  There is one other consequence of Frege’s logic of quantification that should be mentioned. Frege took claims of the form \(\exists x\phi\) to be existence claims. He suggested that existence is not a concept under which objects fall but rather a second-level concept under which first-level concepts fall. A concept \(F\) falls under this second-level concept just in case \(F\) maps at least one object to The True. So the claim ‘Martians don’t exist’ is analyzed as an assertion about the concept martian, namely, that nothing falls under it.  Frege therefore took existence to be that second-level concept which maps a first-level concept \(F\) to The True just in case \(\exists xFx\). Some philosophers have thought that this analysis validates Kant’s view that existence is not a (real) predicate.