In syllogistic logic
, the fundamental idea proposed by Alfred Tarski
that a proposition
is true if it correctly describes the state of the world, and is false if it incorrectly describes the state of the world.
In logical terms, a proposition "P"is true if and only if the condition described in P is true. For example:
- The proposition "The sky is blue" is true if and only if the sky is blue.
- The proposition "The sky is blue" is false if and only if the sky is not blue.
In most human languges
, we can write sentences that describe other sentences
. For example, the sentence "The sky is blue" contains four words. Tarski points out that the only statement you can make about a sentence that is equivalent
to the original sentence, is to say that that sentence is true.
Tarski's claim is that this is a powerful correspondence theory, where we can literally see a correspondence between the words "The sky is blue" and the world itself, where the sky is blue. That is, we can be satisfied with the truth of a logical proposition by examining the actual state of reality. However, it is important to note that Tarski is referring to the logical concept of a true statement, and not to the metaphysical concept of truth.
The second (and less read) part of his theory is that it is impossible to define truth in a given language using the language itself, and avoid contradictions. The English language allows us to construct paradoxical statements such as "This statement is false," which have no solid truth value to them.
Tarski proposes that a metalanguage would be required to define truth in a given object language, acknowledging the limitations of conversational linguistics when applied to pure logic. His theory, then, is more sound when applied to mathematical languages such as symbolic logic, than to "ordinary" human conversational languages.