Basic Logic - What Makes a Argument Valid?

Corollary 1: IF the argument is Invalid, then no conclusion can be supported by the premise, regardless of the actual truth of either the premise or the conclusion. In other words, the conclusion may actually be true or false, but the chain of reasoning does not support the conclusion.

Corollary 2: If an argument is valid, and the premises are true, then the conclusion will be true.

For example, both of the following are valid propositions (these are examples of syllogisms, a particular type of proposition containing a major and minor premise):

1. All humans have 2 eyes. (major premise, also called the antecedent)
   I am human. (minor premise)
   Therefore I have 2 eyes. (conclusion, also called the consequent.)
    
2. All humans have 4 eyes.
   I am human.
   Therefore I have 4 eyes.

The argument is valid in both propositions, because in every case where the premises are true, the conclusion is also true. Whether the premises are actually true or not is outside the scope of pure logic, and comes instead under the general category of critical thinking.

Logic is not concerned about the truth of the premise that “all humans have 4 eyes.” It is only concerned with the validity of the argument – that the chain of reasoning from premises to conclusion is valid. In other words, if all humans really did have 4 eyes, and if I am human, is it valid to conclude that I have 4 eyes?

Another interesting point is illustrated by the second proposition: there is no case in which the premise can be true. This means that there can be no case in which the premise is true and the conclusion false, i.e. the argument can never be Invalid. Since the argument must be either Valid or Invalid, and since it cannot be Invalid, it has to be Valid! (Of course, since the premise can never be true, then the conclusion will never be true, but the argument is still valid.)