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Logically Absurd and Contradictory

In honing your home logic skills, try reducing any argument to its basic premise at the extremes of its subject.

Once upon a time, I checked my horoscope just for fun. It simply said: Scorpios are skeptical about horoscopes. Wow! What more could a critical thinker want to read?

Don’t get me wrong. It’s true I am quite skeptical about horoscopes, so by admitting to this, I prove the horoscope true — but then I simultaneously contradict my skepticism. This circular reasoning illustrates the importance of developing arguments that are inherently noncontradictory and that cannot be demonstrated false when carried out to extreme examples.

This simple statement captures the essence of one of the basic tenets of thought: Aristotle’s law of noncontradiction and the absurdity of reducing something to its logical extreme. The law states that something cannot be true and not true at the same time; that would be absurd. It allows a person to ask how meaningful would someone’s position on an issue be if it were taken to its logical extreme.

Yet, making a “reduction to the absurd” (reductio ad absurdum) argument can be an effective technique when refuting pseudo-scientific statements and one to consider adding to your repertoire of critical-thinking tools.

Consider the use of this method by mathematician John Allen Paulos, author of Innumeracy. In a Dec.13, 2009, New York Times Magazinearticle, he discussed the angered responses to a scientific panel’s controversial advice that healthy women in their 40s avoid routine mammograms until their 50s. Paulos argued that the public’s reactions derived from an intuition that earlier screenings improve detection of a deadly cancer. However, he said that if this belief were true, then why not screen asymptomatic women in their 30s or, for that matter, beginning at 15?

The panel’s recommendations focused on the increased risk from cumulative radiation over many years outweighing the detection of cancer. Paulos demonstrates the use of the reductio ad absurdum technique to refute the common intuitive reaction in favor of the panel’s more scientific findings. Whatever is true about one statement should then be true of similar statements based on the same premise, even when taken to the absurd limit.

If it’s accurate that earlier screening is better, then even earlier testing would be best. If not, then there is something logically incorrect about the initial statement that earlier is better. It is a proof by contradiction.



So how can these techniques and principles of logical thought be useful for developing strong critical-thinking abilities?

Consider the following: Increasing taxes to allow all Americans to have health care will benefit the economy in the long run. However, let’s take this to a logical extreme: Raising taxes to 100 percent of income should then bring about the best health care and a stronger economy. But devoting all of one’s income to pay taxes would result in a failure to meet other obligations and purchase other goods, thereby bringing doom to the national economy and the health care system.

Increasing taxes beyond a certain point contradicts the initial premise of better health care and a stronger economy result from raising taxes. The policy trick is to figure out what that certain point is and achieve a balance between necessary taxation and economic benefit.

If two statements contradict each other, they cannot both be true. Another example is the argument made by opponents to same-sex marriage who feel that legalizing it would harm the institution of marriage. Carrying this statement to the absurd, James Dobson of Focus on the Family predicted in 2004 (months after Massachusetts courts made these marriages legal) that same-sex marriage “will destroy marriage. It will destroy the Earth."

The law of noncontradiction would have us believe that a state with legalized same-sex marriage would exhibit an increase in the dissolution of different-sex marriages and divorces, since the opposite (no impact or a strengthening of marriage and, I suppose, a continuation of the Earth as we know it) could not also be true. In 2008, after four years of data, Massachusetts’s divorce rate for different-sex marriages declined from the previous year to the lowest level in the country. It was the lowest rate since 1940.

When hearing competing positions held by politicians about health care, for example, or solutions to our economic recovery, take their statements to logical extremes and uncover any potential contradictions. Engaging in a reductio ad absurdum technique and invoking the law of noncontradiction will assist you in critically thinking about people’s arguments on current issues and in dealing with rumors that float around controversial policy plans. And of course actual data often provide some much-needed assistance in the heat of a discussion.

Believe me because Scorpios tell the truth. It’s only this sentence you are now reading that is not true. But that’s another paradox for another column.