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An argument in logic is a set of one or more meaningful declarative sentences (or "propositions") known as the premises along with another sentence known as the conclusion. Some authors refer to the premises and conclusion using the terms declarative sentence, statement, proposition, sentence, or even indicative utterance. The reason for the variety is concern about the ontological significance of the terms, proposition in particular.

There are several kinds of arguments, the best-known of which are "deductive" and "inductive." A deductive argument asserts that the truth of the conclusion is a logical consequence of the premises. An inductive argument, on the other hand, asserts that the truth of the conclusion is supported by the premises. Each premise and the conclusion are truth bearers or "truth-candidates", capable of being either true or false (and not both). While statements in a logical argument are referred to as being either true or false, arguments are referred to as being valid or invalid (see logical truth). A deductive argument is valid if and only if the truth of the conclusion is a logical consequence of the premises, and its corresponding conditional is therefore a necessary truth. A sound argument is a valid argument with true premises.

Other kinds of arguments may have different or additional standards of success or validity. For example, Charles Taylor writes that 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,^[1] 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 (see reflective disclosure).^[2] The late French philosopher Michel Foucault is said to have been a prominent advocate of this latter form of philosophical argument.^[3]

Formal and informal arguments

Informal arguments are studied in informal logic, are presented in ordinary language and are intended for everyday discourse. Conversely, formal arguments are studied in formal logic (historically called symbolic logic, more commonly referred to as mathematical logic today) and are expressed in a formal language. Informal logic may be said to emphasize the study of argumentation, whereas formal logic emphasizes implication and inference. Informal arguments are sometimes implicit. That is, the logical structure –the relationship of claims, premises, warrants, relations of implication, and conclusion –is not always spelled out and immediately visible and must sometimes be made explicit by analysis.

Deductive arguments

A deductive argument is one which, if valid, has a conclusion that is entailed by its premises. In other words, the truth of the conclusion is a logical consequence of the premises—if the premises are true, then the conclusion must be true. It would be self-contradictory to assert the premises and deny the conclusion, because the negation of the conclusion is contradictory to the truth of the premises.

Validity

Deductive arguments may be either valid or invalid. If an argument is valid, and its premises are true, the conclusion must be true: a valid argument cannot have true premises and a false conclusion.

The validity of an argument depends, however, not on the actual truth or falsity of its premises and conclusions, but solely on whether or not the argument has a valid logical form. The validity of an argument is not a guarantee of the truth of its conclusion. A valid argument may have false premises and a false conclusion.

Logic seeks to discover the valid forms, the forms that make arguments valid arguments. An argument form is valid if and only if all arguments of that form are valid. Since the validity of an argument depends on its form, an argument can be shown to be invalid by showing that its form is invalid, and this can be done by giving another argument of the same form that has true premises but a false conclusion. In informal logic this is called a counter argument.

The form of argument can be shown by the use of symbols. For each argument form, there is a corresponding statement form, called a corresponding conditional, and an argument form is valid if and only its corresponding conditional is a logical truth. 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 we might say that the conclusion necessarily follows from the premises, or follows of logical necessity. The conclusion of a valid argument is not necessarily true, it depends on whether the premises are true. The conclusion of a valid argument need not be a necessary truth: if it were so, it would be so independently of the premises.

For example:

Some Greeks are logicians; therefore, some logicians are Greeks. Valid argument; it would be self-contradictory to admit that some Greeks are logicians but deny that some (any) logicians are Greeks.

All Greeks are human and all humans are mortal; therefore, all Greeks are mortal. : Valid argument; if the premises are true the conclusion must be true.

Some Greeks are logicians and some logicians are tiresome; therefore, some Greeks are tiresome. Invalid argument: the tiresome logicians might all be Romans (for example).

Either we are all doomed or we are all saved; we are not all saved; therefore, we are all doomed. Valid argument; the premises entail the conclusion. (Remember that this does not mean the conclusion has to be true; it is only true if the premises are true, which they may not be!)

Arguments can be invalid for a variety of reasons. There are well-established patterns of reasoning that render arguments that follow them invalid; these patterns are known as logical fallacies.

Soundness

A sound argument is a valid argument with true premises. A sound argument, being both valid and having true premises, must have a true conclusion. Some authors (especially in earlier literature) use the term sound as synonymous with valid.

Inductive arguments

Non-deductive logic is reasoning using arguments in which the premises support the conclusion but do not entail it. Forms of non-deductive logic include the statistical syllogism, which argues from generalizations true for the most part, and induction, 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 problem of induction is the philosophical question of whether inductive reasoning is valid.

