Many-valued Logic - History

History

The first known classical logician who didn't fully accept the law of excluded middle was Aristotle (who, ironically, is also generally considered to be the first classical logician and the "father of logic"). Aristotle admitted that his laws did not all apply to future events (De Interpretatione, ch. IX), but he didn't create a system of multi-valued logic to explain this isolated remark. Until the coming of the 20th century, later logicians followed Aristotelian logic, which includes or assumes the law of the excluded middle.

The 20th century brought back the idea of multi-valued logic. The Polish logician and philosopher, Jan Łukasiewicz, began to create systems of many-valued logic in 1920, using a third value, "possible", to deal with Aristotle's paradox of the sea battle. Meanwhile, the American mathematician, Emil L. Post (1921), also introduced the formulation of additional truth degrees with n ≥ 2, where n are the truth values. Later, Jan Łukasiewicz and Alfred Tarski together formulated a logic on n truth values where n ≥ 2. In 1932 Hans Reichenbach formulated a logic of many truth values where n→infinity. Kurt Gödel in 1932 showed that intuitionistic logic is not a finitely-many valued logic, and defined a system of Gödel logics intermediate between classical and intuitionistic logic; such logics are known as intermediate logics.

Read more about this topic:  Many-valued Logic

Famous quotes containing the word history:

    Postmodernism is, almost by definition, a transitional cusp of social, cultural, economic and ideological history when modernism’s high-minded principles and preoccupations have ceased to function, but before they have been replaced with a totally new system of values. It represents a moment of suspension before the batteries are recharged for the new millennium, an acknowledgment that preceding the future is a strange and hybrid interregnum that might be called the last gasp of the past.
    Gilbert Adair, British author, critic. Sunday Times: Books (London, April 21, 1991)

    No matter how vital experience might be while you lived it, no sooner was it ended and dead than it became as lifeless as the piles of dry dust in a school history book.
    Ellen Glasgow (1874–1945)

    It is true that this man was nothing but an elemental force in motion, directed and rendered more effective by extreme cunning and by a relentless tactical clairvoyance .... Hitler was history in its purest form.
    Albert Camus (1913–1960)