Paradoxes … Interesting Mental Sports

Paradoxes are interesting logical structures which might look as true but are internally contradicting.. They are many times ‘invalid’ (logically) , but are very helpful in promoting critical thinking … They are very interesting in literature and philosophy, and a very good mental sport


The Liar Paradox

A basic form of paradoxes is the ‘liar’ paradox …If I say : “This statement is False.” …. If it was false, then the statement itself is true, then it is false , then it is true and so on …

Many people mention the Epimenides “Cretans are always Liars” as a paradox,well … it is a paradox only in one condition … here it is  :

Epimenides, wrote: “The Cretans, always liars, evil beasts, idle bellies!” —(Epimenides was a Cretan) :

  • If he is NOT lying, then cretans are always liars (obviously) and his statement is false (He is a Lying Cretan), so they (Cretans) are not always liars but he is NOT Lying, and they are always Lying .. and we’re stuck
  • If he is Lying , then cretans are not always liars this is where we can resolve it :

If Epimenides is a Cretan and a liar, then his statement, “The Cretans, always liars” is a lie and False ..  (it can be so if Epimenides knows at least one other cretan who is not a liar: Epimenides is a liar now, his statement is a lie (and false), but this other guy isn’t, so Cretans aren’t always Liars and the statement is False !!!!) — Time for a small  headache of consideration, but it works : Epimenides is a Cretan Liar, but not all Cretans are liars always.


Let’s try one more :

A Prediction Paradox

A monster steals a son from his father, and promises to return the child if the father can correctly guess what the monster will do. What happens if the father guesses that the child will not be returned to him?

Here … there seems to be no resolution … . If the monster keeps the child, then the father predicted correctly, and the monster should return the child , but then the father was wrong and the child shouldn’t have been returned , but if that happened then the father was right … and on and on … If the monster returns the child, then the father guessed wrong and the child shouldn’t haven’t been returned but if it hadn’t been then again the father was right … and on and on …


Now for a relatively more popular one :

Back to Future … ?

A man goes back in time, and kills his grandfather before he can meet his grandmother! Simple – right ? No …  This means that one of the man’s parents will not have been born, and the man in turn, will not have been born. This would mean that he could not have traveled back in time after all, which means the grandfather would still be alive, and the traveler would have been conceived allowing him to travel back in time and kill his grandfather….

Wait … What ? Ok this works if you believe in parallel universes (somehow), and at every jump back in time there is a split of universes …


For a more religious one :

A Divine Paradox

Can God create something so heavy, that He cannot lift it?

God by definition is omnipotent – he can do anything & everything … If he can create something so heavy he can’t lift, then his lack of strength means he is not omnipotent , but by definition he is .. so he can create that … but if he does then he can’t lift it … then he is not omnipotent … and we’re stuck …

Some resolutions of this statement include saying that “can not lift” does not make sense, or that the question itself is a contradiction, like a “square circle”.


An interesting paradox that relates logic to identity , and thinking about being is the paradox known as the Ship of Theseus … ( See this ) …. Also if you do get the chance , watch the brilliant movie with the same title..


Visual Paradoxes

A great genius created amazing visual paradoxes … the artistic/mathematical/geometric genius here is the great M.C. Escher (Maurits Cornelis Escher) … he created many amazing paintings that exploit illusions to create brilliant visual paradoxes and here are some of them :

Maruits Escher - Illusion 1

Maruits Escher – Illusion 1



Escher - Relativity - Which way is Which ?

Escher – Relativity – Which way is Which ?


Escher - How is the water flowing ... Up or Down ?

Escher – How is the water flowing … Up or Down ?


There are many examples and geometric manipulations now that create the same surprising effects…


The Beauty of the Paradox

Søren Kierkegaard, in the Philosophical Fragments, that

(..) The paradox is the passion of thought, and the thinker without the paradox is like the lover without passion: a mediocre fellow. But the ultimate potentiation of every passion is always to will its own downfall, and so it is also the ultimate passion of the understanding to will the collision, although in one way or another the collision must become its downfall. This, then, is the ultimate paradox of thought: to want to discover something that thought itself cannot think


Can’t agree more …



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