Arguments

 In the last section we said that inference is a relation between premises and a conclusion. We call the combination of premises and a conclusion an argument

An argument is a set of propositions, one of which is the conclusion and the others at least purport to support the conclusion. 

Logicians are interested in locating and analyzing arguments.  While no two arguments are exactly alike, many arguments can be classified, and the inferences involved evaluated, and this is the heart of the enterprise of logic.  Before long, this point will seem very familiar to you. But for now, let's motivate it by looking at two arguments:
 
 

Argument 1: Argument 2:
If Ignat wins the election, the Dow will plunge. 
The Dow will plunge. 
Therefore, Ignat wins the election.
If this ball is red, then it is colored. 
This ball is colored. 
Therefore, this ball is red.
 

These are two arguments, because they are composed of different propositions. But they share a common form or structure. Can you describe that structure?  Going one step further, can you see how describing that structure makes it possible to determine whether the two arguments are good arguments or bad arguments?  Remember that we said that good arguments are truth preserving: Ask yourself: If the premises were true, would the conclusion also be true?  It should be clear that in Argument 2 truth isn't preserved.  If a ball is colored, then it doesn't follow that it is red, even when it's true that if a ball is red, then it is colored.  The structure of both arguments is:
 

If A, then B. 

Therefore A
 

We will soon be able to show that any argument of this form is a non-truth preserving or invalid argument.

How do we distinguish arguments from non-arguments?  In ordinary prose, this is often a difficult matter.  Arguments have conclusions. So when we're looking to see if there is an argument, we need to see whether something in the text indicates that there is a conclusion, or something indicates a set of premises.  Sometimes there's no explicit indication, and one has to determine that a bit of text  is an argument from the context.   But often there are explicit premise-indicating or conclusion-indicating words or phrases.
 
 
Premise indicators Conclusion indicators
because 
for the reason that 
since 
while
therefore 
it follows that 
hence 
thus
 

The definition of "argument" given above is the most fundamental definition in all of logic. It is crucial that you understand it. How do you know you understand a concept? Do you understand it if you read it and feel that you understand it? What if such a feeling is unreliable? The real test of understanding is that you can correctly complete the assignments which make use of the concept in question. The exercise below, and the exercises throughout this text are essential. Whenever you read a section, make sure you do the associated exercises. If you don't, you might as well have not read the text.

Exercise: Distinguishing arguments from non-arguments

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