I would be grateful if you could direct me to relevant passages in Aristotle where I can read more about the nature of "principle." Not exacty about the principle of non-contradiction but what a principle is exactly. I am having difficulty trying to pin down what a principle really is and how it differs from logical implication.
Aristotle discusses the nature and role of principles in several works, though he does not provide an explicit definition of what constitutes a principle. Here are a few key passages and themes to glean insight:
Posterior Analytics - Aristotle sees principles as stating the primordial causes, origins, or sources of knowledge from which demonstrations can be constructed. Principles are primary, unproven starting points (72a18-25).
Metaphysics - Principles are the first irreducible 'elements' at the foundation of being from which everything originates (982a4-10). Principles underlie entities, truth, and knowledge.
Nicomachean Ethics - Practical principles are the unproven starting points of ethics that guide action. First principles relate to the ultimate end or highest good of human life (1095b18).
On Sense and the Sensible - Principles are the primary 'acts' that enable perception and set the conditions for sensation. They are implicit foundations (436a10-15).
Across Aristotle, principles seem to refer to the basic self-evident origins that define a system of thought or existence and enable further reasoning. Principles are primary rather than derived through logic. Unlike logical implications, principles are starting assumptions rather than consequents. They form the undemonstrated bedrock that grounds logical development. Discerning correct principles is thus crucial for Aristotle to obtain true knowledge.