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I am taking a Scala programming course. At one point the instructor said:
Functions blah and bladdy are the universal and existential quantifiers of first-order logic.
Could someone translate "universal and existential quantifiers of first-order logic" into English please?
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The universal quantifier, meaning "for all", "for every", "for each", etc. The existential quantifier, meaning "for some", "there exists", "there is one", etc. Universal Conditional. Statement. A statement of the form: x, if P(x) then Q(x).
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some".
Quantifiers in First-order logic: There are two types of quantifier: Universal Quantifier, (for all, everyone, everything) Existential quantifier, (for some, at least one).
The Existential Quantifier For example, "Someone loves you" could be transformed into the propositional form, x P(x), where: P(x) is the predicate meaning: x loves you, The universe of discourse contains (but is not limited to) all living creatures.
That sentence is full of jargon. You can find a description of universal and existential logical quantifiers here.
Universal Quantifier is a logical statement that applies to all elements of a set.Existential Quantifier is a logical statement that applies to at least one element of a set.You can also look here for a quick description of first-order logic. The term is meant to separate first-order from higher-order logic:
First-order logical statements are the usual ones; they act on members of a set.Higher-order logical statements act on other logical statements; think of them as meta-logic.
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