Example 1: La trahison des images also known as The Treachery of Images by René Magritte.
Ceci n’est pas une pipe. Translation: This is not a pipe.
Example 2: Liar’s Paradox
This sentence is false.
I am lying.
Everything I say is false.
Every person is a liar.
If this sentence is true, then the sentence is false, but if the sentence is false, then it must be true…
Example 3: *Zeno’s Paradox
The idea that motion is but an illusion. As Aristotle put it, locomotion must arrive at the halfway stage before it arrives at the goal. Eventually, you are stuck in an infinite loop.
*Thank you, Martin Grandjean, for the image.
The bottom line: There are things in our world that are totally true but cannot be proven. Sometimes we are stuck on difficult problems. Problems that are infinite in length. Instead of being caught in a loop, humans have a special ability to jump out of the system to ask why, to think about contradictions. Mechanical thinking is great for improving yields, crunching big data. Meta-thinking, the idea of thinking about thinking, helps us understand our place in the world, meaning and ultimately why we do the things we do.