Argumentation

• argument

• premise

• inference rule

• conclusion

• logical form

• symbolic language

• formal language

Argument:

• premises, preconditions

• inference rules, material conditionals

• conclusion, logical consequence

Argument

An argument is a group of statements, called premises, intended to determine the truth of the final statement, called 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 constructed in math.

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, premises necessitate the conclusion, even if one or more of the premises is false and the conclusion is false; in a sound argument, true premises necessitate a true conclusion.

Inductive arguments, by contrast, can have different degrees of logical strength: the stronger or more cogent the argument, the greater the probability that the conclusion is true, the weaker the argument, the lesser that probability.

The standards for evaluating non-deductive arguments may rest on different or additional criteria than truth; for example, the persuasiveness of so-called "indispensability claims" in transcendental arguments, the quality of hypotheses in retroduction, or even the disclosure of new possibilities for thinking and acting.

An argument, in its simplest form, is a group of 3 related statements: two premises (propositions) and the conclusion (logical consequence). An argument can be seen as a claim stating that its premises will justify the conclusion.

A premise is a statement that assumes something as being true; an assumption that something is true.

The purpose of an argument is to provide a reason for accepting the truth of its conclusion (which must be a declarative statement).

The principle of bivalence stays that a statement has a truth value, that is, it can either be true or false, not both, not neither.

Bad arguments are those in which the premises do not support the conclusion, contrary to their claim. Conversely, in good arguments the premises do support the conclusion.

The proof of a conclusion depends on both, the truth of the premises and the validity of the argument.

The premises should be true to accept the conclusion of an argument as true, but also the premises should constitute evidence in favor of the truth of the conclusion. The steps leading from premises to conclusion should be truth-preserving - logical steps taken from true premises should lead to a true conclusion.

Regress argument

According to the regress argument, any proposition requires a justification. However, any justification provided is bound to contain arguments that will themselves require justification. And so on, ad infinitum, in the downward spiral of infinite regression.

Throughout philosophic history many responses to this problem have been generated; we present the major counter-arguments:

• some statements do not need justification

• the chain of reasoning loops back on itself

• the sequence never finishes

• belief cannot be justified as beyond doubt