Simanaitis Says

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FOUR THINGS LOGICIANS DON’T WANT YOU TO KNOW!

WELL, IT ISN’T that they don’t want you to know. (And, by the way, do you too find these “don’t want you to know” headlines a bit ludicrous?) Rather, it’s that logicians may have been less than successful in conveying these logical processes of thought.

To wit:

Implication versus its inverse. Mom says, “If you don’t stop that, you’re getting no ice cream!”

What if he does stop and she doesn’t give him any ice cream? Can Little Murgatroyd protest mom’s lack of logic?

Her original statement is an implicational statement of the form Not P → Not Q, where P is stopping the bad behavior and Q is getting the ice cream. However, “nots” don’t cancel out: P → Q is logically a different kettle of er… ice cream.

PQComp

For instance, consider “If it’s too sunny, let’s eat inside.” This says nothing about plans if it’s not too sunny. Maybe it’s raining or snowing.

Logically, what mom really means is, “If you stop that, then you’ll get ice cream.”

On the other hand, her original statement sounds properly threatening. Her correctly logical version sounds slyly inveigling, doesn’t it? Maybe mom is right to be illogical.

Syllogism and the fallacy of the undistributed middle. A syllogism starts with two or more truths, and then uses logic to reach a conclusion: “All men are mortal. Socrates is a man. Therefore Socrates is mortal.”

m

A Venn diagram displays the logic of this particular syllogism.

On the other hand, syllogisms can be misused: “Some immigrants are bad. Some bad people rob banks. Therefore some immigrants rob banks.”

m

This Venn diagram shows the fallacy of the undistributed middle.

The fallacy lies in one or more of the premises being less than inclusive. This is the undistributed middle.

It’s as logical as “Some cats are calico. Some calico things are skirts. Therefore, some cats are skirts.”

Correlation versus causality. Correlation is a mutual relationship between two or more things. Statistically, there’s an interdependence of variables.

By contrast, as the word suggests, causality is a relationship describing cause and effect; one thing logically or scientifically leads to the other.

Both correlation and causality are useful in science. But they are different. For instance, there’s a factual correlation between alcohol sales in a community and its teachers’ pay. Loosely, the higher the teachers’ incomes, the more booze is sold.

Thus, teachers are drunkards.

Of course, the fallacy here is confusing correlation with causality. If there is any causality, it’s between a community’s affluence (the cause) and what it does with its money (the effect).

Word order matters. The order of words in a statement affects its meaning. My favorite example of this appeared here at SimanaitisSays: “Flabby Fun with the Word ‘Only.’ ”

Briefly, consider the basic statement, “I poked him in his eye.” Next, put the word “only” in each of the seven possible places in this sentence.

Cyclops

Of these seven new statements, only three share the same logical meaning. Try it! ds

© Dennis Simanaitis, SimanaitisSays.com, 2016

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