|Summary||Predicate logic is the more complicated of the two modern classical logics. It does not consider atomic propositions as indivisible, notwithstanding the etymology, but also considers the structure within propositions. In its treatment of the general, as opposed to the singular, propositions, it achieves the aims of Aristotelian logic in combination with the aims of propositional logic. In the classification structure chosen by the general editors, second-order and higher-order logics are separate categories, and are therefore not classified as (ordinary) predicate calculus. This may seem a curiosity; it is exlpored in Eklund 1996. In its treatment of singular propositions, relations are permitted, too, as is the special predicate, identity. In classical predicate logic, molecular or compound propositions are built up from atomic propositions by means of the connectives, whose meaning is given by their truth tables. Likewise, one way of understanding the meaning of the two classical quantifiers, existential and universal, is by taking them to be expanded disjunctions and conjunctions, respectively, over the universe of discourse. The principle by which the meaning or truth conditions of compound propositions can be recovered by this "building up" process is known as compositionality. Aside from an appropriate way to understand the meaning of the quantifiers, there is the additional issue of existential import. This leaf node is a sub-category of classical logic. As such, non-standard predicate logics are not generally classified in this category—unless a comparison between classical logic and another logic is being drawn or one is reduced to the other—although restrictions of predicate logic in which nothing not a theorem in ordinary predicate logic is a theorem in the restriction do fit here. Also appropriate are modest extensions of predicate logic, excluding higher-order logics as noted above, provided that Boole's three laws of thought are not violated, viz. a proposition is either true or false, not neither, and not both. Meta-theoretical results for predicate logic are generally also classified as "proof theory," "model theory," "mathematical logic," etc.|
|Key works||See below.|
|Introductions||Because of the age of predicate logic there are literally hundreds of introductions to logic which cover this subject reasonably well. Instructors will have their own favorites. In selecting a book for classroom use, I recommend checking two things: (1) The correctness and clarity of the restrictions on universal generalization and existential instantiation; (2) how much meta-theory is included, so that the book is neither below nor above the level students can handle.|
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David Bourget (Western Ontario)
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