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:
“That anger can be expressed through words and non-destructive activities; that promises are intended to be kept; that cleanliness and good eating habits are aspects of self-esteem; that compassion is an attribute to be prized—all these lessons are ones children can learn far more readily through the living example of their parents than they ever can through formal instruction.”
—Fred Rogers (20th century)
“He uses his folly like a stalking-horse, and under the presentation of that he shoots his wit.”
—William Shakespeare (1564–1616)