Semantic theory of truth

A semantic theory of truth is a kind of theory of truth that belongs to the philosophy of language. This idea says that truth is something that belongs to sentences. In other words, when we talk about what is true or false, we are really talking about the sentences we use to express our ideas.

This theory helps us understand how we can tell when a sentence really matches what is happening in the world. It gives philosophers and thinkers a way to study meaning and truth more carefully. By looking at sentences, we can explore big questions about what it means for something to be true.

The semantic theory of truth is important because it connects how we talk and write with what actually happens. It shows us that our words and sentences can be checked against the world to see if they are right or wrong. This helps in many areas, from everyday conversations to serious discussions in schools and universities.

Origin

The idea of truth as something we can describe with words comes from the work of Alfred Tarski, a logician from Poland. In 1935, Tarski wrote about truth in formal languages to solve a puzzle known as the liar paradox. While doing this, he discovered important facts about what can and cannot be proven in a system, similar to another famous mathematician named Kurt Gödel. One key finding is that a proper way to talk about truth for a language cannot be created using only the words of that same language.

Tarski's theory of truth

To study how we talk about language without getting into tricky puzzles, we need to separate the language we are discussing (called the object language) from the language we use to discuss it (the metalanguage). For example, when we quote a sentence like "P", we are using the metalanguage to describe the object language.

Tarski's theory of truth, created by Alfred Tarski in 1935, says that the object language must be part of the metalanguage. This theory includes a key idea called Convention T, which states that for any sentence "P", a true theory of truth must include a sentence like:

"P" is true if, and only if, P.

For example:

'Snow is white' is true if, and only if, snow is white.

Tarski originally designed this theory for formal languages, but it was later expanded by Davidson to work with natural languages. Tarski also provided a step-by-step way to define what makes a sentence true, starting with simple statements and building up to more complex ones using rules for "not", "and", "or", "for all", and "there exists". This helps us understand how the truth of longer sentences depends on the truth of their smaller parts.

Kripke's theory of truth

See also: Truth § Kripke's semantics

Kripke's theory of truth, from 1975, looks at how we understand what is true using a special kind of logic. This logic works with ideas that are not always completely clear, unlike another way of thinking about truth. It uses a method called the strong Kleene evaluation scheme to help explain these ideas.