What is a paradox? 

A paradox  is a logically self-contradictory statement or a statement that runs contrary to one’s expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. Many paradoxes arise because there is one or more hidden invalid argument. Most of us have played around with 2×0=5×0, and therefore 2=5. Or it’s generalised version ax0=b x0, and therefore a=b, or the generalised version that all numbers are equal. 

All grown ups ( teachers, elders and parents) have to deal with queries from the children, which often involve resolution of paradoxes ; for example, why does it get colder as we approach a hill station, when as a matter of fact we are getting closer to the Sun? Or when we describe God as omnipotent, omnipresent and omniscient we may be accosted with “If God is omnipotent ( all powerful) can God make/create a stone that he cannot lift ?”. 

Or the following series of arguments on avoiding studying:

The more you study,the more you forget,

The more you forget the less you know,

The less you know the less you forget

The less you forget the more you know

So, why study?

In common usage, the word “paradox” often refers to statements that are ironic or unexpected, such as “the paradox that standing is more tiring than walking”. 

Here is another teaser “If I plan to fail, and succeed in failing, have I failed or succeeded?”

What is a paradox ? https://youtu.be/kJzSzGbfc0k

The classification of paradoxes:

According to Quine’s classification of paradoxes:

• A veridical paradox produces a result that appears absurd, but is demonstrated to be true nonetheless.
• A falsidical paradox establishes a result that not only appears false but actually isfalse, due to a fallacy in the demonstration. The invalid mathematical proof that showed all numbers are equal, given in the first para of this article, relies on a hidden division by zero. 
• A paradox that is in neither class may be an  antinomy which reaches a self-contradictory result by properly applying accepted ways of reasoning. 

There are many well known paradoxes that are analysed and resolved to build better critical thinking skills :

The Abilene paradox : https://youtu.be/BVAuhcVy0xo

Zeno’s paradox? https://youtu.be/EfqVnj-sgcc

How to resolve the liar’s paradox : https://youtu.be/7zVTzedNpAw

Russell’s paradox: https://en.wikipedia.org/wiki/Russell%27s_paradox

Curry’s paradox: https://en.wikipedia.org/wiki/Curry%27s_paradox

The ship of Theseus: https://en.wikipedia.org/wiki/Ship_of_Theseus

Protagoras’s paradox: https://puzzling.stackexchange.com/questions/35296/protagorass-paradox-an-unsolved-court-case

The  Fermi  paradox : https://youtu.be/sNhhvQGsMEc

EPR paradox : https://www.thoughtco.com/epr-paradox-in-physics-2699186

15 paradoxes that will blow your mind: https://www.businessinsider.in/strategy/15-paradoxes-that-will-make-your-head-explode/articleshow/49557873.cms

Difference between paradox and a fallacy: https://wikidiff.com/paradox/fallacy

Most paradoxes are fallacies, but some are not, the paradox of the Liar, ( https://iep.utm.edu/par-liar/ ) for example.

As I close, I want to draw attention to a paradox of present times that arises out of a universally cherished idea, the idea of freedom of choice. It is considered axiomatic that the more choices we have, the better off we will be. So much so that we even have laws to break monopolies in businesses. But in terms of human consumer experience, the more choices available to you, the less satisfied you are with each one. This is the old ‘paradox of choice’. Research shows that when we are presented with more options, we become less satisfied with any particular one we choose. The reason  is that when we have so many options, we have greater opportunity cost in selecting each particular one; therefore, we’re less happy with our decision. Please do watch this video where Barry Schwartz explains the paradox of choice : https://youtu.be/VO6XEQIsCoM

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