Via the excellent Best of Wikipedia blog comes this entry:

The politician’s syllogism, also known as the politician’s logic or the politician’s fallacy, is a logical fallacy of the form:

We must do something
This is something
Therefore, we must do this.

Allow me to present a similar argument:

“A cat has one more tail than no cat.
No cat has eight tails.
Therefore a cat has nine tails.”

These are both classic examples of the fallacy of Equivocation. Equivocation is when a speaker uses a word with multiple meanings without making clear which meaning is intended. Generally, the speaker will tend to use two different meanings interchangeably.

Let me show you what I mean. First, let’s turn our attention to my proof that all cats have nine tales. In this instance, the equivocated term is the word ‘no’. In the first premise it indicates “zero cats” and in the second premise it indicates “there does not exist a cat”. By using the same word for both concepts we cover up the fact that we’re making a giant leap between our two premises. This allows us to smuggle two disjoint premises in the side door before anyone can stop us.

In the Politician’s Syllogism, the equivocated term is much more subtle. The word “something” is used in the first premise to indicate “a particular, but unknown course of action” and, in the second premise, to mean “any course of action at all”.

To be more formal, the first premise asserts “there exists a course of action that we must take.” The second premise asserts that the course of action at hand is “a member of the set of all possible courses of action”. When rewritten this way, the syllogism becomes a non-sequitor and it becomes obvious that the politician’s conclusion is far from proven:

“There exists a course of action that we must take.
This is a course of action.
Therefore we must do this.”

This lack of linkage between the proposed course of action in the second premise and the correct course of action in the first is hidden by the fact that the word “something” is used in each case. In this way, Equivocation is often used to hide particular logical leaps in invalid arguments. One last example demonstrates this, stolen straight from the Wikipedias:

A feather is light.
What is light cannot be dark.
Therefore, a feather cannot be dark.

In the case of the cats and the feathers, this little bit of sophistry results only in freakish nine-tailed felines and a suspicious lack of swans. In the case of the politicians, however, it results in horrible, knee-jerk legislation.