“Hello, and welcome to another episode of “Logic for Y’all”. Today we are going to tackle a rather controversial topic - “Using logic to model real-world thinking”. Asked to comment on it, most people went: “Pff, logic!” and our resident logicians prepared the following summary: “Pff, the real world!”. But still, among our listeners, there were some wannabe philosophers who insisted that this is the most important thing ever, so it appears that we have no choice but to get someone to talk about it (there will be booze at the end). So let’s give a warm welcome to the only guy who agreed to speak about this boring topic, Boris Marinoooov!”

Whenever I think about good physical theories, I immediately think of Boltzmann’s statistical mechanics (the theory of entropy, you can say), not because he basically discovered the science of atoms and molecules, but simply because every time I see an ice cube in a glass, I see the particles, the Brownian motion, the way the heat and coldness dissolve etc.

I don’t think about the number of grand important open issues that were solved by this theory, but I think about way the way that a person like me can use it in their thinking. Like for example that one time when my frined told me to leave the oven opened after using it, because they wanted for the heat in the oven to warm the room, and I explained to them that the heat from the oven will always warm the room, simply because it had nowhere else to go.

And I think of category theory in a similar way — not as a tool that delivers results I use to solve some important problems, that were otherwise unsolvable, but it is a tool that broadens my perception of the world, which is much more important and fruitful. I don’t care if all problems which are solved by category theory happen to also be solved by other mathematical theories, nor how many of them are actually solved this way, I care only about the categories and functors in my head.