This was Wittgenstein's first publication, I believe, and it shows. As someone once wrote, not Wittgenstein's finest hour.
> It does not even allow, strictly speaking, to take "Horse is an animal" and derive "a horse's head is an animal's head".
This is because it doesn't permit relations in a systematic way. In FOL, you would express "head of" as binary relations (one for horse, one for animal since you cannot quantify over predicates; you would need a HOL for that). But traditional logic can be extended with relations as Sommers has done in term functor logic.
Interestingly, Veatch argues that FOL cannot tell you what a thing is. If predicates are modeled after relations—and Russell also includes the unary predicate here as a relation between subject and property instead of multiple subjects—then you cannot say what a thing is because relations don't say what their relata are. So you're left with a peculiar situation where individuals are bare particulars which brings up all sorts of other questions.
Sommers and Englebretsen have interesting things to say in response to Russell and Frege as well as their defenders (like Geach and Dummett).
> It does not even allow, strictly speaking, to take "Horse is an animal" and derive "a horse's head is an animal's head".
This is because it doesn't permit relations in a systematic way. In FOL, you would express "head of" as binary relations (one for horse, one for animal since you cannot quantify over predicates; you would need a HOL for that). But traditional logic can be extended with relations as Sommers has done in term functor logic.
Interestingly, Veatch argues that FOL cannot tell you what a thing is. If predicates are modeled after relations—and Russell also includes the unary predicate here as a relation between subject and property instead of multiple subjects—then you cannot say what a thing is because relations don't say what their relata are. So you're left with a peculiar situation where individuals are bare particulars which brings up all sorts of other questions.
Sommers and Englebretsen have interesting things to say in response to Russell and Frege as well as their defenders (like Geach and Dummett).