In this video, Noah Goodman presents his “Probabilistic Language of Thought Hypothesis”:

Mental representations (concepts) are functions in a stochastic lambda calculus (eg. Church).

It seems crazy indeed. A thought, or the meaning of a sentence, would be an expression in a probabilistic language. Even more crazy is that it seems to work.

It can model complex reasoning (in the video at around 25:13) and communication (44:56) with some nested inferences.

Noah Goodman has another great video about Probabilictic languages here. I also recommend this playlist.