Logic Basics

Arguments are collections of sentences that prove a claim.  There are two kinds of statements in an argument: premises and conclusions..  An argument must have at least one premise.  Premises are statements that support the conclusion of the argument.   Conclusions are exactly what they sound like.  They are what that argument is trying to prove; they are the point of the argument.

Here is a sample argument:

1.  All undergrads read Facebook during lecture.
2. Simon is an undergrad.
3. Therefore, Simon reads Facebook during lecture.

In this argument, sentences #1 and #2 are the premises and #3 is the conclusion.  The argument is of this form:

1.  All X’s are Y’s. (If P, then Q)
2. S is an X. (P)
3. S is a Y. (Therefore, Q)

Because this argument has proper logical form, if all the premises are true, then the conclusion must also be true.  In other words, the argument is valid.  A sound argument is a valid argument where all premises are true.  A valid argument  just has proper logical form.

Here is an argument that has true premises but is neither valid nor sound:

1.  When it rains, the sidewalk is wet.
2. This morning, the sidewalk was wet.
3.  Hence, it rained.

In this argument, both of the premises are true. However, because the logic is flawed, it is an invalid argument.  One way to test for validity is to ask the following question: if I assume that the premises are all true, is there a possibility for the conclusion to be false?  In the previous argument, it could be possible that the conclusion could be false even if all premises are true (sprinklers could have made the sidewalk wet).

Here is an argument that is valid but not sound:

1. All undergrads can breathe underwater.
2. Simon is an undergrad.
3. Simon can breathe underwater.

Premise #1 is obviously false.  This means that the argument is unsound.  However, because the form of the argument (the same as the first argument) is proper, the argument is valid.