## Sunday, December 4, 2011

### A Word (or two) A Day...

A THOUGHT FOR TODAY:
If a homological adjective is one that is true of itself, e.g. "polysyllabic", and a heterological adjective is one which is not true of itself, e.g., "bisyllabic", then what about "heterological?" Is it heterological or not? -Grelling's Paradox.

...which, of course, leads logically to:

Naive Set Theory (NST) , defined as the theory of predicate logic with a binary predicate $\in$, with the following as axioms:
$\exists y \forall x (x \in y \iff P(x))$ for all expressions P(x) with just x free
Substitute $x \notin x$ for P(x). Then by existential instantiation and universal instantiation we have
$z \in z \iff z \notin z$
a contradiction. Therefore NST is inconsistent.

So, Naive Set Theory is a Metaprime Example?
Thanks, Pheas.  (I think!)

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