Definitions
Proposition
A proposition is a central concept in logic, often characterized as the primary bearer of truth or falsity.
Fundamental :
A proposition[1] is a mathematical precise statement that is either true or false, but not both.
Example :
The statement "
" is false while statement "
" is true, both statement are propositions.
The statement "What a great Boole!" is not a proposition some one is simply expressing an opinion.
The statement "
" is not a proposition, the truth value of this statement relies on what the variable
is assigned.
The statement "
" is not a proposition, because it has a truth value, namely true.
Paradox
A paradox is a statement that can not be assigned a truth value.
Example :
"This statement is false". If true, than false and if false then true.
Example :
A classic example of a paradox is the barber paradox, it states the barber shaves every man in town who does not shave him self. If the barber shaves him self, then this means the barber does not shave him self and if he does not shave himself then he must shave himself, neither is possible and so it is a paradox.