The Fallacy Of The Inverse
I first heard of the fallacy of the inverse from a former Magic the Gathering player David Mills.
The fallacy of the inverse describes certain instances where our minds predictably screws up. It is a flaw in logic that our mind will perceive as sound.
In order to avoid confusion I will first use a few examples before fully describing the fallacy of the inverse.
Example 1
Lets say we have a student. The student wants to achieve good grades. The student sets a goal of a 95% final grade for a particular subject. The student will reason in their mind that if they achieve a final grade of 95% or more, they will be happy. This is most likely true.
Unfortunately for the student they will believe that if they do not achieve a score of 95% or more, they will be unhappy. This is not true, it is flawed thinking.
We will look at this in a slightly more mathematical sense.
P= 95% grade or more.
Q= happiness.
→ (implies)
Since we know that the student will be happy with a grade of 95% or more…
P → Q
[95% or higher implies happiness]
If we take the inverse.
Not P → Not Q
[Not getting 95% or higher implies unhappiness]
This is a false assumption. There may be other reasons why that student could be happy. It is possible they will be sad, but it isn’t for sure. They may have won the lottery, a family member may have recovered from an illness, etc. They may even be happy if they scored 90%.
Unfortunately, the fallacy of the inverse may stop a lot of people from setting worthy goals, because those people fear negative emotions if those goals are not entirely met.
Example 2
If it rains, the sidewalk will get wet. This will always be true Right now, as I type this it is raining heavily, and the sidewalk outside my house is definitely wet.
Lets again look at this mathematically.
P= Rain
Q= sidewalk is wet
→ [implies]
P → Q. This is true.
The fallacy of the inverse states that if it does not rain then the sidewalk will not be wet. This is not true (a fallacy).
Mathematically the fallacy of the inverse states:
Not P → Not Q
Some may be wondering why this is a false assumption.
Simple.
There are other reasons why the sidewalk may be wet, someone may be watering their garden, there may be a water fight, someone might be washing their car near the sidewalk, etc. There are many reasons why the sidewalk might be wet without it raining.
Conclusion
We can now describe the fallacy of the inverse.
The fallacy of the inverse states that if a first even implies a second event, then the opposite of the first even occurring will cause the opposite of the second even occurring. You must be careful of this flawed thinking and actively train your mind to oppose it.
Ultimately, the fallacy of the inverse is our minds confusing the notion of cause and effect. I will be writing about cause and effect later on.
Regards
-Simon