In his review of Peter Coffey's book : The Science of Logic (1st ed 1912), published in The Cambridge Review, Vol.34, 1913, Wittgenstein criticizes it as a representative of "old" logic, precedent to the new mathematical logic of Frege, Peano and Russell [the first volume of Principia Mathematica by Alfred North Whitehead and Bertrand Russell was first published in 1910].
See Gottlob Frege, Begriffsschrift (1879), ยง3:
A distinction between subject and predicate does not occur in my way of representing a judgment. [...] We can imagine a language in which the proposition "Archimedes perished at the capture of Syracuse" would be expressed thus: "The violent death of Archimedes at the capture of Syracuse is a fact". To be sure, one can distinguish between subject and predicate here, too, if one wishes to do so, but the subject contains the whole content, and the predicate serves only to turn the content into a judgment. Such a language would have only a single predicate for all judgments, namely, "is a fact". We see that there cannot be any question here of subject and predicate in the ordinary sense.