• forms of logical argument

    TITLE: logic: Scope and basic concepts
    SECTION: Scope and basic concepts
  • status in deductive system

    TITLE: metaphysics: Nature of an a priori science
    SECTION: Nature of an a priori science made from propositions that are generally taken to be true, and the procedure is to demonstrate with rigorous logic what follows if they are indeed true. It is not necessary that the primary premises of an a priori science should in fact be truths; for the purposes of the system they need only be taken as true, or postulated as such. The main interest is not so much in the premises as in...
  • syllogistic of Aristotle

    TITLE: history of logic: Syllogisms
    SECTION: Syllogisms
    ...of Aristotle: The Revised Oxford Translation, ed. by Jonathan Barnes, 1984, by permission of Oxford University Press). But in practice he confined the term to arguments containing two premises and a conclusion, each of which is a categorical proposition. The subject and predicate of the conclusion each occur in one of the premises, together with a third term (the middle) that is...
    TITLE: history of logic: Theophrastus of Eresus
    SECTION: Theophrastus of Eresus
  • technique of semantic tableaux

    TITLE: formal logic: Semantic tableaux
    SECTION: Semantic tableaux
    ...the Dutch logician Evert W. Beth, it was more fully developed and publicized by the American mathematician and logician Raymond M. Smullyan. Resting on the observation that it is impossible for the premises of a valid argument to be true while the conclusion is false, this method attempts to interpret (or evaluate) the premises in such a way that they are all simultaneously satisfied and the...
  • validity and truth in formal logic

    TITLE: formal logic: General observations
    SECTION: General observations
    ...argument can be roughly characterized as one in which the claim is made that some proposition (the conclusion) follows with strict necessity from some other proposition or propositions (the premises)—i.e., that it would be inconsistent or self-contradictory to assert the premises but deny the conclusion.