Girard is one of the top logicians of his time. He can write standard mathematical prose when he wants to. In turn, when he chooses to use the continental philo

Girard is one of the top logicians of his time. He can write standard mathematical prose when he wants to. In turn, when he chooses to use the continental philosophy style, it's a deliberate choice: people who can't read it are not in the target audience anyway. Somebody who worked through the two volumes of "Proof Theory and Logical Complexity", and worked through the later chapters of "The Blind Spot" will already be used to the style, so won't find it an obstacle when reading the Transcendental Syntax papers. And those who didn't read these works? Well, they don't know the prerequisites anyway (the author assumes), so making the style more palatable to them is not a priority. The aforementioned works are better starting points: they cover classical proof theory, so there are many other textbooks that can be consulted while the reader develops familiarity with Girard's style. And one needs to know the material to understand Transcendental Syntax anyway.