Predicate Logic allows sentences to be analyzed into subject and argument in several different ways, unlike Aristotelian syllogistic logic, where the forms that the relevant part of the involved judgments took must be specified and limited (see the section on Deductive Logic above). Predicate Logic is also able to give an account of quantifiers general enough to express all arguments occurring in natural language, thus allowing the solution of the problem of multiple generality that had perplexed medieval logicians.
For instance, it is intuitively clear that if:
Some cat is feared by every mouse
then it follows logically that:
All mice are afraid of at least one cat
but because the sentences above each contain two quantifiers ('some' and 'every' in the first sentence and 'all' and 'at least one' in the second sentence), they cannot be adequately represented in traditional logic.
Predicate logic was designed as a form of mathematics, and as such is capable of all sorts of mathematical reasoning beyond the powers of term or syllogistic logic. In first-order logic (also known as first-order predicate calculus), a predicate can only refer to a single subject, but predicate logic can also deal with second-order logic, higher-order logic, many-sorted logic or infinitary logic. It is also capable of many commonsense inferences that elude term logic, and (along with Propositional Logic - see below) has all but supplanted traditional term logic in most philosophical circles.
Predicate Logic was initially developed by Gottlob Frege and Charles Peirce in the late 19th Century, but it reached full fruition in the Logical Atomism of Whitehead and Russell in the 20th Century (developed out of earlier work by Ludwig Wittgenstein).