Material vs. Conceptual Coherence

When it comes to matters of fact, logical interactions become very simple, indeed because logic doesn’t organize facts. Still, there’s a way things are, ways things could have been, and ways things couldn’t have been. Einstein told us that information cannot travel faster than the speed of light, and we learned from his theories that gravity curves space-time and changes the trajectory of light. There’s a coherence to Einstein’s theory, but the coherence is purely material; it’s about the world of things. Understanding the material world in a scientific way means being able to account for the organization of things and make predictions about the future organization of things.

For this type of reasoning, logic really isn’t all that useful, other than guarding coherence in simple chains of logical reasoning, just as it does with daily reasoning. It’s really the power of mathematics that is effective for material predictions, because mathematics can make precise and measurable predictions—predictions that can be tested in the world. Logic, on the other hand, becomes much more influential in conceptual endeavors. Theories like moral or ethical theories, theories about the existence or non-existence of God, or theories about pure concepts such as the concept of truth, won’t be settled by material things.

Those who have theorized about the concept of truth have tried to identify first principles of truth, for instance, that a statement about the world is true if the world is according to the statement. The truth is about what we say, not about how things are. And those who have tried to find first principles have quickly figured out, with the help of logic, that things get weird in conceptual spaces. At the risk of creating a false dilemma, then, logic is about conceptual coherence, and mathematics about material “coherence.”