Contradiction


Time to move on to the next critical-thinking topic that will help you make sense of news that refuses to stop coming, a topic that underlies every aspect of the logical reasoning process you have been learning about: contradiction.


Actually, it is the human mind’s visceral dislike of contradiction that plays such an important role in reasoning. In logic, for example, the greatest victory you can have over debate opponents is to prove that their argument ends in a logical contradiction. For if you can boil down what they are saying into an argument that concludes “therefore A and NOT A,” you have not just checkmated them but smashed their king to rubble.


To give you a sense of how deeply we as a species hate logical contradictions, back in the twelfth century—a period when Aristotle’s logic was being rediscovered in Medieval Europe and used by cutting-edge religious thinkers to prove the existence of God—conservatives in the church condemned the use of the pagan Aristotle as blasphemy.


Part of their complaint was that religious thinkers were using Aristotelian proofs to determine what God was not as part of a process of elimination that they hoped would clarify what an ultimately unknowable deity might be like. “No dice’” said more conservative clerics, who refused to allow any sort of logic to limit the Almighty in any way. If logic showed that God could not do something or be something, then such logic was wrong and had to be rejected.


The only exception they made to this rule was a limitation that said God could not create a logical contradiction. In other words, even the most dogmatic thinkers during one of history’s most doctrinal religious eras were not willing to accept a break with consistency, even on behalf of the deity.


Why such hostility—even among true believers—to the very idea of believing something and its opposite? Well logically speaking, belief in even a single contradiction requires everything—no matter how ridiculous—to be logically true.


For example, let’s say you decide to simultaneously believe that the COVID crisis requires us to stay in lockdown no matter what, while simultaneously believing that certain instances (be they providing for your family or protesting against injustice) requires you to be out in public in potentially dangerous, non-lockdown situations. While you can construct an argument that says one priority outweighs the other, if you try to hold both beliefs in your head at the same time without modification, you are essentially accepting an argument that says A and NOT A.


This contradictory belief can be cast as the premise of an informal argument in this form:


Premise 1: A is true, and A is NOT true


Any logical statement with an AND can be broken into its constituent parts, so if we accept that contradictory Premise 1, we must also accept this premise:


Premise 2: A is true


Any premise can also be extended with the simple use of the word “OR.” For example, if “All dogs are animals” then “All dogs are animals OR all birds can fly” is a true statement (since the first half is true, even if the second half isn’t). So, continuing with our logical argument:


Premise 3: A is true OR the world is made of snow


Having broken our original Premise 1 into two parts, we can now use the second part of that premise to create a fourth premise which reads:


Premise 4: A is NOT true


Tying it all together, we end up with the following argument:


Premise 1: A is true, and A is NOT true

Premise 2: A is true

Premise 3: A is true OR the world is made of snow

Premise 4: A is NOT true


Conclusion: The world is made of snow


This ludicrous conclusion derives entirely from our acceptance of a single contradiction. In fact, you can prove any conclusion, no matter how false, dangerous or immoral, by simply accepting a single instance of A and NOT A simultaneously being true, which is why belief in contradictions is such a dangerous practice.


Now many things in real life which we believe to be contradictions, such as a politician not keeping his or her campaign promises, turn out to actually be complex but non-contradictory situations that we would like to boil down to A and NOT A (especially when done by people we detest). So as we explore the role contradiction plays in both the news and our lives, we need to be aware of when we are faced with a genuine contradiction (versus more explicable inconsistencies) while simultaneously avoiding the practice of justifying our belief in something and its opposite.

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