I've been reading the original of what was perhaps Ramsey's most famous paper -- "On a problem of formal logic." (See the below URL at the end). The paper is divided into two parts. The first part consists of theorems in what we now know as Ramsey theory. The second part attempts (perhaps successfully) to apply these results to logic. Although I'm fully aware that only the Ramsey theory parts of that paper are considered of major historical importance, I would still like to understand the way Ramsey is applying this to logic. However, although I fully understood the Ramsey theory part of the paper, I am completely unable to understand the logical part. The logic section of the paper would probably not be regarded as rigorous by the standards of modern mathematical logic. The language of mathematical logic seems to have changed far more since 1930 than the language needed to develop Ramsey theory.
Could anyone give me any guidance as to the logical part of the paper? Has anyone rewritten this in the language of modern mathematical logic?