  It is important to mention here that the predicate calculus formulable in Frege’s logic is a ‘second-order’ predicate calculus. This means it allows quantification over functions as well as quantification over objects; i.e., statements of the form ‘Every function \(f\) is such that …’ and ‘Some function \(f\) is such that …’ are allowed. Thus, the statement ‘objects a and b fall under the same concepts’ would be written as follows in Frege’ notation: