 For suppose it is false that some individual has the following conjunctive property: he\(x\) is a patient; and he\(x\) saw every young doctor (i.e., every individual\(y\) is such that if she\(y\) is a young doctor, then he\(x\) saw her\(y\)); and he\(x\) is healthy. Then intuitively, and also given the rules of Frege’s logic, it is false that some individual has the following conjunctive property: he\(x\) is a patient; and he\(x\) saw every doctor; and he\(x\) is healthy. This captures the fact that the direction of valid inference is from ‘every young doctor’ in (13) to ‘every doctor’ in (14), despite the fact that in simpler cases, replacing ‘every doctor’ with ‘every young doctor’ is valid. More generally, Frege’s logic handles a wide range of inferences that had puzzled medieval logicians. But the Fregean logical forms seem to differ dramatically from the grammatical forms of sentences like (13–16). Frege concluded that we need a Begriffsschrift, distinct from the languages we naturally speak, to depict (and help us discern) the structures of the propositions we can somehow express by using ordinary sentences in contexts.