The Laws of Thought
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The Laws of Thoughts are the fundamental axioms of rational logic as it is practised by humans. They are of specific interest to philosophers and logicians alike.
A violation of these laws is either impossible or paradoxical. Many logic puzzles hinge around these properties of logic.
Law of Identity
Whatever is, is.
\[ \left ( P = P \right ) \forall P \]
Law of Non-Contradiction
Nothing can be and not be.
\[ \sim \left ( P = ( \sim P ) \right ) \forall P \]
Law of Excluded Middle
Everything must be or not be.
\[ \left ( P \lor ( \sim P ) \right ) \forall P \]