Defeasible arguments

An argument is defeasible when additional information (such as new counterreasons) can have the effect that it no longer justifies its conclusion. The term "defeasibility" goes back to the legal theorist H.L.A. Hart, although he focused on concepts instead of arguments. Stephen Toulmin's influential argument model includes the possibility of counterreasons that is characteristic of defeasible arguments, but he did not discuss the evaluation of defeasible arguments. Defeasible arguments give rise to defeasible reasoning.

Argument by analogy

Argument by analogy may be thought of as argument from the particular to particular.^[4] An argument by analogy may use a particular truth in a premise to argue towards a similar particular truth in the conclusion.^[4] 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.^[5]

Transitional arguments

In epistemology, transitional arguments attempt to show that a particular explanation is better than another because it is able to make sense of a transition from old to new. That is, if explanation b can account for the problems that existed with explanation a, but not vice versa, then b is regarded to be the more reasonable explanation. A common example in the history of science is the transition from pre-Galilean to Galilean understandings of physical motion.^[6]

Explanations and arguments

While arguments attempt to show that something is, will be, or should be the case, explanations try to show why or how something is or will be. If Fred and Joe address the issue of whether or not Fred's cat has fleas, Joe may state: "Fred, your cat has fleas. Observe the cat is scratching right now." Joe has made an argument that the cat has fleas. However, if Fred and Joe agree on the fact that the cat has fleas, they may further question why this is so and put forth an explanation: "The reason the cat has fleas is that the weather has been damp." The difference is that the attempt is not to settle whether or not some claim is true, it is to show why it is true.

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.^[7]

Fallacies and non arguments

A fallacy is an invalid argument that appears valid, or a valid argument with disguised assumptions. First the premises and the conclusion must be statements, capable of being true and false. Secondly it must be asserted that the conclusion follows from the premises. In English the words therefore, so, because and hence typically separate the premises from the conclusion of an argument, but this is not necessarily so. Thus: Socrates is a man, all men are mortal therefore Socrates is mortal is clearly an argument (a valid one at that), because it is clear it is asserted that Socrates is mortal follows from the preceding statements. However I was thirsty and therefore I drank is NOT an argument, despite its appearance. It is not being claimed that I drank is logically entailed by I was thirsty. The therefore in this sentence indicates for that reason not it follows that.

Elliptical arguments

Often an argument is invalid because there is a missing premise the supply of which would make it valid. Speakers and writers will often leave out a strictly necessary premise in their reasonings if it is widely accepted and the writer does not wish to state the blindingly obvious. Example: All metals expand when heated, therefore iron will expand when heated. (Missing premise: iron is a metal). On the other hand a seemingly valid argument may be found to lack a premise – a ‘hidden assumption’ – which if highlighted can show a fault in reasoning. Example: A witness reasoned: Nobody came out the front door except the milkman therefore the murderer must have left by the back door. (Hidden assumption- the milkman was not the murderer).

Notes

^ Charles Taylor, "The Validity of Transcendental Arguments", Philosophical Arguments (Harvard, 1995), 20-33.
^ Nikolas Kompridis, "Two Kinds of Fallibilism", Critique and Disclosure (Cambridge: MIT Press, 2006), 180-183.
^ 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?"
^ ^a ^b Shaw 1922: p. 74.
^ Shaw 1922: p. 75.
^ Charles Taylor, "Explanation and Practical Reasoning", Philosophical Arguments, 34-60.
^ Critical Thinking, Parker and Moore

References

Shaw, Warren Choate (1922). The Art of Debate. Allyn and Bacon. Retrieved 4 December 2008.
Robert Audi, Epistemology, Routledge, 1998. Particularly relevant is Chapter 6, which explores the relationship between knowledge, inference and argument.
J. L. Austin How to Do Things With Words, Oxford University Press, 1976.
H. P. Grice, Logic and Conversation in The Logic of Grammar, Dickenson, 1975.
Vincent F. Hendricks, Thought 2 Talk: A Crash Course in Reflection and Expression, New York: Automatic Press / VIP, 2005, ISBN 87-991013-7-8
R. A. DeMillo, R. J. Lipton and A. J. Perlis, Social Processes and Proofs of Theorems and Programs, Communications of the ACM, Vol. 22, No. 5, 1979. A classic article on the social process of acceptance of proofs in mathematics.
Yu. Manin, A Course in Mathematical Logic, Springer Verlag, 1977. A mathematical view of logic. This book is different from most books on mathematical logic in that it emphasizes the mathematics of logic, as opposed to the formal structure of logic.
Ch. Perelman and L. Olbrechts-Tyteca, The New Rhetoric, Notre Dame, 1970. This classic was originally published in French in 1958.
Henri Poincaré, Science and Hypothesis, Dover Publications, 1952
Frans van Eemeren and Rob Grootendorst, Speech Acts in Argumentative Discussions, Foris Publications, 1984.
K. R. Popper Objective Knowledge; An Evolutionary Approach, Oxford: Clarendon Press, 1972.
L. S. Stebbing, A Modern Introduction to Logic, Methuen and Co., 1948. An account of logic that covers the classic topics of logic and argument while carefully considering modern developments in logic.
Douglas Walton, Informal Logic: A Handbook for Critical Argumentation, Cambridge, 1998
Carlos Chesñevar, Ana Maguitman and Ronald Loui, Logical Models of Argument, ACM Computing Surveys, vol. 32, num. 4, pp. 337–383, 2000.
T. Edward Damer. Attacking Faulty Reasoning, 5th Edition, Wadsworth, 2005. ISBN 0-534-60516-8
Charles Arthur Willard, A Theory of Argumentation. 1989.
Charles Arthur Willard, Argumentation and the Social Grounds of Knowledge. 1982.

