P and Q. 2. This example illustrates two facts about valid arguments. First of all, an argument can be valid even though some or most of the premises are not used to deduce the conclusion. A second point illustrated by this example is that some arguments, though deductively valid, can be extremely dull. The conclusion of the preceding argument is already asserted by just one of the premises.
Socks is a cat.
Therefore, Socks is a cat. In other words, it contains its own conclusion as a premise. As a result, only someone who was already convinced that the conclusion is true would find this argument rationally persuasive, so the argument is rather pointless. A good argument is one that is rationally persuasive to someone who is not already convinced of the conclusion. Therefore, probably it rained last night.