Starting from a natural number like 3 can we go in a chain, 3, 4,5, and get back to 3? It seems obvious that we can’t. This seemingly simple proposition is difficult to prove? Can we trick ourselves into thinking we have proven it?
If we start with the Peano Axioms and do order first as Dedekind did in 1888, then we find this is a rather difficult thing to prove and be sure we have not fooled ourselves. This is discussed in more detail in the book Pre-Algebra New Math Done Right Peano Axioms.
Math teachers us humility. But humility does not mean giving up or accepting losing. Humility is to recognize how we are short on understanding and try to fill the gaps by persistence.
Understanding when cycles are ruled out is key to understanding causality. We rule out causal cycles just like we rule out cycles in the chain of natural numbers.
One motive of this blog was to recognize that Faith had lessons to teach us in learning and teaching. This motive is a cause of the blog in the sense of causing it to come into existence. It is also a cause that the blog promotes.
But also, math is key to understanding Faith and may be a route for some to Faith or deepen Faith. We see this in the way that the Peano Axioms and cycles in numbers helps us understand weighty theological arguments such as whether the First Cause Argument for the existence of God is valid. Or even just to understand what it says and see if it contains holes or hidden assumptions. Without math and logic we can’t do that. We also need set theory to understand ordered pairs and chains of ordered pairs. So the math we need for Faith is the New Math.
The 1888 book by Dedekind on natural numbers contains the math of the natural numbers including basic set theory and functions. This book should also be required reading for theology.
This Dedekind book is available on line for free in English, links to it are below.
The Dedekind book is so close to perfection that one can believe it is directly inspired by God, almost as if God had dictated it to Dedekind to write down.
Understanding the Dedekind book well is a good foundation for understanding theological arguments that involve sets, logic, ordered pairs and causal or other chains. This is quite a lot actually. One could call it Mathematical Theology.
About 2,510 results (0.23 seconds) for this search on August 20, 2012. This post should add a link. When we pass on math, we pass on the spirit of inquiry that is fundamental to faith.