# Predicate logic translations

I'm attempting to translate the following sentence:

"Some Germans are famous mathematicians."

I came up with two solutions, but neither seem right.

Solution #1) (∃x)(Gx & Fx)
G_: _ is german
F_: _ is famous mathematician

Solution #2) (∃x)((Gx & Fx) & Mx)
G_: _ is german
F_: _ is famous
M_: _ is mathematician

Suggestions?

• Both look fine... Nov 3 '16 at 13:40

I agree with Mr. Allegranza that both are adequate but the second seems awkward. The first is to the point, but if you want to break up famous and mathematician you could also:

there exists a person that is ((German and famous) and (German and a mathemetician))

or,

there exists a person that is (German and (famous and a mathematician))

I'm not crazy about lots of parentheticals but I like the latter. The former seems overstated.

Hope that helps.

The first is better than the second. One can be famous and a mathematician without being a famous mathematician. "Famous mathematician" implies that one is famous for being a mathematician (or possibly that one is famous among mathematicians).

This is related to Geach's distinction between predicative and attributive adjectives. "Yellow" is predicative because "x is a yellow book" simply means that x is yellow and x is a book, but terms like "large" or "good" are attributive. "X is a large flea" does not mean that x is large simpliciter, only that x is large as fleas go. "John is a good thief" does not necessarily mean John is good, only that he is good at stealing.

• glad you brought that up, I wasn't sure how in basic quantificational notation to make this distinction (e.g. for all Germans there exists a Mathematician where that M is Famous... for being a mathematician) and thought maybe sets would do the trick (e.g. famous mathenerds as a subset of mathematicians as a subset of Germans), but I couldn't really get at the predicative/attributive distinction. How would you formally express this with "Some Germans are famous mathematicians?" Nov 4 '16 at 19:58
• good stuff: pitt.edu/~mthompso/readings/geach2.pdf Nov 4 '16 at 20:14