Formal Presentation
Define Naive Set Theory (NST) as the theory of predicate logic with a binary predicate and the following axiom schema of unrestricted comprehension:
for any formula P with only the variable x free. Substitute for . Then by existential instantiation (reusing the symbol y) and universal instantiation we have
a contradiction. Therefore NST is inconsistent.
Read more about this topic: Russell's Paradox
Famous quotes containing the words formal and/or presentation:
“The manifestation of poetry in external life is formal perfection. True sentiment grows within, and art must represent internal phenomena externally.”
—Franz Grillparzer (1791–1872)
“He uses his folly like a stalking-horse, and under the presentation of that he shoots his wit.”
—William Shakespeare (1564–1616)