The following post was inspired by a debate at the talking philosophy blog that concerned a recent poll about humanism in the U.K.

Black and white. On and off. Left and right. Alive and dead. 7 and 22. You and me. Hillary Clinton and Barack Obama (their inclusion will make sense later). These are a few pairs of things that conform to the law of the excluded middle. So, what’s that?

I have just begun to learn about formal logic and am currently reading Logic Made Easy: How to know when language deceives you by Deborah J. Bennett. Two of the first things that are introduced in the book are the law of the excluded middle and the law of noncontradiction. Simply put: A is B or A is not B, it cannot be both, no middle ground, i.e. black is white or black is not white; and something is A or it is not-A, otherwise we have a contradiction, i.e. I cannot be both Martin and not-Martin.

It would be nice if the “real” world were so structured. There would be no room for confusion. Maybe, I don’t know. But life isn’t that way. It’s full of grayness and nuance, and thank goodness for that! And we forget that at our own expense.

Bennett writes in Logic Made Easy :

How many times have you heard an argument (intentionally?) exclude the middle position when indeed there is a middle ground? Either you’re with me or you’re against me. Either you favor assisted suicide or you favor people suffering a lingering death. America, love it or leave it. These are not instances of the excluded middle; in a proper statement of the excluded middle, there is no in-between. Politicians frequently word their arguments as if the middle is excluded, forcing their opponents into positions they do not hold.

If we are not allowed any alternatives outside of what is presented as our choices when clearly there are other options, then we are faced with a false dilemma. How about this example: The police never use excessive force when arresting a person or the police always use excessive force when arresting a person. Nope, I don’t feel like answering that one.

It’s time to return to the Clinton-Obama pair mentioned earlier. To follow the pattern I employed for the other pairs, we have: Hillary Clinton is Barack Obama or Hillary Clinton is not Barack Obama; and Barack Obama cannot be both Barack Obama and not-Barack Obama. But that’s not why I have introduced this pair of politicians.

Let’s imagine that the race for the Democratic nomination for U.S. president is still ongoing (as it is when this post is written) and that there are eight official candidates (as there are). Two candidates seem to have captured the nation’s attention. They are Hillary Clinton and Barack Obama.

Now let’s imagine that there are two rival newspapers competing for news on this political contest. But it’s early in the campaign and the primaries are months away with all eight candidates still seeking votes. One paper decides to commission a new poll, but this time the paper just wants to know, of the two “popular” contenders, who does the public feel will win the nomination. So the question the pollsters will ask likely Democratic voters is: Are you more likely to vote for Hillary Clinton, or for Barack Obama in the primary? In this poll the respondent is given the third choice of “I don’t know.”

But the other paper has got wind of this new poll and decides to commission one of its own. In order to “scoop” its competitor this newspaper tells the pollsters to leave off the third option and to get the respondents to choose only between Clinton and Obama.

The results are in. The first poll reports: 16% for Clinton, 16% for Obama, and 68% “don’t know.” So the first paper calls the race a dead heat between Clinton and Obama for the nomination. On the other side of town the rival paper reports: 40% for Clinton, and 60% for Obama. The second paper’s headline calls Obama the Democrats’ choice for 2008. So has the second paper “scooped” its rival? Which poll is more accurate? Does Obama have the nomination in hand?

In fact both papers have mislead their readers. With eight candidates still in the race and most likely still on the ballot (it’s possible one or another might drop out before the primaries), both sets of pollsters have presented their respondents with false dilemmas. The other six contenders are left out of the poll, they have become the excluded middle.

Even if we suppose that in the first poll only those voters truly likely to vote for either Clinton or Obama are represented by the first two numbers, and that the remaining 68% is an aggregate of the inclinations of the other six candidates’ supporters, then we still can’t conclude that the race is a dead heat between the two “front runners.” Maybe John Edwards, if he were included in a poll of all eight candidates, would have received 50% and left the remaining 18% to be divided among the other five candidates. Then clearly there would be a sole front runner.

The second paper’s poll is just as inaccurate. If we grant that the 16% received by both Clinton and Obama in the first poll are valid reflections of their standings in the race, so what? We still can’t pull any truth from the second poll, for that remaining 68% have been forced to choose a candidate that is not their preferred choice and no one knows what criteria they used to give the pollsters an answer. The inclusion of their responses is worthless and misleading.

So be wary of pollsters bearing false dilemmas. And anyone else trying to get you to believe that the world is made up of just black and white.