An argument is a series of statements used to persuade someone of something. That "something" is called the conclusion or main claim. The first job in analyzing any argument is to identify its conclusion. One way to identify conclusions, or other parts of an argument, is to look for their indicators.

Premises are statements that directly support the conclusion. A simple argument has two premises and a conclusion; a more complex argument may contain many claims, but these can always be divided up into groups of three--two premises and a conclusion. In an argument, the conclusion is only supported by its two premises, but each premise itself can be supported in a number of ways:

• Supporting arguments. A supporting argument is one which has as its conclusion the same statement as the premise being supported. All premises can be supported in this way, but such supporting arguments are often not stated. A special type of supporting argument is a definition, and while these, too, are usually unstated, at times it is necessary to define a term because either the term itself or the particular denotation being used is unusual.
• Assumptions. Eventually, all support for premises can be traced back to a set of beliefs which the person making the argument considers to be self-evident, and therefore not in need of further support or analysis. These may be called assumptions, presumptions, suppositions, or, in certain situations, postulates and axioms. Such assumptions serve as the premises for supporting arguments and, in general, any premise can be called an assumption.
• Evidence. A premise can be made more acceptable when it supported by various kinds of evidence: statistical studies, historical information, physical evidence, observations, or experiments, eyewitness accounts, and so on. The relative strength of evidence is determined by how reliable a person believes it to be. Almost no evidence is beyond dispute--we might challenge the methodology of a study, the accuracy of the information, the manner in which physical evidence was collected, and the eyesight or motivation of an eyewitness. And remember that the evidence only supports the premises--evidence cannot be an argument itself.
• Authority. Sometimes, we are not in a position to judge supporting evidence for ourselves: there may simply be too much of it, or it may be too technical in nature, or it may not be directly available to us. In those cases we often rely on the judgments of others, authorities whom we believe to be more likely to come to an accurate evaluation of the evidence than we are ourselves. Though we tend to think of such expertise in scientific, medical, or other scholarly fields, authority in arguments can also come from religious teachings, folk wisdom, and popular sayings--anything or anyone that we accept as somehow able to reach a more accurate evaluation. The relative strength of an authority in an argument depends on how willing a person is to accept the judgment of that source, but even in the strongest of cases, use of an authority merely supports a premise, and does not make an argument by itself.
• Explanations and anecdotes. Sometimes, we are more willing to accept a premise if we are given background information or specific examples. Such explanations and accounts are not given the importance of evidence or authority in an argument. Anecdotal evidence, for example, is by definition less statistically reliable than other sorts of evidence, and explanations do not carry the weight of authority. But both anecdotal evidence and explanations may affect our understanding of a premise, and therefore influence our judgment. The relative strength of an explanation or an anecdote is usually a function of its clarity and applicability to the premise it is supporting.

The various sorts of support for a premise--supporting arguments, evidence, authority, and explanations and anecdotes--interact in what we might call a hierarchy of support or evidence, in which one sort is given priority over another. In a murder trial, for example, the prosecution is usually based on the assumption that the jury's hierarchy of evidence will have at the top physical evidence (fingerprints, blood samples), especially as explained by technical authorities (forensic pathologists, ballistics experts), followed by eyewitness accounts, then by other sorts of authorities (psychologists, sociologists), and finally by explanations and anecdotes (character witnesses, personal histories). If the prosecution is right, their strong physical evidence and eyewitness accounts will outweigh the defendant's character witnesses, because of their relative placement in the jury's hierarchy of evidence. However, because that hierarchy is determined by each individual on a case-by-case basis, one can never be totally sure how any one piece of support will be accepted.