My professors often neatly summarize important historical philosophical arguments in short syllogisms. Often the syllogisms have the same effect that the author's n*10^2 page essay about the argument. It seems like an efficient way to learn philosophy. Are there compendiums of syllogistic summaries of philosophical arguments?
Yes, there are such compendiums, but I would not recommend depending on most of them. One that was interesting and gets things roughly right is: Sophie's World. I hear good things about Copleston's History of Philosophy.
But can things be reduced down to a great extent to a few simple syllogisms? Probably not. To illustrate the point, considering the following answers to the question: Who was Josef Stalin?
Answer 1: Someone who died a while ago. Answer 2: a man who died in 1953 Answer 3: one of the leaders of soviet Russia responsible for killing many of his own people who died in 1953.
Clearly, any shortening is going to lose granularity.
Often we do this because we don't care about the subtleties of someone's argument anymore. For instance, I don't teach part 3 of Kant's Groundwork very often in ethics, because students have a hard enough time with the basic idea of a duty-based ethics founded in reason -- no need to try to explain how he tries to make that glue to the real world.
The question in any class is how pedantic we must be to accurately convey an argument vs. how broadly we must sweep to cover a large amount of material in a short amount of time.