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In predicate logic, universal instantiation [1] [2] [3] (UI; also called universal specification or universal elimination, [citation needed] and sometimes confused with dictum de omni) [citation needed] is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class.
The instantiation principle, the idea that in order for a property to exist, it must be had by some object or substance; the instance being a specific object rather than the idea of it; Universal instantiation; An instance (predicate logic), a statement produced by applying universal instantiation to a universal statement
Universal generalization / instantiation; Existential generalization / instantiation; This is a list of rules of inference, logical laws that relate to mathematical ...
Dictum de omni (sometimes misinterpreted as universal instantiation) [2] is the principle that whatever is universally affirmed of a kind is affirmable as well for any subkind of that kind. Example: (1) Dogs are mammals. (2) Mammals have livers. Therefore (3) dogs have livers. Premise (1) states that "dog" is a subkind of the kind "mammal".
The universal quantifier "for every" in this sentence expresses the idea that the claim "if x is a philosopher, then x is a scholar" holds for all choices of x. The negation of the sentence "For every x , if x is a philosopher, then x is a scholar" is logically equivalent to the sentence "There exists x such that x is a philosopher and x is not ...
The full generalization rule allows for hypotheses to the left of the turnstile, but with restrictions.Assume is a set of formulas, a formula, and () has been derived. The generalization rule states that () can be derived if is not mentioned in and does not occur in .
Universal instantiation concludes that, if the propositional function is known to be universally true, then it must be true for any arbitrary element of the universe of discourse. Symbolically, this is represented as
The idea that some of our rules of inference should depend on empirical information, which may not be forthcoming, is so foreign to the character of logical inquiry that a thorough re-examination of the two inferences [existential generalization and universal instantiation] may prove worth our while.