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Constructing a Logical Argument

Introduction ：

There is a great deal of argument on Usenet. Unfortunately, most of it is of very poor quality. This document attempts to provide a gentle introduction to logic, in the hope of improving the general level of debate.
Logic is the science of reasoning, proof, thinking, or inference [Concise OED]. Logic allows us to *yse a piece of reasoning, and determine whether it is correct or not. To use the technical terms, we determine whether the reasoning is valid or invalid.
One does not need to study logic in order to reason correctly. However, a little basic knowledge of logic is often helpful when constructing or *yzing an argument.
Note that I am not claiming that logic is universally applicable. That issue is very much open to debate. This document only explains how to use logic; you must decide whether logic is the right tool for the job.
Note also that this document deals only with simple boolean logic. Other sorts of mathematical logic, such as fuzzy logic, obey different rules. When people talk of logical arguments, though, they generally mean the type being described here.

Basic concepts ：

The building blocks of a logical argument are propositions, also called statements. A proposition is a statement which is either true or false; for example:
"The first programmable computer was built in Cambridge."
"Dogs cannot see colour."
"Berlin is the capital of Germany."
Propositions may be either asserted (said to be true) or denied (said to be false). Note that this is a technical meaning of "deny", not the everyday meaning.
The proposition is the meaning of the statement, not the particular arrangement of words used. So "A God exists" and "There exists a God" both express the same proposition.

What is an argument?

An argument is, to quote the Monty Python sketch, "a connected series of statements to establish a definite proposition". There are three stages to an argument: Premises, inference, and conclusion.

Stage one: Premises
One or more propositions will be are necessary for the argument to continue. They must be stated explicitly. They are called the premises of the argument. They are the evidence (or reasons) for accepting the argument and its conclusions.
Premises (or assertions) are often indicated by phrases such as "because", "since", "obviously" and so on.
(The phrase "obviously" is often viewed with suspicion, as it can be used to intimidate others into accepting dubious premises. If something doesn't seem obvious to you, don't be afraid to question it. You can always say "Oh, yes, you're right, it is obvious" when you've heard the explanation.)

Stage two: Inference
The premises of the argument are used to obtain further propositions. This process is known as inference. In inference, we start with one or more propositions which have been accepted. We then derive a new proposition. There are various forms of valid inference.
The propositions arrived at by inference may then be used in further inference. Inference is often denoted by phrases such as "implies that" or "therefore".

Stage three: Conclusion
Finally, we arrive at the conclusion of the argument, another proposition. The conclusion is often stated as the final stage of inference. It is affirmed on the basis the original premises, and the inference from them. Conclusions are often indicated by phrases such as "therefore", "it follows that", "we conclude" and so on.

Types of argument
There are two traditional types of argument, deductive and inductive. A deductive argument provides conclusive proof of its conclusions; if the premises are true, the conclusion must also be true. A deductive argument is either valid or invalid.
A valid argument is defined as one where if the premises are true, then the conclusion is true.
An inductive argument is one where the premises provide some evidence for the truth of the conclusion. Inductive arguments are not valid or invalid, but we can talk about whether they are better or worse than other arguments. We can also discuss how probable their premises are.
There are forms of argument in ordinary language which are neither deductive nor inductive. However, this document concentrates on deductive arguments, as they are often viewed as the most rigorous and convincing.
Here is an example of a deductive argument:
Every event has a cause (premise)
The universe has a beginning (premise)
All beginnings involve an event (premise)
This implies that the beginning of the universe involved an event (inference)
Therefore the universe has a cause (inference and conclusion)
Note that the conclusion of one argument might be a premise in another argument. A proposition can only be called a premise or a conclusion with respect to a particular argument; the terms do not make sense in isolation.