Daily Archives: September 20, 2012

Godel’s completeness theorem, 2

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Using the compactness and completeness theorems

Godel’s completeness theorem (not to be confused with his incompleteness theorems) says that a theory has a model if and only if it is consistent, i.e. no contradiction is proved by the theory. This is the heart of model theory as it lets us answer questions about theories by looking at models and vice-versa.

One should not confuse the completeness theorem with the notion of a complete theory. A complete theory is a theory that contains every sentence or its negation.

— Wikipedia on Model theory

2012.09.20 Thursday ACHK

The Divine Michelangelo

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Michelangelo was now preparing for the end and how he would be remembered by history. He began to destroy drawings and poems he didn’t think were good enough [in order to create the myth of the divine artist]. He even attacked one of his last works of sculpture: the Florentine Pieta, which was intended for his own tomb.

— The Divine Michelangelo

— BBC

2012.09.20 Thursday ACHK