@@ Line 59: / Line 59: @@
 In [[epistemology]], transitional arguments attempt to show that a particular explanation is better than another because it is able to make sense of a transition from old to new. That is, if explanation ''b'' can account for the problems that existed with explanation ''a'', but not vice versa, then ''b'' is regarded to be the more reasonable explanation. A common example in the history of science is the transition from pre-Galilean to Galilean understandings of [[Motion_(physics)|physical motion]].<ref>Charles Taylor, "Explanation and Practical Reasoning", ''Philosophical Arguments'', 34-60.</ref>
-== "World-disclosing" arguments ==
-{{See|World disclosure|Reflective disclosure}}
-World-disclosing arguments are a group of philosophical arguments with a distinctive form, sometimes called a "style of reasoning",<ref>Ian Hacking, ''Styles of Scientific Reasoning'', John Rajchman and Cornel West, eds., ''Post-analytic Philosophy'' (New York:Columbia University Press, 1985), pp.145-65.</ref> that start with a [[world disclosure|disclosive approach]] instead of, or in addition to methods that are deductive, inductive, etc.<ref>"[D]eductive, inductive, or abductive [logic does] not count as a style of reasoning. This is as it should be… People everywhere make inductions, draw inferences to the best explanation, make deductions; those are not peculiarly scientific styles of thinking." Ian Hacking, ''Historical Ontology'' (Harvard, 2002), 90.</ref> Disclosive forms of argument attempt to reveal features of a wider [[ontology|ontological]] or cultural-linguistic understanding, in order to clarify or transform the background of meaning<ref>"[T]hrough a clarification of the conditions of intentionality, we come to a better understanding of what we are as knowing agents – and hence also as language beings – and thereby gain insight into some of the crucial anthropological questions that underpin our moral and spiritual beliefs… What reflection in this direction would entail is already fairly well known. It involves… our being able to articulate the background of our lives perspicuously." Charles Taylor, ''Philosophical Arguments" (Harvard, 1995), 14-15.</ref> and "logical space" on which an argument implicitly depends.<ref>"[World disclosing] arguments cannot assume that the logical space necessary to rendering visible the inferential relations between the premises and the conclusions ''already'' exists; rather, their success depends on the degree to which they can expand existing logical space in order to make room for the conclusions to which they lead." Nikolas Kompridis, "World Disclosing ''Arguments''?" in ''Critique and Disclosure'' (MIT Press, 2006), 119."</ref> A major example of this type of argument is said to be that of [[immanent critique]], although it is not the only kind.<ref>We can use the word "disclosure" for this, following Heidegger. And along with this goes a conception of critical reasoning… of which "immanent critique" is only the best-known example." Charles Taylor, ''Philosophical Arguments'' (Harvard, 1995), 15.</ref><ref>"[Immanent] critique and reflective disclosure are practically indistinguishable, and that is because they are structurally homologous." Nikolas Kompridis, ''Critique and Disclosure'' (MIT Press, 2006), 254-255.</ref>
-The concept of disclosure is associated with the American pragmatist philosopher [[John Dewey]] and the 20th century German philosopher [[Martin Heidegger]].<ref>Nikolas Kompridis, "On World Disclosure: Heidegger, Habermas and Dewey," Thesis Eleven, Vol. 37, No. 1, 29-45 (1994).</ref> Another thinker closely associated with this idea, [[Ludwig Wittgenstein]] famously wrote that:
-<blockquote> All testing, all confirmation and disconfirmation of a hypothesis takes place already within a system. And this system is not a more or less arbitrary and doubtful point of departure for all our arguments: no, it belongs to the essence of what we call an argument… as the element in which arguments have their life.‬‎<ref>Ludwig Wittgenstein, ''On Certainty'' (Oxford: Blackwell, 1975), 107.</ref></blockquote>
