Some literature also state that the three parts of an argument are: Premise, inference, and conclusion. Premises are statements that a person presents as a fact. Inferences are the reasoning part of an argument. The conclusion is the final inference and is constructed from the premise and inferences.

Arguments can be broken down into three elements:

1. The claim or statement that the writer wants to reader to agree with.

2. The "argument" itself, which provides support, evidence and reasons for why the reader should agree with the claim for statement.

3. A rebuttal where the writer anticipates at least one objection to his/her argument and shows why or how the objection is weak or faulty. (The rebutal really has 2 parts to it, but we can consider the rebutall one element of an argument.)

I use a slightly different format in teaching liteature: point, proof, deduction. Students therefore make the point they are trying to prove, offer some form of proof to support that point (usually in the form of a quotation) and then finally explain that proof, relating it explicitly back to the point.

I like to encourage my students to break their arguments down into three parts:

STATEMENT OF THE ARGUMENT

EVIDENCE FOR THE ARGUMENT

EXPLANATION OF THE EVIDENCE

Another claim is that lower taxes make for a stronger economy.  This is a major tenet of the Republican Party today.  They take, as their evidence, such things as the fact that the economy improved in the 1980s after President Reagan lowered taxes.  Their warrant is that the improvement in the economy was caused by the tax cuts, not by something else.

I have not read the exact work, but you can look at an argument as being a position (or asserrion, claim, or idea, or suggestion), with reasons and evidence. For example, you could argue that salads are not healthy for you, your reason being most people load them with high calorie dressing and toppings. The evidence might come from calorie counts on salad dressings, cheese and whatever else you could add to a salad.

Another set of examples: One could make the claim that drinking alcoholic beverages before driving is dangerous. The supporting material would include statistical records of accidents in which the driver had elevated blood alcohol levels and the consequences. A simplified warrant might conclude that drunk drivers are a danger to themselves and others. A more refined warrant might propose a limit to the amount of alcohol one should be allowed to consume prior to driving, might set forth a legal benchmark limit for blood alcohol reading in a driver, or might suggest types of penalties for those who drive after drinking.

An argument has 3 parts: supporting material, a claim, and a warrant. A claim is the conclusion. (An example of this is that violent video games make children violent.) Supporting material is the evidence one has to support their claim. (An example is the research conducted on violent children and video games.) A warrant is the interpretation made regarding the supporting material by the writer (in hopes that the reader will interpret the supporting material in the same way). (An example of a warrant is: Research overwhelming proves that violent video games influence violent behavior in children.)