  The preceding analysis of simple mathematical predications led Frege to extend the applicability of this system to the representation of non-mathematical thoughts and predications. This move formed the basis of the modern predicate calculus. Frege analyzed a non-mathematical predicate like ‘is happy’ as signifying a function of one variable which maps its arguments to a truth-value. Thus, ‘is happy’ denotes a concept which can be represented in the formal system as ‘\(H(\:)\)’. \(H(\:)\) maps those arguments which are happy to The True, and maps everything else to The False. The sentence ‘John is happy’, represented as ‘\(H(j)\)’, is thereby analyzed as: the object denoted by ‘John’ falls under the concept signified by ‘\((\:)\) is happy’. Thus, a simple predication is analyzed in terms of falling under a concept, which in turn, is analyzed in terms of functions which map their arguments to truth values. By contrast, in the modern predicate calculus, this last step of analyzing predication in terms of functions is not assumed; predication is seen as more fundamental than functional application. The sentence ‘John is happy’ is formally represented as ‘\(Hj\)’, where this is a basic form of predication (‘the object \(j\) instantiates or exemplifies the property \(H\)’). In the modern predicate calculus, functional application is analyzable in terms of predication, as we shall soon see.