The Way That Things Are- Gödel and the Incompleteness Theorem

Kurt Gödel was a logician and mathematician born in the early 20th century. He was a contemporary and friend of Albert Einstein’s, and as influential to the world of logic as Einstein was to the world of Physics.

Gödel’s most famous contribution were his Incompleteness Theorems, which proved that for any system there are truths which cannot be defined by the system itself. There are some things which are true, but which cannot be proven until you utilize outside sources.

Now this is a very crude example meant only as an illustration, but think of it this way: if we have a system called integer numbers (1, 2, 3, 4…) then there are patterns about those integers which do exist, but which we will never be able to discover with integers alone. We will have to add something else, perhaps fractions, in order to prove them. But now we have a new system, one of integers and fractions, and there are new patterns about this larger system which we will never be able to explain until we add something like irrational numbers, and so it goes on.

Now Gödel’s Incompleteness Theorem was related to logical and mathematical systems, but they raise a strong philosophical question as well. I have always been baffled that we humans are so arrogant as to believe that we could ever fully understand ourselves. It seems to me that we are much too close to the subject matter to ever find all of the objective truths locked within our souls. I find it far easier to accept that the only complete understanding of myself would have to come from a being that existed in a higher system than our own.

Thus when society decides that truth must be one thing, but God’s word declares that the truth is something else…it frankly is not difficult to for me to side with the unknowable omniscient. Indeed, the fact that God is unknowable gives his argument greater weight to me, not less. If God was comprehensible to me, then there’s no way He’d be great enough to comprehend all of me.

Justice and Mercy- Question

If there’s one principle in the gospel we love, it is mercy. And if there is one that we fear, it is justice. Yet both of these principles are of God, and so we must assume that both of them are good. Though Satan has many creations in this world, Justice is not one of them.

In fact, the more I think about these two principles, the more I start to think that they are far more similar to one another than they first appear. Honestly I think they might just be two sides of the exact same coin. Distinct from one another, yes, but rooted in the exact same law.

Throughout this study we will take a closer look at each, the systems by which they operate, the opportunities to use both for our advantage, and the way that each intersects at the moment of Christ’s atoning sacrifice. In the meanwhile I’d love to hear your take on Justice and Mercy. What are ways you have been blessed by each? Are there times where you have seen that Justice to one person appears as Mercy to another?