In order to look at the concept of first principles, it is essential to examine the two important elements of first principles and then to discuss how one works from first principles. The two terms that are absolutely necessary to understand first principles are axioms and principles.
Axioms are the empirical, irreducible starting assumptions and self-evidential truths which become the foundation for any field of knowledge or study. What does this mean? Quite simply, it means that one starts out with a basic assumption that does not require a prior assumption to hold it up. They are self-evidential because they do not require proof, either because they are just assumed to be true or because they cannot be disproved. It should be mentioned that the terms ‘self-evident’ and ‘intuitive’ are not the same thing. That the earth is round and not flat is not intuitive to a child, or to a citizen of the middle-ages who has no means of testing the assumption.
Let’s take an example from the late philosopher Ayn Rand:
Rand explained that a statement such as existence exists fits every requirement for an axiom. More importantly, she explains, we know this is an axiom because it cannot be disproved. Can you refute the axiom that existence exists without using that axiom at all? It is impossible, since we must exist in order to refute the axiom that existence exists! If you have no choice but to use the axiom to disprove the axiom, then that axiom is said to be valid. Once we’ve all agreed with this axiom we can derive some principles from it.
So what are principles? A principle is a normative statement based on the axioms that precede it which determines how we should interact with reality. You can think of the difference between empirical and normative as the difference between is and ought. I have already described how axioms establish what is, now we move on to principles that, from the axioms, tell us what ought to be the case.
For example, we could have an axiom that says objects in reality behave according to consistent rules. The principle we can derive from that is that we would not expect to find rocks to fall up and down at the same time. Another example is the axiom ‘reality is consistent and provable’. The exemplary principle of that could be the standards of physics. If reality was not consistent and provable then the study of physics (as well as other sciences) would be impossible.
So axioms are statements about what reality is and principles are statements about how we interact with those axioms. From there we can move on to secondary principles, postulates, laws, etcetera. However, since this article is only concerned with first principles, other items mentioned above will not be discussed now.
Do axioms always have to come before principles? The answer is yes. Observable facts always trump our normative principles. For example, many people once assumed that blacks were inferior to whites. This is the principle, but observable fact contradicts this assertion, because axiomatically there is no evidence to show that skin color makes anybody superior or inferior to anybody else of a different skin color. Therefore, the supposed principle was incorrect and not a valid principle at all. Philosophers are fond of saying that one should work from first principles. One of the reasons we should do so is that we have a solid foundation to work from and so that we are less likely to fall into error, as the above example demonstrates.
In summation, we can use first principles to establish generalised statements about the world according to axioms. Following that we can make some normative statements that follow from those axioms to become our first principles. All fields of study (especially the sciences) were once philosophical inquiries. Every field of inquiry began with a few philosophers pondering the axioms of a certain subject and then deriving the first principles from there. Once first principles are established, you have a solid foundation from which to enquire further about reality and nature.