Argument

An argument is a finite series of coherent propositions that support a conclusion.

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The foundation of logic is based on the proposition that something cannot be supported or proven except by means of something else. Any conclusion, it's own, without proof, is held to be an assertion.

In logical argument, therefore, there is the proposition to be proved, the claim, also called the conclusion and the propositions by which the claim is supported or proven, the premises. A proposition X is said to be supportable or provable in a system if there is a finite chain of statements S1 -> S2 ->S3 ->X where Sn is either an axiom of the system or is 'justified' from previous S's by means of a 'rule of inference.'

The inferential rules are those of a formal system, logic.

Naked Assertions
It is most vital to understand that a mere assertion in of itself is not an argument. When one merely trades assertions back and forth, one is not arguing - one is simply bickering without any point, purpose, profit or means of concluding. An argument requires more than just a firmly held proposition, it also requires a set of statements that support this conclusion. The statements that support the conclusion of the argument are called premises. A premise is a proposition that makes a commitment to the truth. As per the rule of bivalence, a premise is either true or false.

Ruling out Non propositions
For this reason, we can rule out, as possible premises, any statements that do not make a commitment to the truth. Explanations and Illustrations are not arguments for this reason. In an explanation, it is assumed by both the speaker and the listener that the phenomena in question, (the "conclusion") is true. Since the phenomena in question is assumed to be true, the speaker of an explanation does not take a stand, or imply truth. One merely accepts the truth.

Illustrations, descriptions, and conditional statements also are confused for arguments. In general, these non-arguments can be delineated from arguments because they do not contain premises that make a commitment to the truth. For example, a conditional statement (IF you give me some chocolate, THEN I will be your friend) is not an argument in itself because all that is being stated is that IF such a condition exists, then the consequent action will take place. This can become an argument only if the speaker makes a commitment to the truth of one of the premises - i.e. "You have given me some chocolate..."

Logical Argument Form
Once an argument has been delineated by ascertaining that it contains a series of statements that make a commitment to the truth, a set of premises and a conclusion, it should be presented in proper argument form, wherein each premise is listed in some logical order, followed by the conclusion. Here is an example of an argument; I will present it in proper argument form:

(P1 = premise 1, C = conclusion):

"Hey, is that a gun in your pocket, or are you happy to see me?"

P1 Either that's a gun in your pocket, or you're happy to see me   P2 You don't have a gun in your pocket(This is implied - implied premises are called "enthymemes") C: You must be happy to see me

Notice how this argument makes a transition from the premises to the conclusion. A connection from each premise to conclusion is brought about when each proposition possesses at least one element in common with at least one other proposition. In this example, each proposition (gun in a pocket, happy to see me, ) appears twice. This is why we can say that valid arguments help us preserve truth, as long as the premises are true, a valid argument form will preserve this truth and 'carry the truth safely" to the conclusion. This is why we 'preserve truth" or carry along the truth from the premises so carefully: because if we carry the truth along without making a mistake, then the conclusion MUST true.

This argument is a valid deductive argument (these terms will be explained in the next two sections), and as we will also see later, it is called a disjunctive syllogism.

We should also notice that in deductive arguments, nothing necessarily "new" is being discovered, for all the elements of the conclusion can be found in the premises. Deductive arguments work just like mathematical equations: a set of categories or definitions that are equivalent to each other. So, we can best think of most deductive logical arguments as a coherent way to present our thoughts - a point the philosopher Wittgenstein famously made at the turn of the last century. Now, that's one great reason to learn logic, isn't it?

Those following the Course in Logic 101 should proceed to the next section: Deductive and Inductive Logic