In 2002, I learnt about paradoxes.
This is content from a book called, Vicious Circles & Infinity – An Anthology of Paradoxes by Patrick Hughes & George Brecht.
To start off, they explain that there are self-referential propositions, contradictory propositions, self-contradiction propositions which are not paradoxes & other forms of self-reference & contradiction of a “stronger” kind which approach the paradoxical state.
Example of a Self-Referential Proposition =
This sentence has five words.
Example of a Contradictory Proposition =
Round square.
Example of a Self-Contradiction Proposition =
This sentence has six words.
Here’s an example of the Self-referential & Contradiction that heads toward a paradox =
Please ignore this notice.
So, to do what this notice says, you mustn’t have done it.
However paradoxical, this one isn’t a paradox. A paradox has the self-reference and contradiction but it also contains a third factor = vicious circularity.
‘Please ignore this notice,’ goes round, but it doesn’t continue going round.
Other examples of this kind of paradoxical propositions are =
All rules have exceptions.
In principle, I am against principles – Tristan Tzara
No general proposition is worth a damn! – Oliver Wendell Holmes, Jr.
Never say never.
Check this out =
How can a witness reply to a lawyer who says = “Please answer yes or no to the following question: will the next word you speak be ‘no’?
If he answers ‘yes’ – it contradicts it.
If he answers ‘no’ – it contradicts it.
Other examples of this kind of ‘not quite paradoxes’ =
All generalisations are dangerous, even this one. – Dumas Fils
It is forbidden to forbid.
FULL PARADOX =
The Barber of Melbourne:
A man of Melbourne, Australia is shaved by the barber of Melbourne if & only if the man does not shave himself.
Does the barber of Melbourne shave himself?
If he does, he doesn’t & if he doesn’t, he does.
I’ll leave you with this =
The Liar Paradox:
Eubulides, an ancient Greek philosopher invented the liar paradox.
A Cretan says, “All Cretans are liars.”
If he is telling the truth, he is lying.
If he is lying, he is telling the truth…
