Classical Logic - Examples of Classical Logics

Examples of Classical Logics

  • Aristotle's Organon introduces his theory of syllogisms, which is a logic with a restricted form of judgments: assertions take one of four forms, All Ps are Q, Some Ps are Q, No Ps are Q, and Some Ps are not Q. These judgments find themselves if two pairs of two dual operators, and each operator is the negation of another, relationships that Aristotle summarised with his square of oppositions. Aristotle explicitly formulated the law of the excluded middle and law of non-contradiction in justifying his system, although these laws cannot be expressed as judgments within the syllogistic framework.
  • George Boole's algebraic reformulation of logic, his system of Boolean logic;
  • The first-order logic found in Gottlob Frege's Begriffsschrift.

Read more about this topic:  Classical Logic

Famous quotes containing the words examples of, examples, classical and/or logics:

    Histories are more full of examples of the fidelity of dogs than of friends.
    Alexander Pope (1688–1744)

    No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.
    André Breton (1896–1966)

    Compare the history of the novel to that of rock ‘n’ roll. Both started out a minority taste, became a mass taste, and then splintered into several subgenres. Both have been the typical cultural expressions of classes and epochs. Both started out aggressively fighting for their share of attention, novels attacking the drama, the tract, and the poem, rock attacking jazz and pop and rolling over classical music.
    W. T. Lhamon, U.S. educator, critic. “Material Differences,” Deliberate Speed: The Origins of a Cultural Style in the American 1950s, Smithsonian (1990)

    When logics die,
    The secret of the soil grows through the eye,
    And blood jumps in the sun;
    Above the waste allotments the dawn halts.
    Dylan Thomas (1914–1953)