-In deductive arguments, the "test" of the argument's success is its [[validity]] and [[soundness]]. However, in a disclosive argument, the primary criterion for success is the solution of some previously unresolvable problem, e.g., an [[epistemological]] crisis (see [[Paradigm shift]]). Its form (the "element in which arguments have their life"), while not arbitrary, is open-ended — said to be "possibility-disclosing" rather than "truth-preserving" or "truth-tracking."<ref>"Since we are not dealing with deductive or inductive styles of reasoning (which are truth-preserving, not possibility disclosing), we cannot know in advance what form [they] will take." Nikolas Kompridis, ''Critique and Disclosure'' (Cambridge: MIT Press, 2006), 174.</ref> The "claim" made by such an argument is that of a new insight, resulting from the adoption of a new stance or perspective that reveals, or ''discloses'' a new possibility for thinking and acting.<ref>"[S]uccessful critique depends not just on showing that ''x'' is a disguised effect of ''y'', which effect in turn requires the exclusion or repression of ''r''. For this to be shown in the first place, critique needs to find the normative stance, the new interpretive perspective, in light of which what is familiar is defamiliarized, seen again, as if for the first time." Nikolas Kompridis, ''Critique and Disclosure'' (MIT Press, 2006), 254-255. See also "The test of disclosure" in the same volume, 139-146.</ref>
-[[Nikolas Kompridis]] has described two kinds of [[fallibilism]] in this regard. The first consists in being open to new evidence that could disprove some previously held position or belief (the taken-for-granted position in the [[natural science]]s). The second refers to the consciousness of "the degree to which our interpretations, valuations, our practices, and traditions are temporally indexed" and subject to (possibly arbitrary) historical flux and change. Such time-responsive fallibilism consists in an openness to the confirmation or disconfirmation of a possibility that one anticipates or expects in the future.<ref>Nikolas Kompridis, "Two kinds of fallibilism", ''Critique and Disclosure'' (Cambridge: MIT Press, 2006), 181.</ref>
-While some philosophers, notably [[Jürgen Habermas]] and [[Richard Rorty]], claim that disclosure is an [[aesthetic]] phenomenon (supposedly, neither [[reason|rational]] nor [[cognitive]], and therefore not philosophical), disclosive arguments have been identified in many contexts that are not primarily considered literary or "aesthetic."<ref>Nikolas Kompridis, "World Disclosing ''Arguments''?" in ''Critique and Disclosure'', Cambridge: MIT Press, 2006, 116-125.</ref> Furthermore, the consequences of such characterizations are ambiguous, since Habermas himself suggests that aesthetic "reflection" is possible,<ref>"In and after Nietzsche, the aesthetic appears principally as the 'other of reason,'… [while] Habermas himself, of course, believes that aesthetic reflection is possible—that aesthetic expression raises a validity claim about its own authenticity… [and is realized] in the contributions that its creative discovery of new forms of experience makes to social life." Jane Braaten, ''Habermas's Critical Theory of Society'' (Albany: SUNY Press, 1995), 135.</ref> and a number of philosophers have argued for the importance of disclosure's place in human [[reason]], most notably Nikolas Kompridis and [[Charles Taylor (philosopher)|Charles Taylor]].<ref>Fred Dallmayr, "[http://ndpr.nd.edu/review.cfm?id=15167 Critique and Disclosure: Critical Theory between Past and Future], ''University of Notre Dame Philosophical Reviews''.</ref><ref>Charles Taylor, ''Philosophical Arguments'' (Harvard University Press, 1997), 12; 15.</ref>
-Examples of world disclosing arguments include:
-* [[Transcendental arguments|"Transcendental" arguments]], in which an understanding of some feature of experience is shown to logically entail certain necessary conceptual pre-suppositions (e.g. Kant's transcendental self; Heidegger's elucidation of ontological being in ''[[Being and Time]]'');
-* Dialectical arguments, where the premises argued from are shown to be logically ''weaker'' than the argument's conclusion (e.g. Hegel's [[master-slave dialectic]] and T.W. Adorno's [[Dialectic of Enlightenment]]);
-* "Historical ontologies," such as those articulated by [[Michel Foucault]] (the historical ontology of power), [[Jacques Derrida]] (the historical ontology of meaning) and philosopher of science [[Ian Hacking]], who coined the term "historical ontology"; and
-* Forms of argument that, "through the use of [[hermeneutics|hermeneutic arguments]] and creative redescriptions" of our practices and cultural [[paradigms]], re-disclose the background of cultural meaning and "logical space of possibility."<ref>Nikolas Kompridis, "World Disclosing ''Arguments''?" in ''Critique and Disclosure'', Cambridge:MIT Press (2006), 118-121.</ref>
-Other [[modern philosophy|modern philosophers]] who are said to employ world-disclosing arguments include [[Hans-Georg Gadamer]], [[George Herbert Mead]] and [[Maurice Merlau-Ponty]].
 == Explanations and arguments ==