# Spiritual Principle #1

A Well Ordering Principle

In set theory, we describe a set $X$ as being totally ordered if there exists a binary relation, $\leq$, that is antisymmetric, transitive and total.

• A binary relation, $\leq$ is antisymmetric if $a\leq b$ and $b \leq a \ \Rightarrow \ a=b$
• A binary relation, $\leq$ is transitive if $a \leq b$ and $b \leq c \ \Rightarrow \ a \leq c$
• A binary relation, $\leq$ is total if either $a \leq b$ or $b \leq a$ for every $a, b$

Now, a totally ordered set is said to be well-ordered if every subset has a least element, that is, $\forall \ A \subset X, \ \exists \ m \in A \ \ni \ m \leq a \ \forall a \in A$. In other words, if a set has the property that every subset, or part, of it will have a least element. For example, the set of positive integers, $\{1, 2, 3, 4, \ldots \}$ is well-ordered since no matter which group of those numbers you pick, there will be a smallest one. On the other hand, the set of all integers, $\{ \ldots, -3, -2, -1, 0, 1, 2, 3 \ldots \}$ is not well-ordered since you could take a subset that contains all the numbers down to negative infinity and thus, has no least element.

By now, I have probably lost all of my current readers so let me get to my point. As I was pondering this concepted of well-ordered sets, I recognized a something applicable outside of the world of mathematics. In today’s world, we are told to leave our work at the office, to leave our family life at home and to keep our faith to ourselves, all so as to not offend anyone. So, we compartmentalize. We put each part of our life separate from the other. Now there is something to be said for this but clearly the faith that we have cannot be kept separate from the rest of our life.

So I propose a new definition. Let us say that a well-ordered LIFE is one in which every part of our life has a “least element.” And by “least element”, I am thinking in terms of a foundational element or a most important element or maybe even a guiding element.

This definition brings new light to the often quoted passage, “Seek first the kingdom of God.” When Jesus said this, he could have meant that we are to put Him first, chronologically. The first thing we are to do each morning is seek the kingdom. When Jesus said this, he could have meant that we are to put Him first, by importance. For example, any time there is a scheduling conflict between church and family, work or play, we must put the church first. Now, certainly our life is better off through prioritizing our faith, and yet, doesn’t Jesus mean more than either of these. The principle of seeking first the kingdom is summarized well by the well-ordering principle. Every area of our life should be built on our faith, informed by our faith, permeated by our faith and inseparable from our faith. That is putting the kingdom first and that is a principle I need to work on.

Do you have a well-ordered life?