By Roy T. Cook

ISBN-10: 0748625593

ISBN-13: 9780748625598

This worthwhile reference introduces undergraduate and post-graduate scholars to the most difficulties and positions of philosophical good judgment. components comprise an important figures, positions, terminology, and debates inside philosophical common sense in addition to concerns that pertain to comparable, overlapping disciplines, akin to set conception and the philosophy of arithmetic. Entries are greatly cross-referenced for identity in the context of wider debates.

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The theory was intended to replace set theory within science and philosophy, providing these disciplines with a nominalistically respectable foundation. See also: Atom, Classical Mereology, Individual, Parthood CANTOR PARADOX The Cantor paradox shows that there cannot be a set of all sets – a universal set – and depends on Cantor’s theorem, which demonstrates that the powerset of a set cannot be placed into one-to-one correspondence with that set itself. To derive the paradox, assume that there is a set of all sets.

O-proposition: Some P are not Q. ” See also: Distribution, Existential Import, Quality, Quantity, Square of Opposition CATEGORICAL SYLLOGISM A categorical syllogism is an argument in categorical logic which has two premises, and where each term occurs twice. Categorical syllogisms are characterized in terms of syllogistic figure and syllogistic mood. The mood of a categorical syllogism is determined by which type of categorical proposition (A-proposition, E-proposition, I-proposition, or O-proposition) occurs as first premise, second premise, and conclusion.

See also: Aristotle’s Thesis BOOLEAN ALGEBRA A Boolean algebra is a type of lattice consisting of a set of objects A which contains two distinguished members (typically represented by 1 and 0) along with two binary functions on A (typically represented by ∩ and ∪) and a unary function on A (typically represented by ~) which satisfy the following axioms: Associativity: A ∩ (B ∩ C) = (A ∩ B) ∩ C A ∪ (B ∪ C) = (A ∪ B) ∪ C Commutativity: A∩B=B∩A A∪B=B∪A Absorbsion: A ∩ (A ∪ B) = A A ∪ (A ∩ B) = A Distributivity: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) Complement: A∪~A=1 A∩~A=0 The function ∩ is meet, the function ∪ is join, the function ~ is complement, 0 is the minimal element, or the bottom, and 1 is the maximal element, or the top.

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A Dictionary of Philosophical Logic by Roy T. Cook

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