havingP

havingP is a phrase used in discussions of properties and predicates to denote that a given object possesses a specified property P. It is not a formal term with a fixed canonical definition in standard mathematical logic, but rather a descriptive way to talk about the relationship between an object x and a predicate P.

In formal notation, the same idea is usually expressed as P(x) or HasProperty(x, P). The phrase 'havingP' emphasizes the subject's status with respect to the property and is often used in informal explanations, proofs, or pseudo-code. Whether P is a unary predicate or a higher-order predicate, 'havingP' means that P holds for the object in question.

Examples: If P is 'is a prime number', then the object 5 hasP, i.e., has the property P. If P is 'is red', a red apple hasP. In programming, one might write hasProperty(x, P) as a condition to test during execution. In databases or knowledge representations, 'havingP' may correspond to membership in a class defined by P.

Limitations: Since 'havingP' is informal, its precise meaning depends on context. When a formal treatment is required, it is better to use explicit predicates or relation symbols. The concept is closely related to ideas of predicates, properties, and attribute possession in logic, philosophy of language, and computer science.

See also: predicate, property (logic), predicate logic, has-property notation.