Deduction and Debates

I am often disappointed by a lack of fundamental logic that arises from common conversation regarding all sorts of issues. Sometimes this disappointment is directed toward those readers and listeners who fail to grasp this logic; other times, the writers, speakers, and professional persuaders who attempt to circumvent (often intentionally) the rules of logic are the object of my disappointment. Since I cannot prevent folks from spewing logical nonsense, I thought I’d share a thought on decoding logic in arguments.

A deduction in the logic sense is a conclusion which is reached as a result of particular premises. Look at the statements below:

A: Dogs can’t fly.

B: A collie is a type of dog.

C: Therefore, collies can’t fly.

Statements A and B are the premises, and statement C is a direct and definitive result of statements A and B (*Edit: This is referred to as a valid deduction.). It is important to note that the premises need not be true statements on their own. A [valid] deduction can logically follow from illogical premises:

A: Humans live on Mars.

B: John Travolta is a human.

C: Therefore, John Travolta lives on Mars.

Even though statement A may not be true, the deduction of statement C is true were statements A and B to be true. Now, this seems simple enough. But there are many instances in the news where it can be easy to miss a deductive contradiction. Suppose I held the following two views:

1) Government spending doesn’t create jobs in the economy.

2) Cutting government spending on the military will cause jobs to be lost in the economy.

While it may seem reasonable to maintain both stances within a platform of ideas, using a simple deduction, we can show that in fact, they present a deductive contradiction. I will use the fact that military spending is done by the government, as well as the (reasonable) assumption that a government cannot create jobs without also possessing the ability to take those jobs away (and likewise, that a government which cannot create jobs lacks that same ability):

A: Government spending doesn’t create jobs in the economy.

B: The US Military is funded by government spending.

C: Therefore, spending on the US Military doesn’t create jobs.

Using a straightforward deduction, the combination of beliefs in statements 1 and 2 are incompatible with logic. So, what makes it difficult for us to pick such errors in common conversation?

One initial explanation could be the amount of noise surrounding the premises of the last deduction above. The burden is on the listener or reader to construct such a deduction to reveal the contradiction. But doing so requires drawing a connection between two perhaps-otherwise-seemingly-unrelated statements on a newscast, from a speech, or in an opinion article. Part of the exercise of becoming an intelligent and informed citizen is a willingness to engage in endeavors in deduction construction. Sadly, we cannot count on the faces on television to avoid making such errors.


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