This Article Doesn’t Mention Itself… Or Does It? The Russel’s Paradox Explained!

Think of a catalog containing a list of books. Some catalogs include themselves and some do not.

Now there’s a catalog drawn up that lists all the catalogs that do not contain themselves. Confused?

Don’t be. What I really mean is that every catalog that includes itself should not be included in this

list.

Now the question is: should this catalog include its own self?

This goes two ways:

1. If it does: it shouldn’t! This is because it only lists catalogs that do not include themselves.

2. If it doesn’t: It should! This is because it lists all the catalogs that do not list themselves like

its own current self.

I know it feels like a dizzying Doctor Strange time loop, but this is actually considered to be one of

the greatest paradoxes of the 1900s.

This is called ‘Russell's Paradox’ named after philosopher and mathematician Bertrand Russell, who

casually shattered the foundation of set theory with a simple question: "Does the set of all sets that

do not contain themselves contain itself?"

This sparked an existential crisis in the 20 th century.

The paradox exposed a fundamental flaw that was previously overlooked in the naive set theory.

The core idea of this was that any collection of things can be defined by a property and that forms a

set. Does it really? Nope.

This caused logicians to redefine it altogether till we reached the Zermelo-Fraenkel set theory.

Russell’s Paradox wasn’t just a riddle for centuries to break their heads upon. It was the foundation

for logic and philosophy in mathematics, helping in constructing logical frameworks rather than a

sugar-high set in a candy store.