..A

abstract

not tangible or concrete
 abstract algebra
 The generalisation of algebraic methods originally concerned with number systems to deal with arbitrary algebraic structures over arbitrary domains.

abstraction

the process or result of forming some abstract idea from a number of more particular or concrete examples
 (in set theory)
 The process of forming a set, typically by binding a free variable in a formula which expresses the truth condition, for membership in the set, of the value denoted by the variable.
Comprehension and separation are particular kinds of set abstraction.
Abstraction to properties (predicates or propositional functions) is analogous.
 (functional)
 Forming a function, typically by binding a free variable in an expression which denotes the value of the function for the argument whose value is denoted by the variable.

ad
 the Latin preposition meaning "to" or "towards"
 ad hoc
 for a particular purpose.
An inelegant feature in an otherwise well structured system to fix a particular problem.
A hack.
 ad hoc polymorphism
 (after [CardelliTDP]) a kind of polymorphism in programming languages in which a function taking a polymorphic parameter will execute different code according to the type of the parameter supplied (by contrast with universal polymorphism in which the same code is used).
Special cases include overloading and inclusion polymorphism.

algebra

the systematic study of number systems using symbolic formulae involving variables
 see also:
 abstract algebra
 computer algebra

altruism
 unselfishness, concern for others

analytic
 (logic)
 a proof which proceeds by analysis of the desired conclusion showing that it is derivable from accepted premises (from classical Greece).
Such proofs are now sometimes known as a backward or goal oriented proofs.
 (philosophy)
 expressing a relationship between concepts.
A statement or proposition which lacks empirical content and is true in virtue of its meaning.
 (philosophy)
 a kind of philosophy particularly concerned with logical or linguistic analysis (see: Varieties of Philosophical Analysis).
 (recursion theory)
 definable in second order arithmetic

anarchism

 the doctrinal abhorrence of coercion, usually including advocacy of the abolition of the state
 violent opposition to established authorities, especially those considered oppressive

antinomy
 a brittle silvery white metalic element
 (philosophy)
 a paradox or contradiction

antinomian
 relating to the belief that christians are absolved from the obligation to observe the moral law.
 antinomianism
 A religious sect in sixteenth century Germany which held to the antinomian belief.

a posteriori
 knowable or justifiable only on the basis of experience

a priori
 knowable or justifiable prior to experience based on purely rational considerations
 arithmetization
 the process of translating statements or problems from their usual domain into the language of arithmetic, usually so that the methods of arithmetic or logic can be brought to bear on the problem.
 arithmetization of analysis
 the reduction of the theory of real numbers to that of arithmetic, accomplished by defining a real number as some aggregate of rational numbers, e.g. a Dedkind cut or a Cauchy sequence.
 see also:
 gödelization

axiom
 in a logic or an axiomatic theory an axiom is a sentence which is accepted as true without demonstration.
The axioms are the starting points for the derivations of all other theorems.

axiomatic method
 a method of doing mathematics in which subject areas are presented and studied as axiomatic theories
 axiomatic semantics (computing)
 a semantics for a programming language given by defining axioms which permit reasoning about the effects of execution of the various parts of a program.

axiomatic theory
 a mathematical (or other) theory presented as a system of axioms.

axiomatisation

The process of formalising some subject as an axiomatic theory.
©
created 1994/9/22 modified 2007/2/1