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Why can “George Washington” and “the first president of the United States” have the same truth conditions but different meanings?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — Truth Detail of a Roman copy (2nd century bce) of a Greek alabaster portrait bust of Aristotle (c. 325 bce); in the collection of the Museo Nazionale Romano, Rome.

In the study of truth and semantics, the distinction between "George Washington" and "the first president of the United States" illustrates the difference between a referent and its sense.

While both expressions share the same referent—the individual George Washington—they possess different senses, or "modes of presentation". According to the philosopher Gottlob Frege, the sense of an expression is the way in which it refers to an object. Because these expressions present the same individual in different ways, they contribute differently to the thoughts expressed by sentences.12

This explains why sentences containing these terms can have identical truth conditions in some contexts but differ in others. For example, if a person is unaware that George Washington was the first president, they might believe one statement while rejecting the other. Donald Davidson later addressed this by suggesting that meaning can be analyzed through the circumstances in which a speaker holds a sentence to be true, accounting for these differences without relying on abstract senses.23