9.1 Blank referents (Existential quantifier)


A referent may be blank. For example:

   "There is a bus"


When the referent of a concept is blank, it simply means "there is a". We haven't specified what the referent is, only that it exists.

Existential quantifier

What the blank referent really means is that we have an invisible "existential quantifier", usually denoted "". This quantifier just means "there exists a", and is part of predicate logic. Fuller explanations can be found in all introductions to predicate logic.

The referent need not be blank

The referent need not be blank in order to mean "there exists". If there is no quantifier, then the existential quantifier is assumed. Thus, the following concept:

   [Rhino: Otto]

means "there exists a Rhino called Otto". This is equivalent to:

   [Rhino:  Otto]

Universal quantifier

The other quantifier is the universal quantifier, , meaning "for all". It is the opposite of the existential quantifier.

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