This course was part of a tutorial focusing on the state of computational semantics, i.e., the state of work on natural language within the artificial intelligence (AI) paradigm. The discussion in the course centered on the philosophers Richard Montague and Ludwig Wittgenstein. The course was divided into three sections: (1) Introduction--discussing trends in the philosophy of language in regard to the role and importance of formalization, and describing and giving some history of the three fundamental notions of logical syntax, meta-language, and an "Lsemantic" definition of truth; (2) Montague--describing his work on the formalization of natural language and giving an account of Montague grammar with examples; and (3) Wittgenstein--showing how some of his ideas are relevant to the present situation of AI and the way they clash with the views of the formalist school. The course emphasized the importance of partial/inductive knowledge in our understanding of language and concluded that to handle language "formally" on a computer, it is in no way necessary to accept tenets based on formal logic. The most fruitful approaches to understanding language are precisely those not subservient to a powerful logical or semantic theory. (TL)