I have two sentences that I need to translate from English to the language of predicate logic (which includes a semantics for identity)
- Ortcutt admires the inventor of bifocals.
- The first Postmaster General is the inventor of Bifocals.
I know how to symbolize a claim about both existence and uniqueness, i.e., $\exists x (Fx \land \forall y (Fy \rightarrow y=x))$.
However, my first intuitions about how to translate these make the task way too easy, I think. With respect to (1), I just want to let "I" stand for the monadic predicate "is the inventor of bifocals" and put something about Orcutt existing in the admiring relation in there (where "b" denotes Ortcutt...
$\exists x (Abx \land (Ix \land \forall y (Iy \rightarrow y=x)))$
Moreover, translating (2) just intuitively seems to be tantamount to symbolizing, via Russell's Theory, the two definite descriptions and joining them with an = sign.
Does anyone have any tips about how to proceed translating these? Doing so cannot be as simple or straightforward as I think.