Is language-of-thought the best game in the town we live?

There are towns in which language-of-thought (LoT) is the best game. But do we live in one? I go through three properties that characterize the LoT hypothesis: Discrete constituents, role-filler independence, and logical operators, and argue that in each case predictions from the LoT hypothesis are a poor fit to actual human cognition. As a hypothesis of what human cognition ought to be like, LoT departs from empirical reality.