In this lecture a few topics are pulled together.
After comments bearing on last week’s lecture, Dallas around 9:00 starts with a main topic for the day. Students have read Bertrand Russell’s “Mathematical Logic as Based on the Theory of Types” and Dallas is taking them through the argument. Namely, granted there is class of all classes not included in itself and granted the law of the excluded middle, you can prove (deduce) anything. For example you can deduce that you are a millionaire. Russell, obviously, thinks this is nonsense and develops a theory of types to solve the problem. Dallas discusses this theory of types (17:30), which is important because it became a big deal in 20th century philosophy, at least for a while. Dallas calls it, along with Russell’s theory of descriptions, one of two sources of analytic and linguistic philosophy.
The second main topic is a big deal today. Dallas begins, as he says, to work on the individual categories (44:30) and he will structure the rest of the course around these. The first of these is what he called individuals and the second he calls first level predicates. Of particular interest is how he classifies some major schools of philosophy based on their trying to reduce individuals to predicates or vice versa. He drops a clue to his own view when he speaks of haecceity and haecceitism.