The Holy Trinity-dialethic?

Typical logicians at the mention of a dialethia might start spitting up blood or something just as crazy as this according to Eric Dietrich who should and according to my list makes one of the top 100 most dangerous professors. A dialethia he taught us is a true contradiction. At first we all scratched our heads, looked a little funny and gave a little nervous laugh but eventually we all came around. Let me explain what I mean.

When we think of a contradiction we think of something where one has to be true and one has to be false. I cannot be both at the supermarket and at home at the same time. I cannot be sick and healthy at the same time. Contradictions we think of as typically one or the other, not both. But take something like the following example:
“This sentence is false”
it’s false-but if it’s false then it’s true because it’s false that it’s false making it true
it’s true-but if it’s true then it’s false because it says it’s false and it’s telling the truth so it must be false

This is what is called the Liars Paradox. If it is assigned one truth value it comes out the other. There is no definite answer as to the truth value of this statement. It is both false and true which makes it a contradiction. Let’s take a look at another example:
Imagine that you’re sitting 10 feet away from the wall. Now, if you were going to walk halfway to the wall you’d walk 5 feet. Now walk another half and so on and so on. Closing the gap… 10 feet, 5 feet, 2.5 feet, 1.25 feet, etc. if you continue dividing in half you will technically always have another halve to cross. Now, stop the math for a minute and get up and walk to the wall. There is no tiny half stopping you from getting to the wall. You can walk over and press yourself against it. So, mathematically, you should have to cross an infinite number of halves to get to the wall, but you can just walk right over to the wall in a finite amount of time. That is another contradiction.

One more math driven example. Take the set of all things. The set of all things is going to contain everything including itself because the set of all things fits into the set of all things. What this means is that it displays features of transcendence and closure meaning that it is both inside and outside of itself making it contradictory.

Let’s take this new knowledge of dialethias and apply it to something else. Christianity teaches about the holy trinity: the Father, the Son and the Holy Spirit who are supposed to be separate “entities” but all part of one “God”. This sounds like it may have the makings of a true contradiction. Let’s look a little closer.
Christianity holds to the claim that there is only one God
God is part of the Holy Trinity-Father, Son and the Holy Spirit
The Holy Trinity put together is God (the father)
Therefore: God is inside the trinity and outside the trinity giving him transcendence and closure making him dialethic. This is certainly not in any way a proof of God’s existence or a lack thereof, it is just an observation about Christianity’s view of God. It makes me wonder what implications it might have if God were dialethic in the sense of the Holy Trinity? It says nothing about his existence so it looks like all we can conclude from this exercise is that if God exists and the Holy Trinity does exist, then God is dialethic in that sense.

I think it is important that logicians begin accepting dialethias because they are out there. It doesn’t ruin logic as we know it, it doesn’t change everything, it just adds a new dimension into our thoughts.

If this is a topic that interests you I highly recommend Sophie’s World and Graham Priests Beyond the Limits of Thought.

Thank you to Eric Dietrich for opening my eyes.