Predicate Logic

This lesson introduces predicate logic in comparison and continuation of the previous two historical attempts at theorizing logic—Aristotelian syllogism and propositional logic.

Review of the first theory

Aristotle’s colossal contributions to the foundations of logic can never be forgotten, just like his contributions to almost all major knowledge domains.

Summary of Aristotelian syllogism

Aristotle laid the foundations for the formal study of logic but scoped his study to categorical syllogisms, restricted to four standard formsA proposition has to talk in terms of all, none, or some. of propositions. A syllogism is a form of deductive reasoning that consists of two premises and a conclusion. It typically involves categorical statements about relationships between categories or classes of things.

The power of the theory

Even with such constraints, logicians could represent many real-world situations and judge the arguments as valid or invalid. Here’s an instance of a valid form of argument:

By speaking of two categories in every proposition, the sentence structure creates qualitative and quantitative relations between the subjects and predicates. These are important features for those who want to study language logically because it lets them step into every sentence and look at its constituent terms and their relation with each other.

Limitations of the theory

A theory has to explain how humans judge an argument as valid or invalid (logical reasoning) using intelligence. That’s precisely what Aristotle’s attempt at theorizing logical reasoning did. However, as is the case with almost every theory on earth, it had its established set of limitations, mostly due to the restricted structure that it imposed on logicians. For instance, it forced everyone to create an argument, always using categories and placing them in three propositions; the two premises must maintain a sequential order, with the major premise always preceding the minor premise, etc.

Review of the second theory

Leibniz and Boole formulated a more modern logic that improved upon Aristotle’s first attempt.

Summary of propositional logic

This modern logic—propositional or symbolic logic—assigns one symbol to a complete sentence. The ...