014).
External links[edit]
Wikimedia Commons has media related to Arguments.
* Argument at PhilPapers
* Argument at the Indiana Philosophy Ontology Project
*
Dutilh Novaes, Catarina. "Argument and Argumentation". In Zalta, Edward
N. (ed.). Stanford Encyclopedia of Philosophy.
McKeon, Matthew. "Argument". Internet Encyclopedia of Philosophy.
* v
* t
* e
Fallacies (list)
Formal
In propositional logic
* Affirming a disjunct
* Affirming the consequent
* Denying the antecedent
* Argument from fallacy
* Masked man
* Mathematical fallacy
In quantificational logic
* Existential
* Illicit conversion
* Proof by example
* Quantifier shift
Syllogistic fallacy
* Affirmative conclusion from a negative premise
* Negative conclusion from affirmative premises
* Exclusive premises
* Existential
* Necessity
* Four terms
* Illicit major
* Illicit minor
* Undistributed middle
Informal
Equivocation
* Equivocation
* False equivalence
* False attribution
* Quoting out of context
* Loki's Wager
* No true Scotsman
* Reification
Question-begging
* Circular reasoning / Begging the question
* Loaded language
+ Leading question
* Compound question / Loaded question / Complex question
* No true Scotsman
Correlative-based
* False dilemma
+ Perfect solution
* Denying the correlative
* Suppressed correlative
Illicit transference
* Composition
* Division
* Ecological
Secundum quid
* Accident
* Converse accident
Faulty generalization
* Anecdotal evidence
* Sampling bias
+ Cherry picking
+ McNamara
* Base rate / Conjunction
* Double counting
* False analogy
* Slothful induction
* Overwhelming exception
Ambiguity
* Accent
* False precision
* Moving the goalposts
* Quoting out of context
* Slippery slope
* Sorites paradox
* Syntactic ambiguity
Questionable cause
* Animistic
+ Furtive
* Correlation implies causation
+ Cum hoc
+ Post hoc
* Gambler's
+ Inverse
* Regression
* Single cause
* Slippery slope
* Texas sharpshooter
Appeals
* Law/Legality
* Stone / Proof by assertion
Consequences
* Argumentum ad baculum
* Wishful thinking
Emotion
* Children
* Fear
* Flattery
* Novelty
* Pity
* Ridicule
* In-group favoritism
* Invented here / Not invented here
* Island mentality
* Loyalty
* Parade of horribles
* Spite
* Stirring symbols
* Wisdom of repugnance
Genetic /
Gene based
Ad hominem
* Appeal to motive
* Association
+ Reductio ad Hitlerum
o Godwin's law
+ Reductio ad Stalinum
* Bulverism
* Poisoning the well
* Tone
* Tu quoque
* Whataboutism
* Authority
+ Accomplishment
+ Ipse dixit
+ Poverty / Wealth
* Etymology
* Nature
* Tradition / Novelty
+ Chronological snobbery
Other fallacies
of relevance
Arguments
* Ad nauseam
+ Sealioning
* Argument from anecdote
* Argument from silence
* Argument to moderation
* Argumentum ad populum
* Cliche
* I'm entitled to my opinion
* Ignoratio elenchi
* Invincible ignorance
* Moralistic / Naturalistic
* Motte-and-bailey fallacy
* Rationalization
* Red herring
+ Two wrongs make a right
* Special pleading
* Straw man
Category
* v
* t
* e
Mathematical logic
General
* Axiom
+ list
* Cardinality
* First-order logic
* Formal proof
* Formal semantics
* Foundations of mathematics
* Information theory
* Logical consequence
* Model
* Set
* Theorem
* Theory
* Type theory
Theorems (list)
& Paradoxes
* Goedel's completeness and incompleteness theorems
* Tarski's undefinability
* Banach-Tarski paradox
* Cantor's theorem, paradox and diagonal argument
* Compactness
* Halting problem
* Lindstroem's
* Loewenheim-Skolem
* Russell's paradox
Logics
Traditional
* Classical logic
* Logical truth
* Tautology
* Proposition
* Inference
* Logical equivalence
* Consistency
+ Equiconsistency
* Argument
* Soundness
* Validity
* Syllogism
* Square of opposition
* Venn diagram
Propositional
* Boolean algebra
* Boolean functions
* Logical connectives
* Propositional calculus
* Propositional formula
* Truth tables
* Many-valued logic
