Blackwell Reference Online

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The expression ‘free logic,’ coined by the author in 1960, is an abbreviation for ‘logic free of existence assumptions with respect to its terms, singular and general, but whose quantifiers are treated exactly as in standard quantifier logic.’ In more traditional language, such logics do not presume that either singular or general terms — the two distinct categories of terms emphasized in modern logical grammar — have existential import. A singular term ‘ t ’ has existential import just in case t exists (or, equivalently, there exists an object the same as t ) and a general term (or predicate) ‘ G ’ has existential import just in case G exist (or, equivalently, there exists an object that is G ). Examples from colloquial English customarily taken to be singular terms are expressions such as ‘Socrates’, ‘the planet causing perturbations in the orbit of Mercury’, ‘5’, ‘5/0’, ‘the square of 3’ and ‘having a heart’. Some of these do not have existential import — in particular, ‘5/0’ and ‘the planet causing perturbations in the orbit of Mercury’. Examples from colloquial English customarily taken to be general terms are expressions such as ‘is a philosopher’, ‘is a planet causing perturbations in the orbit of Mercury’, ‘number’, ‘is divisible by 0’, and ‘has a heart’. Some of these general terms do not have existential import — in particular, ‘is a planet causing perturbations ... log in or subscribe to read full text