In logic, Richard's paradox is a semantical antinomy in set theory and natural language first described by the French mathematician Jules Richard in 1905. Today, the paradox is ordinarily used in order to motivate the importance of carefully distinguishing between mathematics and metamathematics. The paradox was also a motivation in the development of predicative mathematics.
Read more about Richard's Paradox: Description, Analysis and Relationship With Metamathematics, Variation: Richardian Numbers, Relation To Predicativism
Famous quotes containing the words richard and/or paradox:
“For every man that Bolingbroke hath pressed
To lift shrewd steel against our golden crown,
God for his Richard hath in heavenly pay
A glorious angel. Then if angels fight,
Weak men must fall; for heaven still guards the right.”
—William Shakespeare (1564–1616)
“The conclusion suggested by these arguments might be called the paradox of theorizing. It asserts that if the terms and the general principles of a scientific theory serve their purpose, i. e., if they establish the definite connections among observable phenomena, then they can be dispensed with since any chain of laws and interpretive statements establishing such a connection should then be replaceable by a law which directly links observational antecedents to observational consequents.”
—C.G. (Carl Gustav)