A deductive system (also called a deductive apparatus of a formal system) consists of the axioms (or axiom schemata) and rules of inference that can be used to derive the theorems of the system.
Such a deductive system is intended to preserve deductive qualities in the formulas that are expressed in the system. Usually the quality we are concerned with is truth as opposed to falsehood. However, other modalities, such as justification or belief may be preserved instead.
In order to sustain its deductive integrity, a deductive apparatus must be definable without reference to any intended interpretation of the language. The aim is to ensure that each line of a derivation is merely a syntactic consequence of the lines that precede it. There should be no element of any interpretation of the language that gets involved with the deductive nature of the system.
Famous quotes containing the word system:
“To care for the quarrels of the past, to identify oneself passionately with a cause that became, politically speaking, a losing cause with the birth of the modern world, is to experience a kind of straining against reality, a rebellious nonconformity that, again, is rare in America, where children are instructed in the virtues of the system they live under, as though history had achieved a happy ending in American civics.”
—Mary McCarthy (1912–1989)