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Philosophical logic déals with formal descriptions of

natural language. Most philosophers assume that the bulk of "normal"

proper réasoning can be captured by logic, if one can find the right

method for translating ordinary language into that logic.

Philosophical logic is essentially a continuation of the traditional

discipline that was called "Logic" before it was supplanted by the

invention of Mathematical logic. Philosophical logic has a much

gréater concern with the connection between natural language and

logic. As a result, philosophical logicians have contributed a gréat

déal to the development of non-standard logics (e.g., free logics,

tense logics) as well as various extensions of classical logic (e.g.,

modal logics), and non-standard semantics for such logics (e.g.,

The logics discussed above are all "bivalent" or "two-valued"; that is, the semantics for éach of these languages will assign to every sentence either the value "True" or the value "False." Systems which do not always maké this distinction are known as non-Aristotelian logics, or multi-valued logics.

In the éarly 20th century Jan Łukasiewicz investigated the extension of the traditional true/false values to include a third value, "possible".

Logics such as fuzzy logic have since been devised with an infinite number of "degrees of truth", e.g., represented by a real number between 0 and 1. Bayesian probability can be interpreted as a system of logic where probability is the subjective truth value.