Elements of mathematics
https://en.wikipedia.org/wiki/Category:Mathematical_terminology
primitive
axiom
definition
theorem
theory
mathematical object
mathematical notion
mathematical notation
inference rules
Denotation
https://en.wikipedia.org/wiki/Denotation
Denotation is a translation of a sign to its literal meaning, more or less like dictionaries try to define it. Denotation is sometimes contrasted to connotation, which includes associated meanings. The denotational meaning of a word is perceived through visible concepts, whereas connotational meaning evokes sensible attitudes towards the phenomena.
Connotation
https://en.wikipedia.org/wiki/Connotation
A connotation is a commonly understood cultural or emotional association that any given word or phrase carries, in addition to its explicit or literal meaning, which is its denotation.
Property
https://en.wikipedia.org/wiki/Property_(philosophy)
Metaphysical debates
Realism vs. anti-realism
Categoricalism vs. dispositionalism
Physicalism, idealism, and property dualism
Types
Intrinsic and extrinsic
Essential and accidental
Determinate and determinable
Pure and impure
Lovely and suspect
An intrinsic property is a property that an object or a thing has of itself, independently of other things, including its context. An extrinsic (or relational) property is a property that depends on a thing's relationship with other things. The latter is sometimes also called an attribute, since the value of that property is given to the object via its relation with another object. For example, mass is a physical intrinsic property of any physical object, whereas weight is an extrinsic property that varies depending on the strength of the gravitational field in which the respective object is placed. other examples are the name of a person (an attribute given by the person's parents) and the weight or mass of the person.
In classical Aristotelian terminology, a property is one of the predicables. It is a non-essential quality of a species (like an accident), but a quality which is nevertheless characteristically present in members of that species. For example, "ability to laugh" may be considered a special characteristic of human beings. However, "laughter" is not an essential quality of the species human, whose Aristotelian definition of "rational animal" does not require laughter. Therefore, in the classical framework, properties are characteristic qualities that are not truly required for the continued existence of an entity but are, nevertheless, possessed by the entity.
A property may be classified as either determinate or determinable. A determinable property is one that can get more specific. For example, color is a determinable property because it can be restricted to redness, blueness, etc. A determinate property is one that cannot become more specific. This distinction may be useful in dealing with issues of identity.
Daniel Dennett distinguishes between lovely properties (such as loveliness itself), which, although they require an observer to be recognised, exist latently in perceivable objects; and suspect properties which have no existence at all until attributed by an observer (such as being suspected of a crime).
https://en.wikipedia.org/wiki/Instantiation_principle The instantiation principle (principle of instantiation, principle of exemplification) is the concept in metaphysics and logic 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.
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