Full Idea
Traditionally many philosophers (Aristotle among them) have considered the law of noncontradiction to be the deepest, most fundamental principle of rationality.
Gist of Idea
The law of noncontradiction is traditionally the most basic principle of rationality
Source
Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.1)
Book Reference
Fogelin,Robert: 'Walking the Tightrope of Reason' [OUP 2004], p.18
A Reaction
For Aristotle, see Idea 1601 (and 'Metaphysics' 1005b28). The only denier of the basic character of the law that I know of is Nietzsche (Idea 4531). Fogelin, despite many qualifications, endorses the law, and so do I.
Related Ideas
Idea 1601 The most certain basic principle is that contradictories can't be true at the same time [Aristotle]
Idea 4531 Our inability to both affirm and deny a single thing is merely an inability, not a 'necessity' [Nietzsche]