# Motivation

In this chapter, we will learn to further decompose statements in terms of their verbs (called predicates) and their nouns (called individuals). This leads to predicate logic (also called first-order logic).

As a motivation of why we want more expressive power, suppose we wanted to translate the following statements to propositional logic:

``````All humans are mortal.
Socrates is a human.
Socrates is mortal.``````

Unfortunately, each statement would be a propositional atom:

``````p: All humans are mortal.
q: Socrates is a human.
r: Socrates is mortal.``````

But what if we wanted to prove that given the premises: “All humans are mortal” and “Socrates is a human”, that the conclusion “Socrates is mortal” naturally followed? This logical argument makes sense – Socrates is a human, and all such individuals are supposed to be mortal, so it should follow that Socrates is mortal. If we tried to write such a proof in propositional logic, though, we would have the sequent:

``p, q ⊢ r``

…and we clearly don’t have enough information to complete this proof.

We need a richer language, which we will get with predicate logic.