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# Proof that you can square a circle

## Question

Theorem: It is possible to square the circle.

Proof:
Given: No mathematician has squared the circle.

Therefore: No one who has squared the circle is a mathematician.
Therefore: All who have squared the circle are nonmathematicians.
Therefore: Some nonmathematician has squared the circle.
Therefore: It is possible to square a circle. [QED]

:-)

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The universal quantifier does not imply existence of an instance.

That is, you can speak reasonably about all of an empty set, but not about some of an empty set.

To illustrate:

A sign posted on a private lot warns: All Trespassers Will Be Prosecuted.
The sign does not imply the existence of a trespasser.
Formally, it says, for all X if X is a trespasser, X will be prosecuted.

OP says: All who have squared the circle are non-mathematicians.
That says: for all X if X has squared the circle, X is a non-mathematician.
It does not imply that the circle has been squared.

Therefore the statement Some non-mathematician has squared the circle is not implied.

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Having removed one proof, I feel obligated to supply a proof of my own that the circle can in fact be squared.

A circle, passing to the son of Daedalus, was thought to be the rarest form one could create: Its transcendent lustre was held in the highest esteem. Comparable only to words comprising six letters.

C I R C L E
I C A R U S
R A R E S T
C R E A T E
L U S T R E
E S T E E M

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Having removed one proof, I feel obligated to supply a proof of my own that the circle can in fact be squared.

A circle, passing to the son of Daedalus, was thought to be the rarest form one could create: Its transcendent lustre was held in the highest esteem. Comparable only to words comprising six letters.

C I R C L E

I C A R U S

R A R E S T

C R E A T E

L U S T R E

E S T E E M

Nice!

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