Most people do not realize that there is a giant difference between logic and intuition.

Our choice of words makes this obvious: "Makes sense."

What does this phrase actually mean?

Does it mean that something is logically correct?

Or does it mean that the thing being referred to aligns with the person's subjective intuition?

Here are two examples from mathematics:

In set theory, you can join two sets by using the union operator.

This operator is derived from a logical OR operation (e.g. include all elements that satisfy predicate A OR B).

However, when joining two sets, most people would rather say: I join set A AND B.

Adding to the confusion, students would commonly add sets together using a plus symbol, and this is correct.

They think of it as set A AND set B, equating + with AND.

It turns out that, logically, + represents OR and * represents AND.

To move a function to the right (e.g. along the positive number line), you need to subtract the number from the x value.

Conversely, to move the function to the left (e.g. along the negative number line), you need to add to x.

This makes sense - hence it is a mathematical fact - but it is unintuitive at first.

The more you think about logic, the more you realize that what most people think of as logic is actually intuition.

Do not follow your intuition.

Instead, bend and break it until you forcefully aligned it with logic.

This is the best way to avoid unnoticed biases.

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