By Roy T. Cook

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

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Thus, the truth table for choice negation (where N is the third value) is: A T N F ~A F N T See also: Boolean Negation, Bottom, DeMorgan Negation, Exclusion Negation, Falsum CHOICE SEQUENCE see Free Choice Sequence CHOICE SET A choice set for a set S is a set containing exactly one member from each set contained in S. The axiom of choice can be understood as asserting that for each non-empty set of sets S there is a choice set for S. See also: Axiom of Countable Choice, Axiom of Dependent Choice, Choice Function, Global Choice, Zorn’s Lemma CHRONOLOGICAL LOGIC see Temporal Modal Logic CHURCH’S THEOREM Church’s Theorem states that validity in first-order logic is not decidable – that is, there is no decision procedure for determining, of an arbitrary formula from a firstorder language, whether or not it is a logical truth.

See also: Bivalence, Constructive Proof, Excluded Middle, Intuitionism, Logical Antirealism BIAS Any factor that prevents a sample from being representative of the population in question is a bias. More generally, a bias can be any factor that gives preference to a particular outcome or belief independently of any evidence for or against that outcome or belief. See also: Gambler’s Fallacy, Hasty Generalization, Informal Fallacy, Probability Calculus, Probability Theory BICONDITIONAL A biconditional is a statement of the form: A if and only if B Within propositional logic, biconditionals are usually represented as: A↔B Or as: A≡B Within classical logic the biconditional has the following truth table: 1004 02 pages 001-322:Layout 1 16/2/09 15:11 Page 33 b i va l e n c e P T T F F Q T F T F 33 P≡Q T F F T See also: Deductive Equivalence, Iff, Logical Equivalence, Material Biconditional, Materially Equivalent, T-schema BIJECTION A bijection is a bijective function.

The distinction, attributed to Aristotle, was intended to help clear up confusions about infinity brought about by puzzles such as the Zeno paradoxes. See also: Absolute Infinite, Dedekind Infinite, Indefinite Extensibility, Simply Infinite COMPLETE SET OF CONNECTIVES see Expressive Completeness COMPLETE THEORY see Negation Completeness, Strong Completeness, Weak Completeness COMPLETENESS1 see Expressive Completeness, Negation Completeness, Strong Completeness, Weak Completeness COMPLETENESS2 A partial ordering is complete if and only if every set of elements in the order that has an upper bound has a least upper bound, and every set of elements that has a lower bound has a greatest lower bound.

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