+ 3
+ Finite
+ infty
Predicate
* First-order
* Second-order
+ Monadic
* Higher-order
* Free
* Quantifiers
* Predicate
* Monadic predicate calculus
Set theory
* Set
+ Hereditary
* Class
* (Ur-)Element
* Ordered pair
* Ordinal number
* Subset
* Equality
* Extensionality
* Forcing
* Relation
+ Equivalence
+ Partition
* Set operations:
+ Intersection
+ Union
+ Complement
+ Cartesian product
+ Power set
+ Identities
Types of Sets
* Countable
* Uncountable
* Empty
* Inhabited
* Singleton
* Finite
* Infinite
* Transitive
* Ultrafilter
* Recursive
* Fuzzy
* Universal
* Universe
+ Constructible
+ Grothendieck
+ Von Neumann
Maps & Cardinality
* Function/Map
+ Domain
+ Codomain
+ Image
* In/Sur/Bi-jection
* Schroeder-Bernstein theorem
* Isomorphism
* Goedel numbering
* Enumeration
* Large cardinal
+ Inaccessible
* Aleph number
* Operation
+ Binary
Set theories
* Zermelo-Fraenkel
+ Axiom of choice
+ Continuum hypothesis
* General
* Kripke-Platek
* Morse-Kelley
* Naive
* New Foundations
* Tarski-Grothendieck
* Von Neumann-Bernays-Goedel
* Constructive
Syntax & Language
* Alphabet
* Arity
* Automata
* Axiom schema
* Expression
+ Ground
* Extension
+ by definition
+ Conservative
* Relation
* Formal
+ Grammar
+ Language
+ Proof
+ System
+ Theory
* Formation rule
* Formula
+ Atomic
+ Closed
+ Ground
+ Open
* Free/bound variable
* Metalanguage
* Logical connective
+ NOT
+ OR
+ AND
+ ->
+ <->
+ =
* Predicate
+ Functional
+ Variable
+ Propositional variable
* Quantifier
+ TE
+ !
+ FA
+ rank
* Sentence
+ Atomic
+ Spectrum
* Signature
* String
* Substitution
* Symbol
+ Function
+ Logical/Constant
+ Non-logical
+ Variable
* Term
Example axiomatic
systems (list)
* of arithmetic:
+ Peano
+ second-order
+ elementary function
+ primitive recursive
+ Robinson
+ Skolem
* of the real numbers
+ Tarski's axiomatization
* of Boolean algebras
+ canonical
+ minimal axioms
* of geometry:
+ Euclidean
+ Elements
+ Hilbert's
+ non-Euclidean
+ Tarski's
* Principia Mathematica
Proof theory
* Formal proof
* Natural deduction
* Logical consequence
* Rule of inference
* Sequent calculus
* Theorem
* Systems
+ Formal
+ Axiomatic
+ Deductive
+ Hilbert
o list
* Complete theory
* Independence (from ZFC)
* Proof of impossibility
* Ordinal analysis
* Reverse mathematics
* Self-verifying theories
Model theory
* Interpretation
* Model
+ Equivalence
+ Finite
+ Saturated
+ Spectrum
+ Substructure
* Non-standard model
+ of arithmetic
* Diagram
+ Elementary
* Categorical theory
* Model complete theory
* Satisfiability
* Semantics of logic
* Strength
* Theories of truth
+ Semantic
+ Tarski's
+ Kripke's
* T-schema
* Transfer principle
* Truth predicate
* Truth value
* Type
* Ultraproduct
* Validity
Computability theory
* Church encoding
* Church-Turing thesis
* Computably enumerable
* Computable function
* Computable set
* Decision problem
+ Decidable
+ Undecidable
+ P
+ NP
+ P versus NP problem
* Kolmogorov complexity
* Lambda calculus
* Primitive recursive function
* Recursion
* Recursive set
* Turing machine
* Type theory
Related
* Abstract logic
* Category theory
* Concrete/Abstract Category
* Category of sets
* History of logic
* History of mathematical logic
+ timeline
* Logicism
* Mathematical object
* Philosophy of mathematics
* Supertask
icon Mathematics portal
* v
* t
* e
Philosophical logic
Critical thinking and
informal logic
* Analysis
* Ambiguity
* Argument
* Belief
* Bias
* Credibility
* Evidence
* Explanation
* Explanatory power
* Fact
* Fallacy
+ List of fallacies
* Inquiry
* Opinion
* Parsimony (Occam's razor)
* Premise
* Propaganda
* Prudence
* Reasoning
* Relevance
* Rhetoric
* Rigor
* Vagueness
Theories of deduction
* Constructivism
* Dialetheism
* Fictionalism
* Finitism
* Formalism
* Intuitionism
* Logical atomism
* Logicism
* Nominalism
* Platonic realism
* Pragmatism
* Realism
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