In logic and philosophy, an argument is a series of statements (in a natural language), called the premises or premisses (both spellings are acceptable) intended to determine the degree of truth of another statement, the conclusion.  The logical form of an argument in a natural language can be represented in a symbolic formal language, and independently of natural language formally defined "arguments" can be made in math and computer science.
Logic is the study of the forms of reasoning in arguments and the development of standards and criteria to evaluate arguments.Deductive arguments can be valid or sound: in a valid argument, premisses necessitate the conclusion, even if one or more of the premisses is false and the conclusion is false; in a sound argument, true premisses necessitate a true conclusion. Inductive arguments, by contrast, can have different degrees of logical strength: the stronger or more cogent the argument, the greater the probability that the conclusion is true, the weaker the argument, the lesser that probability. The standards for evaluating non-deductive arguments may rest on different or additional criteria than truth--for example, the persuasiveness of so-called "indispensability claims" in transcendental arguments, the quality of hypotheses in retroduction, or even the disclosure of new possibilities for thinking and acting.
Informal arguments as 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 rational 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.
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.
A deductive argument is one that, 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.
Deductive arguments may be either valid or invalid. If an argument is valid, it is a valid deduction, and if its premises are true, the conclusion must be true: a valid argument cannot have true premises and a false conclusion.
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, however, not on the actual truth or falsity of its premises and conclusion, 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. Under a given interpretation, 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 either true or false.
Logic seeks to discover the valid forms, 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 solely on its form, an argument can be shown to be invalid by showing that its form is invalid. This can be done by giving 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 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, just so happens to be a necessary truth, it is so without regard to the premises.
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).
A sound argument is a valid argument whose conclusion follows from its premise(s), and the premise(s) of which is/are true.
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.
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 Tweedy example:
This argument is reasonable and the premises support the conclusion unless additional information indicating that the case is an exception comes in. If Tweedy 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. The argumentation schemes provided in (Walton, Reed & Macagno, 2008) describe tentatively the patterns of the most typical arguments. However, the two levels of abstraction are not distinguished. For this reason, under the label of "argumentation schemes" fall indistinctly patterns of reasoning such as the abductive, analogical, or inductive ones, and types of argument such as the ones from classification or cause to effect. A typical example is the argument from expert opinion, which has two premises and a conclusion.
|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 is associated to 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.
|CQ1:||Expertise Question. How credible is E as an expert source?|
|CQ2:||Field Question. Is E an expert in the field that A is in?|
|CQ3:||Opinion Question. What did E assert that implies A?|
|CQ4:||Trustworthiness Question. Is E personally reliable as a source?|
|CQ5:||Consistency Question. Is A consistent with what other experts assert?|
|CQ6:||Backup Evidence Question. Is E's assertion based on evidence?|
If an expert says that a proposition is true, this provides a reason for tentatively accepting it, in the absence of stronger reasons to doubt it. But suppose that evidence of financial gain suggests that the expert is biased, for example by evidence showing that he will gain financially from his claim.
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 of arguments may have different or additional standards of validity or justification. For example, Charles Taylor writes 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, 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 world disclosure). The late French philosopher Michel Foucault is said to have been a prominent advocate of this latter form of philosophical argument.
Argument is an informal calculus, relating an effort to be performed or sum to be spent, to possible future gain, either economic or moral. In informal logic, an argument is a connection between
The argument is neither a) advice nor b) moral or economical judgement, but the connection between the two. An argument always uses the connective because. An argument is not an explanation. It does not connect two events, cause and effect, which already took place, but a possible individual action and its beneficial outcome. An argument is not a proof. A proof is a logical and cognitive concept; an argument is a praxeologic concept. A proof changes our knowledge; an argument compels us to act.
Argument does not belong to logic, because it is connected to a real person, a real event, and a real effort to be made.
The value of the argument is connected to the immediate circumstances of the person spoken to. If, in the first case,(1) John has no money, or knows he has only one year to live, he will not be interested in buying the stock. If, in the second case (2) she is too heavy, or too old, she will not be interested in studying and becoming a dancer. The argument is not logical, but profitable.
World-disclosing arguments are a group of philosophical arguments that are said to 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 and "logical space" on which an argument implicitly depends.
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.
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.
Fallacies are types of argument or expressions which are held to be of an invalid form or contain errors in reasoning. There is not as yet any general theory of fallacy or strong agreement among researchers of their definition or potential for application but the term is broadly applicable as a label to certain examples of error, and also variously applied to ambiguous candidates.
In Logic types of fallacy are firmly described thus: First the premises and the conclusion must be statements, capable of being true or 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.
Often an argument is invalid because there is a missing premise--the supply of which would render 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 assumptions- the milkman was not the murderer, and the murderer has left by the front or back door).