5. Glossary

ad infinitum

To carry on, indefinitely.

apple

If you have to ask, you will never know.

circular reference

See reference, circular.

codomain

A function maps from a domain into a codomain. For example, the sine function maps from the real numbers (its domain) into the real numbers from -1 to 1 (its image or range). However, the codomain of the sign function is also the real numbers (a superset of its image).

comparator

A comparator is a thing to which something may be compared. For example, the historical definition of a foot was the length of some individual's foot. Thus, that foot served as a comparator for all other feet.

concept

A concept is a part of the conceptual universe. It is a reference to percepts, it serves as the basis of thought, and it may in turn be referenced by a (perceptual) symbol.

conception

The act of understanding, or of forming a single concept.

dichotomy

A binary division. A single and thorough cut through an object results in a dichotomy.

dimension

That abstract quantity which is the axis of the thing being measured. It is orthogonal to the divisions which it allows. It may be nominal, ordinal, interval, or ratio.

domain

In mathematical terms, it is the set of values upon which a function may operate. It also is intended to connote the domain of discourse , which refers to the limitation of discourse to a particular topic.

dualism

If you believe in matter and mind as separate, then you are a dualist. En guarde!

Euclidean space

A Euclidean space is one which has unit-length basis vectors and which are orthogonal to each other. The familiar x , y and z axes form a three-dimensional Euclidean space: in the general case, Euclidean spaces may be of any dimensionality.

extension

The extension of a set is comprised of the elements of that set. The extension is often used to define a set: as opposed to definition in terms of properties, an extensive definition is an enumeration of all individuals possessing those properties. See also intension.

extrinsic

An extrinsic (outer) property of a thing is one which relates that thing to external things. See also intrinsic.

hierarchy

A tree-like structure which consists of one or more dimensions.

holism

Holism is the opposite of reductionism: it means that the behavior of a system cannot be determined exclusively through analysis of its parts.

hyperplane, hyperspace

The prefix hyper- in these cases refers to the fact that these concepts can or should be extended to an arbitrary number of dimensions. A hyperplane is an N-dimensional plane. A hyperspace is an N-dimensional space.

intension

The intension of a set is composed of the characteristic property, or definition, of the members of that set. See also extension.

intrinsic

An intrinsic (or internal) property is one which belongs to the object itself. For example, the mass of a thing is an intrinsic property, but the weight of a thing is an extrinsic property (since it depends on gravity). See also extrinsic.

isomorphism

An isomorphism is a term which literally means “the same shape” . In practice, it is a relation between two things which expresses a type of equality or congruence. For example, four points connected in a square create a structure which is isomorphic to another four points connected in a rectangle.

lexeme

A lexeme is a lexical unit, similar to a word. Although “apple” and “apples” represent different words, they are a single lexeme. Lexemes are probably closer to our underlying concepts: various words are produced by applying transformations to these lexemes as dictated by various syntactic rules.

mereology

Mereology means the study of parts. It can be seen as a complementary form of set theory which is particularly amenable to spatial representation (i.e. in terms of parts and wholes).

modality, linguistic

Modality in the linguistic sense refers to possibility. Modal logic, for example, is logic which has introduced possibility and necessity.

modality, sensory

A sensory modality most often refers to one of five types of external senses: taste, smell, touch, sight, and sound.

monism

If you believe that matter and mind are somehow one and the same, then you are a monist. If you further believe that only matter is real, you are a materialist. If you instead believe that only mind is real, you are a materialist.

morpheme

A morpheme is a phoneme which has an associated meaning.

N-space

N-space is a space which consists of N-dimensions (or perhaps more precisely, is of rank N). For example, physical space is a kind of 3-space, and spacetime is a kind of 4-space.

natural kind

A natural kind is an object which truly exists . This means roughly that the object is more valid than an object composed of a part of that object in conjunction with another object (the latter composite, in that case, would not be a natural kind). The front half of a turkey and the back half of a trout, for example, would not be an obvious choice for a natural kind.

nominalism

A belief that the objects in the world are objects in virtue of only their names. In other words, there are no privileged objects or natural kinds: how we conceptually divide the universe is up to us.

object

A physical thing, which may be of high dimensionality (i.e. it is understood to contain temporal and perhaps other parts).

ontology

Ontology literally means the study of being, or existence. For example, a word may also have ontological validity (it is valid as a reference) if it exists as a concept.

ontological priority

A thing which occurs ontologically prior to another thing comes before that thing. For example, if a thing is a concept which is used in the definition of a subsequent thing, then the former thing is (necessarily) ontologically prior.

orthogonal

Orthogonal means perpendicular. In two dimensions, orthogonal vectors (lines) form a right angle to one another.

part

A part is a thing which is contained in another thing, and is smaller than that containing thing (in virtue of which it is technically called a proper part ).

partition

A partition of a thing is a complete or exhaustive decomposition of that thing into parts. Every bit of the whole is contained in some part, and no bit of a part is contained in more than one part.

percept

A subjective referent to a thing (either an object or a concept).

perception

The act of experiencing reality or some part thereof: the witnessing of a percept.

phoneme

A part of a spoken word, such as a syllable.

proper part

A thing which is contained in another thing, and is necessarily smaller than that other thing.

range

The range (or image) of a function consists of all of the values which might be a result of the application of that function. See also domain, codomain.

reductionism

The thesis of reductionism is that the behavior of a system cannot be determined exclusively through analysis of its parts. See also holism.

reference

A reference is a representation of a thing, as opposed to the thing itself.

reference, circular

See circular reference.

relation

A relation is a definition which is established between multiple things.

semantics

The meaning of words. See also syntax.

set

A collection of things which is treated as a singular entity. See also concept.

signified

Saussure's term for a thought or idea, for which we use the term concept .

signifier

Saussure's term for a percept that corresponds to a concept, which we refer to as a symbol.

symbol

A percept which references (represents, denotes) a concept. This is enabled by the act of naming. (the rules by which the semantics of words may be combined)

syntax

The rules by which the semantics of words may be combined. See also semantics.

taxonomy

A taxonomy is a hierarchy of kinds or types.

universe

A universe is a set of things which is a complete whole. It is either the physical universe, or some set of references to it.