 Frege attempted to remedy the situation by completely rethinking the foundations of logic, developing what we now think of as modern symbolic logic. He defined a perfectly precise “formal” language, i.e., a language characterized by the “form” – standardly, the shape—of its expressions, and he carefully set out an account of the syntax and semantics of what are called the “logical constants,” such as “and,” “or,” “not,” “all” and “some,” showing how to capture a very wide class of valid inferences containing them. Saying precisely how the constants are determined is a matter of controversy (see Logical Constants), but, at least roughly and intuitively, they can be thought of as those parts of language that don’t “point” or “function referentially,” aiming to refer to something in the world, in the way that ordinary nouns, verbs, adjectives, adverbs and prepositions seem to do. “Socrates” refers to Socrates, “dogs” to dogs, “(is) clever” to cleverness and/or clever things, but words like “or” and “all” don’t seem to function referentially at all. At any rate, it certainly isn’t clear that there are any ors and alls in the world, along with Socrates, the dogs, and sets or properties of them.