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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 or principle of instantiation or principle of exemplification is the concept in metaphysics and logic (first put forward by David Malet Armstrong) that there can be no uninstantiated or unexemplified properties (or universals). In other words, it is impossible for a property to exist which is not had by some object.
Universal generalization / instantiation; Existential generalization / instantiation; This is a list of rules of inference, logical laws that relate to mathematical ...
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
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 ...
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
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".
Existential instantiation, when conducted in a Fitch style deduction, proceeds by entering a new sub-derivation while substituting an existentially quantified variable for a subject—which does not appear within any active sub-derivation. If a conclusion can be reached within this sub-derivation in which the substituted subject does not appear ...