Exactly: writing out all colors of "maybe" explicitly in programming languages was infeasible, so english is the one programming language that can and will capture fuzzy logic, encoded in weights and connections.
"Deep learning" as used today isn't fuzzy logic, it's actually multi-layered neural networks. (hence the "deep": because it has multiple layers of neural networks instead of a single one).
The reason why researchers on neural networks started to talk about "deep learning" in the 2000's is because neural networks had a bad press and articles were being rejected. Machine learning on the other hand was hot so it was a way to get their papers accepted.
There was a popular conception (like taught in textbooks even) that one hidden layer was enough since a neural network with one hidden layer could approximate any function. Deep learning became a thing when it was found to work great in practice.
logic is binary. yes or no.
classic AI used pure logic via means of rules engine. you could tell exactly which path to take to solve a problem.
fuzzy logic is not binary, but multimodal/range.
what maps unto that today? probability on top of layered NN, aka deep learning. It's no coincidence that no one knows how the deep learning models "think." They are by design very fuzzy.