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Glossary of Principia Mathematica	1/1	https://en.wikipedia.org/wiki/Glossary_of_Principia_Mathematica	reference	science, encyclopedia	2026-05-05T08:45:01.640169+00:00	kb-cron

This is a list of the notation used in Alfred North Whitehead and Bertrand Russell's Principia Mathematica (1910–1913). The second (but not the first) edition of Volume I has a list of notation used at the end.

== Glossary == This is a glossary of some of the technical terms in Principia Mathematica that are no longer widely used or whose meaning has changed.

apparent variable bound variable

atomic proposition A proposition of the form R(x,y,...) where R is a relation.

Barbara A mnemonic for a certain syllogism.

class A subset of the members of some type

codomain The codomain of a relation R is the class of y such that xRy for some x.

compact A relation R is called compact if whenever xRz there is a y with xRy and yRz

concordant A set of real numbers is called concordant if all nonzero members have the same sign

connected connexity A relation R is called connected if for any 2 distinct members x, y either xRy or yRx.

continuous A continuous series is a complete totally ordered set isomorphic to the reals. *275

correlator bijection

couple

1. A cardinal couple is a class with exactly two elements
2. An ordinal couple is an ordered pair (treated in PM as a special sort of relation)

Dedekindian complete (relation) *214

definiendum The symbol being defined

definiens The meaning of something being defined

derivative A derivative of a subclass of a series is the class of limits of non-empty subclasses

description A definition of something as the unique object with a given property

descriptive function A function taking values that need not be truth values, in other words what is not called just a function.

diversity The inequality relation

domain The domain of a relation R is the class of x such that xRy for some y.

elementary proposition A proposition built from atomic propositions using "or" and "not", but with no bound variables

Epimenides Epimenides was a legendary Cretan philosopher

existent non-empty

extensional function A function whose value does not change if one of its arguments is changed to something equivalent.

field The field of a relation R is the union of its domain and codomain

first-order A first-order proposition is allowed to have quantification over individuals but not over things of higher type.

function This often means a propositional function, in other words a function taking values "true" or "false". If it takes other values it is called a "descriptive function". PM allows two functions to be different even if they take the same values on all arguments.

general proposition A proposition containing quantifiers

generalization Quantification over some variables

homogeneous A relation is called homogeneous if all arguments have the same type.

individual An element of the lowest type under consideration

inductive Finite, in the sense that a cardinal is inductive if it can be obtained by repeatedly adding 1 to 0. *120

intensional function A function that is not extensional.

logical

1. The logical sum of two propositions is their logical disjunction
2. The logical product of two propositions is their logical conjunction

matrix A function with no bound variables. *12

median A class is called median for a relation if some element of the class lies strictly between any two terms. *271

member element (of a class)

molecular proposition A proposition built from two or more atomic propositions using "or" and "not"; in other words an elementary proposition that is not atomic.

null-class A class containing no members

predicative A century of scholarly discussion has not reached a definite consensus on exactly what this means, and Principia Mathematica gives several different explanations of it that are not easy to reconcile. See the introduction and *12. *12 says that a predicative function is one with no apparent (bound) variables, in other words a matrix.

primitive proposition A proposition assumed without proof

progression A sequence (indexed by natural numbers)

rational A rational series is an ordered set isomorphic to the rational numbers

real variable free variable

referent The term x in xRy

reflexive infinite in the sense that the class is in one-to-one correspondence with a proper subset of itself (*124)

relation A propositional function of some variables (usually two). This is similar to the current meaning of "relation".

relative product The relative product of two relations is their composition

relatum The term y in xRy

scope The scope of an expression is the part of a proposition where the expression has some given meaning (chapter III)

Scott Sir Walter Scott, author of Waverley.

second-order A second order function is one that may have first-order arguments

section A section of a total order is a subclass containing all predecessors of its members.

segment A subclass of a totally ordered set consisting of all the predecessors of the members of some class

selection A choice function: something that selects one element from each of a collection of classes.

sequent A sequent of a class α in a totally ordered class is a minimal element of the class of terms coming after all members of α. (*206)

serial relation A total order on a class

significant well-defined or meaningful

similar of the same cardinality

stretch A convex subclass of an ordered class

stroke The Sheffer stroke (only used in the second edition of PM)

type As in type theory. All objects belong to one of a number of disjoint types.

typically Relating to types; for example, "typically ambiguous" means "of ambiguous type".

unit A unit class is one that contains exactly one element

universal A universal class is one containing all members of some type

vector

1. Essentially an injective function from a class to itself (for example, a vector in a vector space acting on an affine space)
2. A vector-family is a non-empty commuting family of injective functions from some class to itself (VIB)

== Symbols introduced in Principia Mathematica, Volume I ==

== Symbols introduced in Principia Mathematica, Volume II ==

== Symbols introduced in Principia Mathematica, Volume III ==

== See also == Glossary of set theory

== Notes ==

== References == Whitehead, Alfred North, and Bertrand Russell. Principia Mathematica, 3 vols, Cambridge University Press, 1910, 1912, and 1913. Second edition, 1925 (Vol. 1), 1927 (Vols. 2, 3).

== External links == List of notation in Principia Mathematica at the end of Volume I "The Notation in Principia Mathematica" by Bernard Linsky. Principia Mathematica online (University of Michigan Historical Math Collection): Volume I Volume II Volume III Proposition ✸54.43 in a more modern notation (Metamath)